Showing 1–50 of 60 results for author: Khatami, E

Impact of strain and dark states on spectroscopic measurements of silicon-vacancy centers in diamond

Authors: Tommy Chin, Kesav V. Narayan, Imran Bashir, Kelsey M. Bates, Liam G. Stanton, Ehsan Khatami, Christopher L. Smallwood

Abstract: Negatively charged silicon-vacancy (SiV$^-$) centers in diamond offer an attractive platform for the development of many forms of quantum technology. However, questions remain in connection to how large ensembles of SiV$^-$ centers behave in concert. Here, we develop a computational model designed to simulate recent experiments where optical multidimensional coherent spectroscopy (MDCS) was used t… ▽ More Negatively charged silicon-vacancy (SiV$^-$) centers in diamond offer an attractive platform for the development of many forms of quantum technology. However, questions remain in connection to how large ensembles of SiV$^-$ centers behave in concert. Here, we develop a computational model designed to simulate recent experiments where optical multidimensional coherent spectroscopy (MDCS) was used to examine a high-concentration sample of SiV$^-$ centers in diamond, revealing significant variations in spectral signature depending on the detection scheme. Simulation results reveal that strain effects are highly random in this system, with a characteristic axial strain of $2.8 \times 10^{-4}$ and a shear strain of $3.5 \times 10^{-5}$. They suggest in addition that highly strained centers (with values exceeding $1.5 \times 10^{-5}$) may become significantly decoupled from optical emission. The results have implications for the use of SiV$^-$ centers as quantum sensors. △ Less

Submitted 11 August, 2026; originally announced August 2026.

Comments: 10 pages, 7 figures

Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo

Authors: Ejaaz Merali, Mohamed Hibat-Allah, Mohammad Kohandel, Richard T. Scalettar, Ehsan Khatami

Abstract: Neural-network quantum states have emerged as a powerful variational framework for quantum many-body systems, with recent progress often driven by massively parallel architectures such as transformers. Recurrent neural network quantum states, however, are frequently regarded as intrinsically sequential and therefore less scalable. Here we revisit this view by showing that modern recurrent architec… ▽ More Neural-network quantum states have emerged as a powerful variational framework for quantum many-body systems, with recent progress often driven by massively parallel architectures such as transformers. Recurrent neural network quantum states, however, are frequently regarded as intrinsically sequential and therefore less scalable. Here we revisit this view by showing that modern recurrent architectures can support fast, accurate, and computationally accessible neural quantum state simulations. Using autoregressive recurrent wave functions together with recent advances in parallelizable recurrence, we develop variational ansätze, called parallel scan recurrent neural quantum states (PSR-NQS), which can be trained efficiently within variational Monte Carlo in one and two spatial dimensions. We demonstrate accurate benchmark results and show that, with iterative retraining, our approach reaches two-dimensional spin lattices as large as $52\times52$ while remaining in agreement with available quantum Monte Carlo data. Our results establish recurrent architectures as a practical and promising route toward scalable neural quantum state simulations with modest computational resources. △ Less

Submitted 13 May, 2026; originally announced May 2026.

Comments: 13 pages, 2 figures, 6 tables

Finite-Temperature Ferromagnetic Correlations of the Kagome Lattice Hubbard Model

Authors: Francisco Correia, Kyle Corbett, Ehsan Khatami

Abstract: The Kagome lattice Fermi-Hubbard model is one of the most physically rich, and at the same time most challenging, models to study in strongly-correlated physics. Among its special features are geometric frustration and a flat energy band that create conditions favorable to ferromagnetism near the band insulating limit. Here, we utilize two exact finite-temperature methods, the numerical linked-clu… ▽ More The Kagome lattice Fermi-Hubbard model is one of the most physically rich, and at the same time most challenging, models to study in strongly-correlated physics. Among its special features are geometric frustration and a flat energy band that create conditions favorable to ferromagnetism near the band insulating limit. Here, we utilize two exact finite-temperature methods, the numerical linked-cluster expansion and the determinant quantum Monte Carlo, to study the extent as well as doping and interaction dependence of ferromagnetic correlations and other thermodynamic properties of the model. We find that repulsive interactions enhance ferromagnetic correlations at high electron densities and that increasing the interaction strength, extends the region with strong ferromagnetic correlations towards half filling, smoothly connecting it to Nagaoka ferromagnetism near the Mott insulating region. We also use the charge compressibility to obtain an accurate estimate for the critical interaction strength for the metal-insulator transition at half filling. These results improve our understanding of the magnetic tendencies of the model away from half filling and pave the way for further studies, including with ultracold atoms in optical lattices. △ Less

Submitted 29 April, 2026; originally announced April 2026.

Comments: 9 pages, 11 figures

Spin and Charge Conductivity in the Square Lattice Fermi-Hubbard Model

Authors: Linh Pham, Ehsan Khatami

Abstract: Dynamical properties are notoriously difficult to compute in numerical treatments of the Fermi-Hubbard model, especially in two spatial dimensions. However, they are essential in providing us with insight into some of the most important and less well-understood phases of the model, such as the pseudogap and strange metal phases at relatively high temperatures, or unconventional superconductivity a… ▽ More Dynamical properties are notoriously difficult to compute in numerical treatments of the Fermi-Hubbard model, especially in two spatial dimensions. However, they are essential in providing us with insight into some of the most important and less well-understood phases of the model, such as the pseudogap and strange metal phases at relatively high temperatures, or unconventional superconductivity at lower temperatures, away from the commensurate filling. Here, we use the numerical linked-cluster expansions to compute spin and charge optical conductivities of the model at different temperatures and strong interaction strengths via the exact real-time-dependent correlation functions of the current operators. We mitigate systematic errors associated with having a limited access to the long-time behavior of the correlators by introducing fits and allowing for non-zero Drude weights when appropriate. We compare our results to available data from optical lattice experiments and find that the Drude contributions can account for the theory-experiment gap in the DC spin conductivity of the model at half filling in the strong-coupling region. Our method helps paint a more complete picture of the conductivity in the two-dimensional Hubbard model and opens the door to studying dynamical properties of quantum lattice models in the thermodynamic limit. △ Less

Submitted 3 February, 2026; originally announced February 2026.

Comments: 11 pages, 11 figures

Charge Order in the half-filled bond-Holstein Model

Authors: Charles Jordan, George Issa, Ehsan Khatami, Richard Scalettar, Benjamin Cohen-Stead, Steven Johnston

Abstract: We use determinant quantum Monte Carlo to study the half-filled `bond-Holstein' model on a square lattice. We find that the model exhibits a charge-density-wave (CDW) phase transition with a critical temperature $T_\mathrm{cdw}$ considerably higher than that of the canonical `site-Holstein' model. Using a finite-size scaling analysis of the charge structure factor $S_{\rm cdw}$, we obtain… ▽ More We use determinant quantum Monte Carlo to study the half-filled `bond-Holstein' model on a square lattice. We find that the model exhibits a charge-density-wave (CDW) phase transition with a critical temperature $T_\mathrm{cdw}$ considerably higher than that of the canonical `site-Holstein' model. Using a finite-size scaling analysis of the charge structure factor $S_{\rm cdw}$, we obtain $T_\mathrm{cdw}$ to greater than one percent accuracy. At the same time, local observables also show clear signatures consistent with the transition temperatures inferred from our scaling analysis. We attribute the enhanced CDW tendencies to a phonon-mediated nearest-neighbor electron repulsion that is directly proportional to the dimensionless electron-phonon coupling $λ$ in the atomic ($t\rightarrow 0$) limit. This behavior contrasts with the site-Holstein case, where the same limit yields only an on-site attraction. We supplement our analysis with results from several unsupervised machine learning methods, which not only confirm our estimates of $T_\mathrm{cdw}$ but also provide insight into the high-temperature crossover between a metallic and bipolaron liquid regime. △ Less

Submitted 21 January, 2026; v1 submitted 19 January, 2026; originally announced January 2026.

Comments: Comments are welcome. Updated to fix units in t=0 results

Competition of fermion pairing, magnetism, and charge order in the spin-doped attractive Hubbard gas

Authors: Thomas Hartke, Botond Oreg, Chunhan Feng, Carter Turnbaugh, Jens Hertkorn, Yuan-Yao He, Ningyuan Jia, Ehsan Khatami, Shiwei Zhang, Martin Zwierlein

Abstract: The tension between fermion pairing and magnetism affects numerous strongly correlated electron systems, from high-temperature cuprates to twisted bilayer graphene. Exotic forms of fermion pairing and superfluidity are predicted when attraction between fermions competes with spin doping. Here, we follow the evolution of fermion pairing and charge and spin order in a spin-imbalanced attractive Hubb… ▽ More The tension between fermion pairing and magnetism affects numerous strongly correlated electron systems, from high-temperature cuprates to twisted bilayer graphene. Exotic forms of fermion pairing and superfluidity are predicted when attraction between fermions competes with spin doping. Here, we follow the evolution of fermion pairing and charge and spin order in a spin-imbalanced attractive Hubbard gas of fermionic $^{40}$K atoms, covering a wide range of densities, magnetizations, and interactions with single-atom resolution. At low spin imbalance and weak interactions, we find a mixture of nonlocal fermion pairs coexisting with itinerant excess fermions. For stronger interactions an effective hard-core Bose-Fermi mixture emerges. Spin doping drives a crossover from charge-density wave correlations to a Fermi liquid of polarons. Beyond a certain spin imbalance and interaction strength, we find evidence for the onset of combined spin- and pair-density wave order, a possible precursor for the existence of magnetized superfluidity in the attractive Hubbard system. △ Less

Submitted 13 November, 2025; originally announced November 2025.

Comments: 7 pages, 5 figures

Finite-Temperature Kinetic Ferromagnetism in the Square Lattice Hubbard Model

Authors: Robin C. Newby, Ehsan Khatami

Abstract: While the exact phase diagram of the Fermi-Hubbard model remains poorly understood despite decades of progress, nearly 60 years ago, Nagaoka proved that a single dopant in an otherwise half-filled Hubbard system can bring about ferromagnetism through kinetic means. The phenomenon was recently observed with ultracold atoms in triangular optical lattices. Here, we explore the kinetic ferromagnetism… ▽ More While the exact phase diagram of the Fermi-Hubbard model remains poorly understood despite decades of progress, nearly 60 years ago, Nagaoka proved that a single dopant in an otherwise half-filled Hubbard system can bring about ferromagnetism through kinetic means. The phenomenon was recently observed with ultracold atoms in triangular optical lattices. Here, we explore the kinetic ferromagnetism within the square lattice Hubbard model and its strong-coupling counterpart, the $t-J$ model, at finite temperatures in the thermodynamic limit via numerical linked-cluster expansions. We find evidence of ferromagnetic Nagaoka polarons at dopings up to $\sim 30\%$ away from half filling for a variety of interaction strengths and at temperatures as low as $0.2$ of the hopping energy. We map out the boundaries of this phase through analyzing various correlation functions. △ Less

Submitted 11 June, 2025; v1 submitted 10 February, 2025; originally announced February 2025.

Comments: 11 pages, 10 figures

Journal ref: Physical Review B 111, 245120 (2025)

Learning by Confusion: The Phase Diagram of the Holstein Model

Authors: George Issa, Owen Bradley, Ehsan Khatami, Richard Scalettar

Abstract: We employ the "learning by confusion" technique, an unsupervised machine learning approach for detecting phase transitions, to analyze quantum Monte Carlo simulations of the two-dimensional Holstein model--a fundamental model for electron-phonon interactions on a lattice. Utilizing a convolutional neural network, we conduct a series of binary classification tasks to identify Holstein critical poin… ▽ More We employ the "learning by confusion" technique, an unsupervised machine learning approach for detecting phase transitions, to analyze quantum Monte Carlo simulations of the two-dimensional Holstein model--a fundamental model for electron-phonon interactions on a lattice. Utilizing a convolutional neural network, we conduct a series of binary classification tasks to identify Holstein critical points based on the neural network's learning accuracy. We further evaluate the effectiveness of various training datasets, including snapshots of phonon fields and other measurements resolved in imaginary time, for predicting distinct phase transitions and crossovers. Our results culminate in the construction of the finite-temperature phase diagram of the Holstein model. △ Less

Submitted 11 April, 2025; v1 submitted 8 January, 2025; originally announced January 2025.

Comments: 11 pages, 9 figures

Journal ref: Phys. Rev. B 111, 155140 (2025)

Autoregressive neural quantum states of Fermi Hubbard models

Authors: Eduardo Ibarra-García-Padilla, Hannah Lange, Roger G Melko, Richard T Scalettar, Juan Carrasquilla, Annabelle Bohrdt, Ehsan Khatami

Abstract: Neural quantum states (NQS) have emerged as a powerful ansatz for variational quantum Monte Carlo studies of strongly-correlated systems. Here, we apply recurrent neural networks (RNNs) and autoregressive transformer neural networks to the Fermi-Hubbard and the (non-Hermitian) Hatano-Nelson-Hubbard models in one and two dimensions. In both cases, we observe that the convergence of the RNN ansatz i… ▽ More Neural quantum states (NQS) have emerged as a powerful ansatz for variational quantum Monte Carlo studies of strongly-correlated systems. Here, we apply recurrent neural networks (RNNs) and autoregressive transformer neural networks to the Fermi-Hubbard and the (non-Hermitian) Hatano-Nelson-Hubbard models in one and two dimensions. In both cases, we observe that the convergence of the RNN ansatz is challenged when increasing the interaction strength. We present a physically-motivated and easy-to-implement strategy for improving the optimization, namely, by ramping of the model parameters. Furthermore, we investigate the advantages and disadvantages of the autoregressive sampling property of both network architectures. For the Hatano-Nelson-Hubbard model, we identify convergence issues that stem from the autoregressive sampling scheme in combination with the non-Hermitian nature of the model. Our findings provide insights into the challenges of the NQS approach and make the first step towards exploring strongly-correlated electrons using this ansatz. △ Less

Submitted 8 January, 2025; v1 submitted 11 November, 2024; originally announced November 2024.

Comments: 14 pages, 13 figures

Journal ref: Phys. Rev. Research 7, 013122 (2025)

Structural complexity of snapshots of 2D Fermi-Hubbard systems

Authors: Eduardo Ibarra-García-Padilla, Stephanie Striegel, Richard T. Scalettar, Ehsan Khatami

Abstract: The development of quantum gas microscopy for two-dimensional optical lattices has provided an unparalleled tool to study the Fermi-Hubbard model (FHM) with ultracold atoms. Spin-resolved projective measurements, or snapshots, have played a significant role in quantifying correlation functions which uncover underlying physical phenomena such as antiferromagnetism at commensurate filling on biparti… ▽ More The development of quantum gas microscopy for two-dimensional optical lattices has provided an unparalleled tool to study the Fermi-Hubbard model (FHM) with ultracold atoms. Spin-resolved projective measurements, or snapshots, have played a significant role in quantifying correlation functions which uncover underlying physical phenomena such as antiferromagnetism at commensurate filling on bipartite lattices, and other charge and spin correlations, as well as dynamical properties at various densities. However, in order to interpret these results and to establish temperature scales, comparison against theory is generally needed. Here, we employ a recent concept, the {\em multi-scale structural complexity}, and show that when computed for the snapshots (of either single spin species, local moments, or total density) it can provide a theory-free property, immediately accessible to experiments. Specifically, after benchmarking results for Ising and XY models, we study the structural complexity of snapshots of the repulsive FHM in the two-dimensional square lattice as a function of doping and temperature. We generate projective measurements using determinant quantum Monte Carlo and compare their complexities against those from the experiment. We demonstrate that these complexities are linked to relevant physical observables such as the entropy and double occupancy. Their behaviors capture the development of correlations and relevant length scales in the system. We provide an open-source code in Python which can be implemented into data analysis routines in experimental settings for the square lattice. △ Less

Submitted 22 April, 2024; v1 submitted 25 December, 2023; originally announced December 2023.

Comments: 14 pages, 11 figures, 2 tables

Journal ref: Phys. Rev. A 109, 053304 (2024)

Machine Learning Detection of Correlations in Snapshots of Ultracold Atoms in Optical Lattices

Authors: Stephanie Striegel, Eduardo Ibarra-García-Padilla, Ehsan Khatami

Abstract: Recent proposals have suggested the use of supervised learning with convolutional neural networks to shed light on some of the less well known phases of the Fermi-Hubbard model through the classification of snapshots from the quantum gas microscopy of ultracold atoms in optical lattices. However, there have been challenges in the interpretability of networks with more than one convolutional filter… ▽ More Recent proposals have suggested the use of supervised learning with convolutional neural networks to shed light on some of the less well known phases of the Fermi-Hubbard model through the classification of snapshots from the quantum gas microscopy of ultracold atoms in optical lattices. However, there have been challenges in the interpretability of networks with more than one convolutional filter coupled to the input images. Here, we expand on previous work by considering multiple filters in the first convolutional layer and developing a process for analyzing the physical relevance of patterns obtained in the trained filters. We benchmark our approach at half-filling, where strong antiferromagnetic correlations are known to be present, and we find that upon hole doping, previously unknown patterns arise at temperatures below the tunneling amplitude. These patterns may be a signature of interesting arrangements of fermions in the lattice. △ Less

Submitted 4 October, 2023; originally announced October 2023.

Comments: Submitted to the Proceedings of Conference on Computational Physics 2023

Observation of Nagaoka Polarons in a Fermi-Hubbard Quantum Simulator

Authors: Martin Lebrat, Muqing Xu, Lev Haldar Kendrick, Anant Kale, Youqi Gang, Pranav Seetharaman, Ivan Morera, Ehsan Khatami, Eugene Demler, Markus Greiner

Abstract: Quantum interference can deeply alter the nature of many-body phases of matter. In the paradigmatic case of the Hubbard model, Nagaoka famously proved that introducing a single itinerant charge can transform a paramagnetic insulator into a ferromagnet through path interference. However, a microscopic observation of such kinetic magnetism induced by individually imaged dopants has been so far elusi… ▽ More Quantum interference can deeply alter the nature of many-body phases of matter. In the paradigmatic case of the Hubbard model, Nagaoka famously proved that introducing a single itinerant charge can transform a paramagnetic insulator into a ferromagnet through path interference. However, a microscopic observation of such kinetic magnetism induced by individually imaged dopants has been so far elusive. Here we demonstrate the emergence of Nagaoka polarons in a Hubbard system realized with strongly interacting fermions in a triangular optical lattice. Using quantum gas microscopy, we reveal these polarons as extended ferromagnetic bubbles around particle dopants arising from the local interplay of coherent dopant motion and spin exchange. In contrast, kinetic frustration due to the triangular geometry promotes antiferromagnetic polarons around hole dopants, as proposed by Haerter and Shastry. Our work augurs the exploration of exotic quantum phases driven by charge motion in strongly correlated systems and over sizes that are challenging for numerical simulation. △ Less

Submitted 12 May, 2025; v1 submitted 23 August, 2023; originally announced August 2023.

Comments: 9+12 pages, 4+7 figures, accepted version with author correction

Journal ref: Nature 629, 317 (2024)

Metal-insulator transition and magnetism of SU(3) fermions in the square lattice

Authors: Eduardo Ibarra-García-Padilla, Chunhan Feng, Giulio Pasqualetti, Simon Fölling, Richard T. Scalettar, Ehsan Khatami, Kaden R. A. Hazzard

Abstract: We study the SU(3) symmetric Fermi-Hubbard model (FHM) in the square lattice at $1/3$-filling using numerically exact determinant quantum Monte Carlo (DQMC) and numerical linked-cluster expansion (NLCE) techniques. We present the different regimes of the model in the $T-U$ plane, which are characterized by local and short-range correlations, and capture signatures of the metal-insulator transition… ▽ More We study the SU(3) symmetric Fermi-Hubbard model (FHM) in the square lattice at $1/3$-filling using numerically exact determinant quantum Monte Carlo (DQMC) and numerical linked-cluster expansion (NLCE) techniques. We present the different regimes of the model in the $T-U$ plane, which are characterized by local and short-range correlations, and capture signatures of the metal-insulator transition and magnetic crossovers. These signatures are detected as the temperature scales characterizing the rise of the compressibility, and an interaction-dependent change in the sign of the diagonal spin-spin correlation function. The analysis of the compressibility estimates the location of the metal-insulator quantum critical point at $U_c/t \sim 6$, and provides a temperature scale for observing Mott physics at finite-$T$. Furthermore, from the analysis of the spin-spin correlation function we observe that for $U/t \gtrsim6$ and $T \sim J = 4t^2/U$ there is a development of a short-range two sublattice (2-SL) antiferromagnetic structure, as well as an emerging three sublattice (3-SL) antiferromagnetic structure as the temperature is lowered below $T/J \lesssim 0.57$. This crossover from 2-SL to 3-SL magnetic ordering agrees with Heisenberg limit predictions, and has observable effects on the density of on-site pairs. Finally, we describe how the features of the regimes in the $T$-$U$ plane can be explored with alkaline-earth-like atoms in optical lattices with currently-achieved experimental techniques and temperatures. The results discussed in this manuscript provide a starting point for the exploration of the SU(3) FHM upon doping. △ Less

Submitted 26 September, 2023; v1 submitted 18 June, 2023; originally announced June 2023.

Journal ref: Phys. Rev. A 108, 053312 (2023)

A perspective on machine learning and data science for strongly correlated electron problems

Authors: S. Johnston, E. Khatami, R. T. Scalettar

Abstract: Numerical approaches to the correlated electron problem have achieved considerable success, yet are still constrained by several bottlenecks, including high order polynomial or exponential scaling in system size, long autocorrelation times, challenges in recognizing novel phases, and the Fermion sign problem. Methods in machine learning (ML), artificial intelligence, and data science promise to he… ▽ More Numerical approaches to the correlated electron problem have achieved considerable success, yet are still constrained by several bottlenecks, including high order polynomial or exponential scaling in system size, long autocorrelation times, challenges in recognizing novel phases, and the Fermion sign problem. Methods in machine learning (ML), artificial intelligence, and data science promise to help address these limitations and open up a new frontier in strongly correlated quantum system simulations. In this paper, we review some of the progress in this area. We begin by examining these approaches in the context of classical models, where their underpinnings and application can be easily illustrated and benchmarked. We then discuss cases where ML methods have enabled scientific discovery. Finally, we will examine their applications in accelerating model solutions in state-of-the-art quantum many-body methods like quantum Monte Carlo and discuss potential future research directions. △ Less

Submitted 21 October, 2022; originally announced October 2022.

Journal ref: Carbon Trends 9, 100231 (2022)

Extracting Off-Diagonal Order from Diagonal Basis Measurements

Authors: Bo Xiao, Javier Robledo Moreno, Matthew Fishman, Dries Sels, Ehsan Khatami, Richard Scalettar

Abstract: Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems. However, discerning phases with topological or off-diagonal long range order requires the ability to extract these correlations from site-resolved measurements. Here, we show that a multi-scale complexity measure can pinpoint the transition to and from the bond ordered wave phase of the one-di… ▽ More Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems. However, discerning phases with topological or off-diagonal long range order requires the ability to extract these correlations from site-resolved measurements. Here, we show that a multi-scale complexity measure can pinpoint the transition to and from the bond ordered wave phase of the one-dimensional extended Hubbard model with an off-diagonal order parameter, sandwiched between diagonal charge and spin density wave phases, using only diagonal descriptors. We study the model directly in the thermodynamic limit using the recently developed variational uniform matrix product states algorithm, and draw our samples from degenerate ground states related by global spin rotations, emulating the projective measurements that are accessible in experiments. Our results will have important implications for the study of exotic phases using optical lattice experiments. △ Less

Submitted 7 August, 2024; v1 submitted 21 September, 2022; originally announced September 2022.

Comments: 11 pages including supplementary materials, 8 figures

Journal ref: Phys. Rev. Research 6, L022064 (2024)

Acoustic Cloak Design via Machine Learning

Authors: Thang Tran, Feruza Amirkulova, Ehsan Khatami

Abstract: Acoustic metamaterials are engineered microstructures with special mechanical and acoustic properties enabling exotic effects such as wave steering, focusing and cloaking. The design of acoustic cloaks using scattering cancellation has traditionally involved the optimization of metamaterial structure based on direct computer simulations of the total scattering cross section (TSCS) for a large numb… ▽ More Acoustic metamaterials are engineered microstructures with special mechanical and acoustic properties enabling exotic effects such as wave steering, focusing and cloaking. The design of acoustic cloaks using scattering cancellation has traditionally involved the optimization of metamaterial structure based on direct computer simulations of the total scattering cross section (TSCS) for a large number of configurations. Here, we work with sets of cylindrical objects confined in a region of space and use machine learning methods to streamline the design of 2D configurations of scatterers with minimal TSCS demonstrating cloaking effect at discrete sets of wavenumbers. After establishing that artificial neural networks are capable of learning the TSCS based on the location of cylinders, we develop an inverse design algorithm, combining variational autoencoders and the Gaussian process, for predicting optimal arrangements of scatterers given the TSCS. We show results for up to eight cylinders and discuss the efficiency and other advantages of the machine learning approach. △ Less

Submitted 1 November, 2021; originally announced November 2021.

Comments: 17 pages, 9 figures

Journal ref: Journal of Theoretical and Computational Acoustics 30, 2240005 (2022)

Quantum Simulation of an Extended Fermi-Hubbard Model Using a 2D Lattice of Dopant-based Quantum Dots

Authors: Xiqiao Wang, Ehsan Khatami, Fan Fei, Jonathan Wyrick, Pradeep Namboodiri, Ranjit Kashid, Albert F. Rigosi, Garnett Bryant, Richard Silver

Abstract: The Hubbard model is one of the primary models for understanding the essential many-body physics in condensed matter systems such as Mott insulators and cuprate high-Tc superconductors. Recent advances in atomically precise fabrication in silicon using scanning tunneling microscopy (STM) have made possible atom-by-atom fabrication of single and few-dopant quantum dots and atomic-scale control of t… ▽ More The Hubbard model is one of the primary models for understanding the essential many-body physics in condensed matter systems such as Mott insulators and cuprate high-Tc superconductors. Recent advances in atomically precise fabrication in silicon using scanning tunneling microscopy (STM) have made possible atom-by-atom fabrication of single and few-dopant quantum dots and atomic-scale control of tunneling in dopant-based devices. However, the complex fabrication requirements of multi-component devices have meant that emulating two-dimensional (2D) Fermi-Hubbard physics using these systems has not been demonstrated. Here, we overcome these challenges by integrating the latest developments in atomic fabrication and demonstrate the analog quantum simulation of a 2D extended Fermi-Hubbard Hamiltonian using STM-fabricated 3x3 arrays of single/few-dopant quantum dots. We demonstrate low-temperature quantum transport and tuning of the electron ensemble using in-plane gates as efficient probes to characterize the many-body properties, such as charge addition, tunnel coupling, and the impact of disorder within the array. By controlling the array lattice constants with sub-nm precision, we demonstrate tuning of the hopping amplitude and long-range interactions and observe the finite-size analogue of a transition from Mott insulating to metallic behavior in the array. By increasing the measurement temperature, we simulate the effect of thermally activated hopping and Hubbard band formation in transport spectroscopy. We compare the analog quantum simulations with numerically simulated results to help understand the energy spectrum and resonant tunneling within the array. The results demonstrated in this study serve as a launching point for a new class of engineered artificial lattices to simulate the extended Fermi-Hubbard model of strongly correlated materials. △ Less

Submitted 17 October, 2021; originally announced October 2021.

Thermodynamics of the disordered Hubbard model studied via numerical linked-cluster expansions

Authors: Jacob Park, Ehsan Khatami

Abstract: The interplay of disorder and strong correlations in quantum many-body systems remains an open question. That is despite much progress made in recent years with ultracold atoms in optical lattices to better understand phenomena such as many-body localization or the effect of disorder on Mott metal-insulator transitions. Here, we utilize the numerical linked-cluster expansion technique, extended to… ▽ More The interplay of disorder and strong correlations in quantum many-body systems remains an open question. That is despite much progress made in recent years with ultracold atoms in optical lattices to better understand phenomena such as many-body localization or the effect of disorder on Mott metal-insulator transitions. Here, we utilize the numerical linked-cluster expansion technique, extended to treat disordered quantum lattice models, and study exact thermodynamic properties of the disordered Fermi-Hubbard model on the square and cubic geometries. We consider box distributions for the disorder in the onsite energy, the interaction strength, as well as the hopping amplitude and explore how energy, double occupancy, entropy, heat capacity and magnetic correlations of the system in the thermodynamic limit evolve as the strength of disorder changes. We compare our findings with those obtained from determinant quantum Monte Carlo simulations and discuss the relevance of our results to experiments with cold fermionic atoms in optical lattices. △ Less

Submitted 17 October, 2021; v1 submitted 29 January, 2021; originally announced January 2021.

Comments: 13 pages, 12 figures, same as the published version

Journal ref: Phys. Rev. B 104, 165102 (2021)

Visualizing Strange Metallic Correlations in the 2D Fermi-Hubbard Model with AI

Authors: Ehsan Khatami, Elmer Guardado-Sanchez, Benjamin M. Spar, Juan Felipe Carrasquilla, Waseem S. Bakr, Richard T. Scalettar

Abstract: Strongly correlated phases of matter are often described in terms of straightforward electronic patterns. This has so far been the basis for studying the Fermi-Hubbard model realized with ultracold atoms. Here, we show that artificial intelligence (AI) can provide an unbiased alternative to this paradigm for phases with subtle, or even unknown, patterns. Long- and short-range spin correlations spo… ▽ More Strongly correlated phases of matter are often described in terms of straightforward electronic patterns. This has so far been the basis for studying the Fermi-Hubbard model realized with ultracold atoms. Here, we show that artificial intelligence (AI) can provide an unbiased alternative to this paradigm for phases with subtle, or even unknown, patterns. Long- and short-range spin correlations spontaneously emerge in filters of a convolutional neural network trained on snapshots of single atomic species. In the less well-understood strange metallic phase of the model, we find that a more complex network trained on snapshots of local moments produces an effective order parameter for the non-Fermi-liquid behavior. Our technique can be employed to characterize correlations unique to other phases with no obvious order parameters or signatures in projective measurements, and has implications for science discovery through AI beyond strongly correlated systems. △ Less

Submitted 23 December, 2020; v1 submitted 27 February, 2020; originally announced February 2020.

Comments: 12 pages, 9 figures; updated in accord with the published version

Journal ref: Phys. Rev. A 102, 033326 (2020)

Charge Density Wave and Superconductivity in the Disordered Holstein Model

Authors: Bo Xiao, Natanael C. Costa, Ehsan Khatami, George G. Batrouni, Richard T. Scalettar

Abstract: The interplay between electron-electron correlations and disorder has been a central theme of condensed matter physics over the last several decades, with particular interest in the possibility that interactions might cause delocalization of an Anderson insulator into a metallic state, and the disrupting effects of randomness on magnetic order and the Mott phase. Here we extend this physics to exp… ▽ More The interplay between electron-electron correlations and disorder has been a central theme of condensed matter physics over the last several decades, with particular interest in the possibility that interactions might cause delocalization of an Anderson insulator into a metallic state, and the disrupting effects of randomness on magnetic order and the Mott phase. Here we extend this physics to explore electron-phonon interactions and show, via exact quantum Monte Carlo simulations, that the suppression of the charge density wave correlations in the half-filled Holstein model by disorder can stabilize a superconducting phase. Our simulations thus capture qualitatively the suppression of charge ordered phases and emergent superconductivity recently seen experimentally. △ Less

Submitted 10 March, 2021; v1 submitted 19 October, 2019; originally announced October 2019.

Journal ref: Phys. Rev. B 103, 060501 (2021)

Accelerating lattice quantum Monte Carlo simulation using artificial neural networks: an application to the Holstein model

Authors: Shaozhi Li, Philip M. Dee, Ehsan Khatami, Steven Johnston

Abstract: Monte Carlo (MC) simulations are essential computational approaches with widespread use throughout all areas of science. We present a method for accelerating lattice MC simulations using fully connected and convolutional artificial neural networks that are trained to perform local and global moves in configuration space, respectively. Both networks take local spacetime MC configurations as input f… ▽ More Monte Carlo (MC) simulations are essential computational approaches with widespread use throughout all areas of science. We present a method for accelerating lattice MC simulations using fully connected and convolutional artificial neural networks that are trained to perform local and global moves in configuration space, respectively. Both networks take local spacetime MC configurations as input features and can, therefore, be trained using samples generated by conventional MC runs on smaller lattices before being utilized for simulations on larger systems. This new approach is benchmarked for the case of determinant quantum Monte Carlo (DQMC) studies of the two-dimensional Holstein model. We find that both artificial neural networks are capable of learning an unspecified effective model that accurately reproduces the MC configuration weights of the original Hamiltonian and achieve an order of magnitude speedup over the conventional DQMC algorithm. Our approach is broadly applicable to many classical and quantum lattice MC algorithms. △ Less

Submitted 17 May, 2019; originally announced May 2019.

Comments: 6 pages, 3 figures

MSC Class: 81-08

Journal ref: Phys. Rev. B 100, 020302 (2019)

Effect of Strain on Charge Density Wave Order in the Holstein Model

Authors: B. Cohen-Stead, N. C. Costa, E. Khatami, R. T. Scalettar

Abstract: We investigate charge ordering in the Holstein model in the presence of anisotropic hopping, $t_x, t_y=1-δ, 1 + δ$, as a model of the effect of strain on charge density wave (CDW) materials. Using Quantum Monte Carlo simulations, we show that the CDW transition temperature is relatively insensitive to moderate anisotropy $δ\lesssim 0.3$, but begins to decrease more rapidly at $δ\gtrsim 0.4$. Howev… ▽ More We investigate charge ordering in the Holstein model in the presence of anisotropic hopping, $t_x, t_y=1-δ, 1 + δ$, as a model of the effect of strain on charge density wave (CDW) materials. Using Quantum Monte Carlo simulations, we show that the CDW transition temperature is relatively insensitive to moderate anisotropy $δ\lesssim 0.3$, but begins to decrease more rapidly at $δ\gtrsim 0.4$. However, the density correlations, as well as the kinetic energies parallel and perpendicular to the compressional axis, change significantly for moderate $δ$. Accompanying mean-field theory calculations show a similar qualitative structure, with the transition temperature relatively constant at small $δ$ and a more rapid decrease for larger strains. We also obtain the density of states $N(ω)$, which provides clear signal of the charge ordering transition at large strain, where finite size scaling of the charge structure factor is extremely difficult because of the small value of the order parameter. △ Less

Submitted 16 May, 2019; v1 submitted 14 May, 2019; originally announced May 2019.

Journal ref: Phys. Rev. B 100, 045125 (2019)

Ground state phase diagram of the one-dimensional Bose-Hubbard model from restricted Boltzmann machines

Authors: Kristopher McBrian, Giuseppe Carleo, Ehsan Khatami

Abstract: Motivated by recent advances in the representation of ground state wavefunctions of quantum many-body systems using restricted Boltzmann machines as variational ansatz, we utilize an open-source platform for constructing such ansatz called NetKet to explore the extent of applicability of restricted Boltzmann machines to bosonic lattice models. Within NetKet, we design and train these machines for… ▽ More Motivated by recent advances in the representation of ground state wavefunctions of quantum many-body systems using restricted Boltzmann machines as variational ansatz, we utilize an open-source platform for constructing such ansatz called NetKet to explore the extent of applicability of restricted Boltzmann machines to bosonic lattice models. Within NetKet, we design and train these machines for the one-dimensional Bose-Hubbard model through a Monte Carlo sampling of the Fock space. We vary parameters such as the strength of the onsite repulsion, the chemical potential, the system size and the maximum site occupancy and use converged equations of state to identify phase boundaries between the Mott insulating and superfluid phases. We compare the average density and the energy to results from exact diagonalization and map out the ground state phase diagram, which agrees qualitatively with previous finding obtained through conventional means. △ Less

Submitted 7 March, 2019; originally announced March 2019.

Comments: 8 pages, 5 figures, Proceedings of the Conference in Computational Physics 2018

Numerical linked-cluster expansions for disordered lattice models

Authors: Michael Mulanix, Demetrius Almada, Ehsan Khatami

Abstract: Imperfections in correlated materials can alter their ground state as well as finite-temperature properties in significant ways. Here, we develop a method based on numerical linked-cluster expansions for calculating exact finite-temperature properties of disordered lattice models directly in the thermodynamic limit. We show that a continuous distribution for disordered parameters can be achieved u… ▽ More Imperfections in correlated materials can alter their ground state as well as finite-temperature properties in significant ways. Here, we develop a method based on numerical linked-cluster expansions for calculating exact finite-temperature properties of disordered lattice models directly in the thermodynamic limit. We show that a continuous distribution for disordered parameters can be achieved using a set of carefully chosen discrete modes in the distribution, which allows for the averaging of properties over all disorder realizations. We benchmark our results for thermodynamic properties of the square lattice Ising and quantum Heisenberg models with bond disorder against Monte Carlo simulations and study them as the strength of disorder changes. We also apply the method to the disordered Heisenberg model on the frustrated checkerboard lattice, which is closely connected to Sr$_2$Cu(Te$_{0.5}$W$_{0.5}$)O$_6$. Our method can be used to study finite-temperature properties of other disordered quantum lattice models including those for interacting lattice fermions. △ Less

Submitted 13 December, 2018; v1 submitted 30 October, 2018; originally announced October 2018.

Comments: Added references, figure 7, and discussions surrounding them

Journal ref: Phys. Rev. B 99, 205113 (2019)

Lanczos Boosted Numerical Linked-Cluster Expansion for Quantum Lattice Models

Authors: Krishnakumar Bhattaram, Ehsan Khatami

Abstract: Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the limiting factor for these calculations. Here, we show that a partial diagonalization of the largest clusters in the expansion using the Lanczos algorithm can be as… ▽ More Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the limiting factor for these calculations. Here, we show that a partial diagonalization of the largest clusters in the expansion using the Lanczos algorithm can be as useful as full diagonalization for the method while mitigating some of the time and memory issues. As a test case, we consider a frustrated Heisenberg model on the checkerboard lattice and find that our approach can lead to much more efficient calculations in a parallel environment. △ Less

Submitted 15 October, 2018; originally announced October 2018.

Comments: 6 pages, 6 figures

Journal ref: Phys. Rev. E 100, 013305 (2019)

Machine Learning in Electronic Quantum Matter Imaging Experiments

Authors: Yi Zhang, A. Mesaros, K. Fujita, S. D. Edkins, M. H. Hamidian, K. Ch'ng, H. Eisaki, S. Uchida, J. C. Séamus Davis, E. Khatami, Eun-Ah Kim

Abstract: Essentials of the scientific discovery process have remained largely unchanged for centuries: systematic human observation of natural phenomena is used to form hypotheses that, when validated through experimentation, are generalized into established scientific theory. Today, however, we face major challenges because automated instrumentation and large-scale data acquisition are generating data set… ▽ More Essentials of the scientific discovery process have remained largely unchanged for centuries: systematic human observation of natural phenomena is used to form hypotheses that, when validated through experimentation, are generalized into established scientific theory. Today, however, we face major challenges because automated instrumentation and large-scale data acquisition are generating data sets of such volume and complexity as to defy human analysis. Radically different scientific approaches are needed, with machine learning (ML) showing great promise, not least for materials science research. Hence, given recent advances in ML analysis of synthetic data representing electronic quantum matter (EQM), the next challenge is for ML to engage equivalently with experimental data. For example, atomic-scale visualization of EQM yields arrays of complex electronic structure images, that frequently elude effective analyses. Here we report development and training of an array of artificial neural networks (ANN) designed to recognize different types of hypothesized order hidden in EQM image-arrays. These ANNs are used to analyze an experimentally-derived EQM image archive from carrier-doped cuprate Mott insulators. Throughout these noisy and complex data, the ANNs discover the existence of a lattice-commensurate, four-unit-cell periodic, translational-symmetry-breaking EQM state. Further, the ANNs find these phenomena to be unidirectional, revealing a coincident nematic EQM state. Strong-coupling theories of electronic liquid crystals are congruent with all these observations. △ Less

Submitted 28 March, 2019; v1 submitted 1 August, 2018; originally announced August 2018.

Comments: 44 pages, 15 figures

Journal ref: Nature (2019)

Spin Transport in a Mott Insulator of Ultracold Fermions

Authors: Matthew A. Nichols, Lawrence W. Cheuk, Melih Okan, Thomas R. Hartke, Enrique Mendez, T. Senthil, Ehsan Khatami, Hao Zhang, Martin W. Zwierlein

Abstract: Strongly correlated materials are expected to feature unconventional transport properties, such that charge, spin, and heat conduction are potentially independent probes of the dynamics. In contrast to charge transport, the measurement of spin transport in such materials is highly challenging. We observed spin conduction and diffusion in a system of ultracold fermionic atoms that realizes the half… ▽ More Strongly correlated materials are expected to feature unconventional transport properties, such that charge, spin, and heat conduction are potentially independent probes of the dynamics. In contrast to charge transport, the measurement of spin transport in such materials is highly challenging. We observed spin conduction and diffusion in a system of ultracold fermionic atoms that realizes the half-filled Fermi-Hubbard model. For strong interactions, spin diffusion is driven by super-exchange and doublon-hole-assisted tunneling, and strongly violates the quantum limit of charge diffusion. The technique developed in this work can be extended to finite doping, which can shed light on the complex interplay between spin and charge in the Hubbard model. △ Less

Submitted 28 January, 2019; v1 submitted 27 February, 2018; originally announced February 2018.

Comments: 16 pages, 10 figures

Journal ref: Science 363, 383 (2019)

Exotic pairing symmetry of interacting Dirac fermions on a $π$ flux lattice

Authors: Huaiming Guo, Ehsan Khatami, Yao Wang, Thomas P. Devereaux, Rajiv R. P. Singh, Richard T. Scalettar

Abstract: The pairing symmetry of interacting Dirac fermions on the $π$-flux lattice is studied with the determinant quantum Monte Carlo and numerical linked cluster expansion methods. The extended $s^*$- (i.e. extended $s$-) and d-wave pairing symmetries, which are distinct in the conventional square lattice, are degenerate under the Landau gauge. We demonstrate that the dominant pairing channel at strong… ▽ More The pairing symmetry of interacting Dirac fermions on the $π$-flux lattice is studied with the determinant quantum Monte Carlo and numerical linked cluster expansion methods. The extended $s^*$- (i.e. extended $s$-) and d-wave pairing symmetries, which are distinct in the conventional square lattice, are degenerate under the Landau gauge. We demonstrate that the dominant pairing channel at strong interactions is an exotic $ds^*$-wave phase consisting of alternating stripes of $s^*$- and d-wave phases. A complementary mean-field analysis shows that while the $s^*$- and d-wave symmetries individually have nodes in the energy spectrum, the $ds^*$ channel is fully gapped. The results represent a new realization of pairing in Dirac systems, connected to the problem of chiral d-wave pairing on the honeycomb lattice, which might be more readily accessed by cold-atom experiments. △ Less

Submitted 10 April, 2018; v1 submitted 23 August, 2017; originally announced August 2017.

Comments: 6 pages, 5 figures; format changed, accepted by Phys. Rev. B

Journal ref: Phys. Rev. B 97, 155146 (2018)

Unsupervised machine learning account of magnetic transitions in the Hubbard model

Authors: Kelvin Ch'ng, Nick Vazquez, Ehsan Khatami

Abstract: We employ several unsupervised machine learning techniques, including autoencoders, random trees embedding, and t-distributed stochastic neighboring ensemble (t-SNE), to reduce the dimensionality of, and therefore classify, raw (auxiliary) spin configurations generated, through Monte Carlo simulations of small clusters, for the Ising and Fermi-Hubbard models at finite temperatures. Results from a… ▽ More We employ several unsupervised machine learning techniques, including autoencoders, random trees embedding, and t-distributed stochastic neighboring ensemble (t-SNE), to reduce the dimensionality of, and therefore classify, raw (auxiliary) spin configurations generated, through Monte Carlo simulations of small clusters, for the Ising and Fermi-Hubbard models at finite temperatures. Results from a convolutional autoencoder for the three-dimensional Ising model can be shown to produce the magnetization and the susceptibility as a function of temperature with a high degree of accuracy. Quantum fluctuations distort this picture and prevent us from making such connections between the output of the autoencoder and physical observables for the Hubbard model. However, we are able to define an indicator based on the output of the t-SNE algorithm that shows a near perfect agreement with the antiferromagnetic structure factor of the model in two and three spatial dimensions in the weak-coupling regime. t-SNE also predicts a transition to the canted antiferromagnetic phase for the three-dimensional model when a strong magnetic field is present. We show that these techniques cannot be expected to work away from half filling when the "sign problem" in quantum Monte Carlo simulations is present. △ Less

Submitted 10 August, 2017; originally announced August 2017.

Comments: 11 pages, 8 figures

Journal ref: Phys. Rev. E 97, 013306 (2018)

Competing phases and orbital-selective behaviors in the two-orbital Hubbard-Holstein model

Authors: Shaozhi Li, Ehsan Khatami, Steven Johnston

Abstract: We study the interplay between the electron-electron (e-e) and the electron-phonon (e-ph) interactions in the two-orbital Hubbard-Holstein model at half filling using the dynamical mean field theory. We find that the e-ph interaction, even at weak couplings, strongly modifies the phase diagram of this model and introduces an orbital-selective Peierls insulating phase (OSPI) that is analogous to th… ▽ More We study the interplay between the electron-electron (e-e) and the electron-phonon (e-ph) interactions in the two-orbital Hubbard-Holstein model at half filling using the dynamical mean field theory. We find that the e-ph interaction, even at weak couplings, strongly modifies the phase diagram of this model and introduces an orbital-selective Peierls insulating phase (OSPI) that is analogous to the widely studied orbital-selective Mott phase (OSMP). At small e-e and e-ph coupling, we find a competition between the OSMP and the OSPI, while at large couplings, a competition occurs between Mott and charge-density-wave (CDW) insulating phases. We further demonstrate that the Hund's coupling influences the OSPI transition by lowering the energy associated with the CDW. Our results explicitly show that one must be cautious when neglecting the e-ph interaction in multiorbital systems, where multiple electronic interactions create states that are readily influenced by perturbing interactions. △ Less

Submitted 23 March, 2017; v1 submitted 11 March, 2017; originally announced March 2017.

Comments: 5 pages, 4 figures

Journal ref: Phys. Rev. B 95, 121112 (2017)

Observation of canted antiferromagnetism with ultracold fermions in an optical lattice

Authors: Peter T. Brown, Debayan Mitra, Elmer Guardado-Sanchez, Peter Schauß, Stanimir S. Kondov, Ehsan Khatami, Thereza Paiva, Nandini Trivedi, David A. Huse, Waseem S. Bakr

Abstract: Understanding the magnetic response of the normal state of the cuprates is considered a key piece in solving the puzzle of their high-temperature superconductivity. The essential physics of these materials is believed to be captured by the Fermi-Hubbard model, a minimal model that has been realized with cold atoms in optical lattices. Here we report on site-resolved measurements of the Fermi-Hubba… ▽ More Understanding the magnetic response of the normal state of the cuprates is considered a key piece in solving the puzzle of their high-temperature superconductivity. The essential physics of these materials is believed to be captured by the Fermi-Hubbard model, a minimal model that has been realized with cold atoms in optical lattices. Here we report on site-resolved measurements of the Fermi-Hubbard model in a spin-imbalanced atomic gas, allowing us to explore the response of the system to large effective magnetic fields. We observe short-range canted antiferromagnetism at half-filling with stronger spin correlations in the direction orthogonal to the magnetization, in contrast with the spin-balanced case where identical correlations are measured for any projection of the pseudospin. The rotational anisotropy of the spin correlators is found to increase with polarization and with distance between the spins. Away from half-filling, the polarization of the gas exhibits non-monotonic behavior with doping for strong interactions, resembling the behavior of the magnetic susceptibility in the cuprates. We compare our measurements to predictions from Determinantal Quantum Monte Carlo (DQMC) and Numerical Linked Cluster Expansion (NLCE) algorithms and find good agreement. Calculations on the doped system are near the limits of these techniques, illustrating the value of cold atom quantum simulations for studying strongly-correlated materials. △ Less

Submitted 22 December, 2016; originally announced December 2016.

Journal ref: Science, 357, 1385-1388 (2017)

Machine Learning Phases of Strongly Correlated Fermions

Authors: Kelvin Ch'ng, Juan Carrasquilla, Roger G. Melko, Ehsan Khatami

Abstract: Machine learning offers an unprecedented perspective for the problem of classifying phases in condensed matter physics. We employ neural-network machine learning techniques to distinguish finite-temperature phases of the strongly correlated fermions on cubic lattices. We show that a three dimensional convolutional network trained on auxiliary field configurations produced by quantum Monte Carlo si… ▽ More Machine learning offers an unprecedented perspective for the problem of classifying phases in condensed matter physics. We employ neural-network machine learning techniques to distinguish finite-temperature phases of the strongly correlated fermions on cubic lattices. We show that a three dimensional convolutional network trained on auxiliary field configurations produced by quantum Monte Carlo simulations of the Hubbard model can correctly predict the magnetic phase diagram of the model at the average density of one (half filling). We then use the network, trained at half filling, to explore the trend in the transition temperature as the system is doped away from half filling. This transfer learning approach predicts that the instability to the magnetic phase extends to at least 5% doping in this region. Our results pave the way for other machine learning applications in correlated quantum many-body systems. △ Less

Submitted 10 September, 2017; v1 submitted 8 September, 2016; originally announced September 2016.

Comments: 9 pages, 8 figures

Journal ref: Phys. Rev. X 7, 031038 (2017)

Transport and Optical Conductivity in the Hubbard Model: A High-Temperature Expansion Perspective

Authors: Edward Perepelitsky, Andrew Galatas, Jernej Mravlje, Rok Žitko, Ehsan Khatami, B Sriram Shastry, Antoine Georges

Abstract: We derive analytical expressions for the spectral moments of the dynamical response functions of the Hubbard model using the high-temperature series expansion. We consider generic dimension $d$ as well as the infinite-$d$ limit, arbitrary electron density $n$, and both finite and infinite repulsion $U$. We use moment-reconstruction methods to obtain the one-electron spectral function, the self-ene… ▽ More We derive analytical expressions for the spectral moments of the dynamical response functions of the Hubbard model using the high-temperature series expansion. We consider generic dimension $d$ as well as the infinite-$d$ limit, arbitrary electron density $n$, and both finite and infinite repulsion $U$. We use moment-reconstruction methods to obtain the one-electron spectral function, the self-energy, and the optical conductivity. They are all smooth functions at high-temperature and, at large-$U$, they are featureless with characteristic widths of order the lattice hopping parameter $t$. In the infinite-$d$ limit we compare the series expansion results with accurate numerical renormalization group and interaction expansion quantum Monte-Carlo results. We find excellent agreement down to surprisingly low temperatures, throughout most of the bad-metal regime which applies for $T \gtrsim (1-n)D$, the Brinkman-Rice scale. The resistivity increases linearly in $T$ at high-temperature without saturation. This results from the $1/T$ behaviour of the compressibility or kinetic energy, which play the role of the effective carrier number. In contrast, the scattering time (or diffusion constant) saturate at high-$T$. We find that $σ(n,T) \approx (1-n)σ(n=0,T)$ to a very good approximation for all $n$, with $σ(n=0,T)\propto t/T$ at high temperatures. The saturation at small $n$ occurs due to a compensation between the density-dependence of the effective number of carriers and that of the scattering time. The $T$-dependence of the resistivity displays a knee-like feature which signals a cross-over to the intermediate-temperature regime where the diffusion constant (or scattering time) start increasing with decreasing $T$. At high-temperatures, the thermopower obeys the Heikes formula, while the Wiedemann-Franz law is violated with the Lorenz number vanishing as $1/T^2$. △ Less

Submitted 10 November, 2016; v1 submitted 4 August, 2016; originally announced August 2016.

Comments: 38 pages, 16 figures

Journal ref: Phys. Rev. B 94, 235115 (2016)

Observation of Spatial Charge and Spin Correlations in the 2D Fermi-Hubbard Model

Authors: Lawrence W. Cheuk, Matthew A. Nichols, Katherine R. Lawrence, Melih Okan, Hao Zhang, Ehsan Khatami, Nandini Trivedi, Thereza Paiva, Marcos Rigol, Martin W. Zwierlein

Abstract: Strong electron correlations lie at the origin of transformative phenomena such as colossal magneto-resistance and high-temperature superconductivity. Already near room temperature, doped copper oxide materials display remarkable features such as a pseudo-gap and a "strange metal" phase with unusual transport properties. The essence of this physics is believed to be captured by the Fermi-Hubbard m… ▽ More Strong electron correlations lie at the origin of transformative phenomena such as colossal magneto-resistance and high-temperature superconductivity. Already near room temperature, doped copper oxide materials display remarkable features such as a pseudo-gap and a "strange metal" phase with unusual transport properties. The essence of this physics is believed to be captured by the Fermi-Hubbard model of repulsively interacting, itinerant fermions on a lattice. Here we report on the site-resolved observation of charge and spin correlations in the two-dimensional (2D) Fermi-Hubbard model realized with ultracold atoms. Antiferromagnetic spin correlations are maximal at half-filling and weaken monotonically upon doping. Correlations between singly charged sites are negative at large doping, revealing the Pauli and correlation hole\textemdash a suppressed probability of finding two fermions near each other. However, as the doping is reduced below a critical value, correlations between such local magnetic moments become positive, signaling strong bunching of doublons and holes. Excellent agreement with numerical linked-cluster expansion (NLCE) and determinantal quantum Monte Carlo (DQMC) calculations is found. Positive non-local moment correlations directly imply potential energy fluctuations due to doublon-hole pairs, which should play an important role for transport in the Fermi-Hubbard model. △ Less

Submitted 13 June, 2016; originally announced June 2016.

Journal ref: Science 353, 1260-1264 (2016)

Three-dimensional Hubbard model in the thermodynamic limit

Authors: Ehsan Khatami

Abstract: We employ the numerical linked-cluster expansion to study finite-temperature properties of the uniform cubic lattice Hubbard model in the thermodynamic limit for a wide range of interaction strengths and densities. We carry out the expansion to the 9th order and find that the convergence of the series extends to lower temperatures as the strength of the interaction increases, giving us access to r… ▽ More We employ the numerical linked-cluster expansion to study finite-temperature properties of the uniform cubic lattice Hubbard model in the thermodynamic limit for a wide range of interaction strengths and densities. We carry out the expansion to the 9th order and find that the convergence of the series extends to lower temperatures as the strength of the interaction increases, giving us access to regions of the parameter space that are difficult to reach by most other numerical methods. We study the precise trends in the specific heat, the double occupancy, and magnetic correlations at temperatures as low as 0.2 of the hopping amplitude in the strong-coupling regime. We show that in this regime, accurate estimates for transition temperatures to the Néel ordered phase, in agreement with the predicted asymptotic behavior, can be deduced from the low-temperature magnetic structure factor. We also find evidence for possible instability to the magnetically ordered phase away from, but close to, half filling. Our results have important implications for parametrizing fermionic systems in optical lattice experiments and for benchmarking other numerical methods. △ Less

Submitted 11 September, 2016; v1 submitted 8 March, 2016; originally announced March 2016.

Comments: 8 pages, 6 figures

Journal ref: Phys. Rev. B 94, 125114 (2016)

Cooling Atomic Gases With Disorder

Authors: Thereza Paiva, Ehsan Khatami, Shuxiang Yang, Valery Rousseau, Mark Jarrell, Juana Moreno, Randall G. Hulet, Richard T. Scalettar

Abstract: Cold atomic gases have proven capable of emulating a number of fundamental condensed matter phenomena including Bose-Einstein condensation, the Mott transition, Fulde-Ferrell-Larkin-Ovchinnikov pairing and the quantum Hall effect. Cooling to a low enough temperature to explore magnetism and exotic superconductivity in lattices of fermionic atoms remains a challenge. We propose a method to produce… ▽ More Cold atomic gases have proven capable of emulating a number of fundamental condensed matter phenomena including Bose-Einstein condensation, the Mott transition, Fulde-Ferrell-Larkin-Ovchinnikov pairing and the quantum Hall effect. Cooling to a low enough temperature to explore magnetism and exotic superconductivity in lattices of fermionic atoms remains a challenge. We propose a method to produce a low temperature gas by preparing it in a disordered potential and following a constant entropy trajectory to deliver the gas into a non-disordered state which exhibits these incompletely understood phases. We show, using quantum Monte Carlo simulations, that we can approach the Neél temperature of the three-dimensional Hubbard model for experimentally achievable parameters. Recent experimental estimates suggest the randomness required lies in a regime where atom transport and equilibration are still robust. △ Less

Submitted 11 August, 2015; originally announced August 2015.

Comments: 5 figures, supplement with 5 figures

Journal ref: Phys. Rev. Lett. 115, 240402 (2015)

Finite-temperature superconducting correlations of the Hubbard model

Authors: Ehsan Khatami, Richard T. Scalettar, Rajiv R. P. Singh

Abstract: We utilize numerical linked-cluster expansions (NLCEs) and the determinantal quantum Monte Carlo algorithm to study pairing correlations in the square lattice Hubbard model. To benchmark the NLCE, we first locate the finite-temperature phase transition of the attractive model to a superconducting state away from half filling. We then explore the superconducting properties of the repulsive model fo… ▽ More We utilize numerical linked-cluster expansions (NLCEs) and the determinantal quantum Monte Carlo algorithm to study pairing correlations in the square lattice Hubbard model. To benchmark the NLCE, we first locate the finite-temperature phase transition of the attractive model to a superconducting state away from half filling. We then explore the superconducting properties of the repulsive model for the d-wave and extended s-wave pairing symmetries. The pairing structure factor shows a strong tendency to d-wave pairing and peaks at an interaction strength comparable to the bandwidth. The extended s-wave structure factor and correlation length are larger at higher temperatures but clearly saturate as temperature is lowered, whereas the d-wave counterparts, which start off lower at high temperatures, continue to rise near half filling. This rise is even more dramatic in the d-wave susceptibility. The convergence of NLCEs breaks down as the susceptibilities and correlation lengths become large, so we are unable to determine the onset of long-range order. However, our results extend the conclusion, previously restricted to only magnetic and charge correlations, that NLCEs offer unique window into pairing in the Hubbard model at strong coupling. △ Less

Submitted 12 July, 2015; v1 submitted 20 March, 2015; originally announced March 2015.

Comments: 6 pages, 4 figures

Journal ref: Phys. Rev. B 91, 241107(R) (2015)

Geometry Dependence of the Sign Problem

Authors: V. I. Iglovikov, E. Khatami, R. T. Scalettar

Abstract: The sign problem is the fundamental limitation to quantum Monte Carlo simulations of the statistical mechanics of interacting fermions. Determinant quantum Monte Carlo (DQMC) is one of the leading methods to study lattice models such as the Hubbard Hamiltonian which describe strongly correlated phenomena including magnetism, metal-insulator transitions, and (possibly) exotic superconductivity. Her… ▽ More The sign problem is the fundamental limitation to quantum Monte Carlo simulations of the statistical mechanics of interacting fermions. Determinant quantum Monte Carlo (DQMC) is one of the leading methods to study lattice models such as the Hubbard Hamiltonian which describe strongly correlated phenomena including magnetism, metal-insulator transitions, and (possibly) exotic superconductivity. Here, we provide a comprehensive dataset on the geometry dependence of the DQMC sign problem for different densities, interaction strengths, temperatures, and spatial lattice sizes. We supplement this data with several observations concerning general trends in the data, including the dependence on spatial volume and how this can be probed by examining decoupled clusters, the scaling of the sign in the vicinity of a particle-hole symmetric point, and the correlation between the total sign and the signs for the individual spin species. △ Less

Submitted 17 May, 2015; v1 submitted 12 January, 2015; originally announced January 2015.

Journal ref: Phys. Rev. B 92, 045110 (2015)

Compressibility of a fermionic Mott insulator of ultracold atoms

Authors: Pedro M. Duarte, Russell A. Hart, Tsung-Lin Yang, Xinxing Liu, Thereza Paiva, Ehsan Khatami, Richard T. Scalettar, Nandini Trivedi, Randall G. Hulet

Abstract: We characterize the Mott insulating regime of a repulsively interacting Fermi gas of ultracold atoms in a three-dimensional optical lattice. We use in-situ imaging to extract the central density of the gas, and to determine its local compressibility. For intermediate to strong interactions, we observe the emergence of a plateau in the density as a function of atom number, and a reduction of the co… ▽ More We characterize the Mott insulating regime of a repulsively interacting Fermi gas of ultracold atoms in a three-dimensional optical lattice. We use in-situ imaging to extract the central density of the gas, and to determine its local compressibility. For intermediate to strong interactions, we observe the emergence of a plateau in the density as a function of atom number, and a reduction of the compressibility at a density of one atom per site, indicating the formation of a Mott insulator. Comparisons to state-of-the-art numerical simulations of the Hubbard model over a wide range of interactions reveal that the temperature of the gas is of the order of, or below, the tunneling energy scale. Our results hold great promise for the exploration of many-body phenomena with ultracold atoms, where the local compressibility can be a useful tool to detect signatures of different phases or phase boundaries at specific values of the filling. △ Less

Submitted 31 January, 2015; v1 submitted 29 September, 2014; originally announced September 2014.

Journal ref: Phys. Rev. Lett. 114, 070403 (2015)

Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms

Authors: Russell A. Hart, Pedro M. Duarte, Tsung-Lin Yang, Xinxing Liu, Thereza Paiva, Ehsan Khatami, Richard T. Scalettar, Nandini Trivedi, David A. Huse, Randall G. Hulet

Abstract: Ultracold atoms in optical lattices have great potential to contribute to a better understanding of some of the most important issues in many-body physics, such as high-$T_c$ superconductivity. The Hubbard model describes many of the features shared by the copper oxides, including an interaction-driven Mott insulating state and an antiferromagnetic (AFM) state. Optical lattices filled with a two-s… ▽ More Ultracold atoms in optical lattices have great potential to contribute to a better understanding of some of the most important issues in many-body physics, such as high-$T_c$ superconductivity. The Hubbard model describes many of the features shared by the copper oxides, including an interaction-driven Mott insulating state and an antiferromagnetic (AFM) state. Optical lattices filled with a two-spin-component Fermi gas of ultracold atoms can faithfully realise the Hubbard model with readily tunable parameters, and thus provide a platform for the systematic exploration of its phase diagram. Realisation of strongly correlated phases, however, has been hindered by the need to cool the atoms to temperatures as low as the magnetic exchange energy, and also by the lack of reliable thermometry. Here we demonstrate spin-sensitive Bragg scattering of light to measure AFM spin correlations in a realisation of the 3D Hubbard model at temperatures down to 1.4 times that of the AFM phase transition. This temperature regime is beyond the range of validity of a simple high-temperature series expansion, which brings our experiment close to the limit of the capabilities of current numerical techniques. We reach these low temperatures using a unique compensated optical lattice technique, in which the confinement of each lattice beam is compensated by a blue-detuned laser beam. The temperature of the atoms in the lattice is deduced by comparing the light scattering to determinantal quantum Monte Carlo and numerical linked-cluster expansion calculations. Further refinement of the compensated lattice may produce even lower temperatures which, along with light scattering thermometry, would open avenues for achieving and characterising other novel quantum states of matter, such as the pseudogap regime of the 2D Hubbard model. △ Less

Submitted 31 January, 2015; v1 submitted 22 July, 2014; originally announced July 2014.

Journal ref: Nature 519, 211-214 (2015)

Magnetic correlations and pairing in the 1/5-depleted square lattice Hubbard model

Authors: Ehsan Khatami, Rajiv R. P. Singh, Warren E. Pickett, Richard T. Scalettar

Abstract: We study the single-orbital Hubbard model on the 1/5-depleted square lattice geometry, which arises in such diverse systems as the spin-gap magnetic insulator CaV4O9 and ordered-vacancy iron selenides, presenting new issues regarding the origin of both magnetic ordering and superconductivity in these materials. We find a rich phase diagram that includes a plaquette singlet phase, a dimer singlet p… ▽ More We study the single-orbital Hubbard model on the 1/5-depleted square lattice geometry, which arises in such diverse systems as the spin-gap magnetic insulator CaV4O9 and ordered-vacancy iron selenides, presenting new issues regarding the origin of both magnetic ordering and superconductivity in these materials. We find a rich phase diagram that includes a plaquette singlet phase, a dimer singlet phase, a Neel and a block-spin antiferromagnetic phase, and stripe phases. Quantum Monte Carlo simulations show that the dominant pairing correlations at half filling change character from d-wave in the plaquette phase to extended s-wave upon transition to the Neel phase. These findings have intriguing connections to iron-based superconductors, and suggest that some physics of multiorbital systems can be captured by a single-orbital model at different dopings. △ Less

Submitted 25 September, 2014; v1 submitted 14 April, 2014; originally announced April 2014.

Comments: 8 pages, 8 figures

Journal ref: Phys. Rev. Lett. 113, 106402 (2014)

Linked-cluster expansion for the Green's function of the infinite-U Hubbard model

Authors: Ehsan Khatami, Edward Perepelitsky, Marcos Rigol, B. Sriram Shastry

Abstract: We implement a highly efficient strong-coupling expansion for the Green's function of the Hubbard model. In the limit of extreme correlations, where the onsite interaction is infinite, the evaluation of diagrams simplifies dramatically enabling us to carry out the expansion to the eighth order in powers of the hopping amplitude. We compute the finite-temperature Green's function analytically in th… ▽ More We implement a highly efficient strong-coupling expansion for the Green's function of the Hubbard model. In the limit of extreme correlations, where the onsite interaction is infinite, the evaluation of diagrams simplifies dramatically enabling us to carry out the expansion to the eighth order in powers of the hopping amplitude. We compute the finite-temperature Green's function analytically in the momentum and Matsubara frequency space as a function of the electron density. Employing Pade approximations, we study the equation of state, Kelvin thermopower, momentum distribution function, quasiparticle fraction, and quasiparticle lifetime of the system at temperatures lower than, or of the order of, the hopping amplitude. We also discuss several different approaches for obtaining the spectral functions through analytic continuation of the imaginary frequency Green's function, and show results for the system near half filling. We benchmark our results for the equation of state against those obtained from a numerical linked-cluster expansion carried out to the eleventh order. △ Less

Submitted 4 June, 2014; v1 submitted 30 October, 2013; originally announced October 2013.

Comments: 15 pages, 11 figures, 1 table

Journal ref: Phys. Rev. E 89, 063301 (2014)

Finite-temperature properties of strongly correlated fermions in the honeycomb lattice

Authors: Baoming Tang, Thereza Paiva, Ehsan Khatami, Marcos Rigol

Abstract: We study finite-temperature properties of strongly interacting fermions in the honeycomb lattice using numerical linked-cluster expansions and determinantal quantum Monte Carlo simulations. We analyze a number of thermodynamic quantities, including the entropy, the specific heat, uniform and staggered spin susceptibilities, short-range spin correlations, and the double occupancy at and away from h… ▽ More We study finite-temperature properties of strongly interacting fermions in the honeycomb lattice using numerical linked-cluster expansions and determinantal quantum Monte Carlo simulations. We analyze a number of thermodynamic quantities, including the entropy, the specific heat, uniform and staggered spin susceptibilities, short-range spin correlations, and the double occupancy at and away from half filling. We examine the viability of adiabatic cooling by increasing the interaction strength for homogeneous as well as for trapped systems. For the homogeneous case, this process is found to be more efficient at finite doping than at half filling. That, in turn, leads to an efficient adiabatic cooling in the presence of a trap which, starting with even relatively high entropies, can drive the system to have a Mott insulating phase with substantial antiferromagnetic correlations. △ Less

Submitted 18 September, 2013; v1 submitted 5 July, 2013; originally announced July 2013.

Comments: 11 pages, 11 figures, 1 table, as published

Journal ref: Phys. Rev. B 88, 125127 (2013)

Fluctuation-Dissipation Theorem in an Isolated System of Quantum Dipolar Bosons after a Quench

Authors: Ehsan Khatami, Guido Pupillo, Mark Srednicki, Marcos Rigol

Abstract: We examine the validity of fluctuation-dissipation relations in isolated quantum systems taken out of equilibrium by a sudden quench. We focus on the dynamics of trapped hard-core bosons in one-dimensional lattices with dipolar interactions whose strength is changed during the quench. We find that fluctuation-dissipation relations hold if the system is nonintegrable after the quench. They also hol… ▽ More We examine the validity of fluctuation-dissipation relations in isolated quantum systems taken out of equilibrium by a sudden quench. We focus on the dynamics of trapped hard-core bosons in one-dimensional lattices with dipolar interactions whose strength is changed during the quench. We find that fluctuation-dissipation relations hold if the system is nonintegrable after the quench. They also hold if the system is integrable after the quench if the initial state is an equilibrium state of a nonintegrable Hamiltonian. However, they fail if the system is integrable both before and after quenching. △ Less

Submitted 3 August, 2013; v1 submitted 26 April, 2013; originally announced April 2013.

Comments: 11 pages, 12 figures

Journal ref: Phys. Rev. Lett. 111, 050403 (2013)

Electronic spectral properties of the two-dimensional infinite-U Hubbard model

Authors: Ehsan Khatami, Daniel Hansen, Edward Perepelitsky, Marcos Rigol, B. Sriram Shastry

Abstract: A strong-coupling series expansion for the Green's function and the extremely-correlated Fermi liquid (ECFL) theory are used to calculate the moments of the electronic spectral functions of the infinite-U Hubbard model. Results from these two complementary methods agree very well at both, low densities, where the ECFL solution is the most accurate, and at high to intermediate temperatures, where t… ▽ More A strong-coupling series expansion for the Green's function and the extremely-correlated Fermi liquid (ECFL) theory are used to calculate the moments of the electronic spectral functions of the infinite-U Hubbard model. Results from these two complementary methods agree very well at both, low densities, where the ECFL solution is the most accurate, and at high to intermediate temperatures, where the series converge. We find that a modified first moment, which underestimates the contributions from the occupied states and is accessible in the series through the time-dependent Green's function, best describes the quasiparticle peak location in the strongly-correlated regime. This is examined by the ECFL results at low temperatures, where it is shown that the spectral function is largely skewed towards the occupied states. △ Less

Submitted 30 April, 2013; v1 submitted 11 March, 2013; originally announced March 2013.

Comments: 5 pages, 3 figures

Journal ref: Phys. Rev. B 87, 161120(R), (2013)

A Short Introduction to Numerical Linked-Cluster Expansions

Authors: Baoming Tang, Ehsan Khatami, Marcos Rigol

Abstract: We provide a pedagogical introduction to numerical linked-cluster expansions (NLCEs). We sketch the algorithm for generic Hamiltonians that only connect nearest-neighbor sites in a finite cluster with open boundary conditions. We then compare results for a specific model, the Heisenberg model, in each order of the NLCE with the ones for the finite cluster calculated directly by means of full exact… ▽ More We provide a pedagogical introduction to numerical linked-cluster expansions (NLCEs). We sketch the algorithm for generic Hamiltonians that only connect nearest-neighbor sites in a finite cluster with open boundary conditions. We then compare results for a specific model, the Heisenberg model, in each order of the NLCE with the ones for the finite cluster calculated directly by means of full exact diagonalization. We discuss how to reduce the computational cost of the NLCE calculations by taking into account symmetries and topologies of the linked clusters. Finally, we generalize the algorithm to the thermodynamic limit, and discuss several numerical resummation techniques that can be used to accelerate the convergence of the series. △ Less

Submitted 13 July, 2012; originally announced July 2012.

Comments: 11 pages, 6 figures, 2 tables

Journal ref: Computer Physics Communications 184, 557-564 (2013)

Short-Range Correlations and Cooling of Ultracold Fermions in the Honeycomb Lattice

Authors: Baoming Tang, Thereza Paiva, Ehsan Khatami, Marcos Rigol

Abstract: We use determinantal quantum Monte Carlo simulations and numerical linked-cluster expansions to study thermodynamic properties and short-range spin correlations of fermions in the honeycomb lattice. We find that, at half filling and finite temperatures, nearest-neighbor spin correlations can be stronger in this lattice than in the square lattice, even in regimes where the ground state in the forme… ▽ More We use determinantal quantum Monte Carlo simulations and numerical linked-cluster expansions to study thermodynamic properties and short-range spin correlations of fermions in the honeycomb lattice. We find that, at half filling and finite temperatures, nearest-neighbor spin correlations can be stronger in this lattice than in the square lattice, even in regimes where the ground state in the former is a semimetal or a spin liquid. The honeycomb lattice also exhibits a more pronounced anomalous region in the double occupancy that leads to stronger adiabatic cooling than in the square lattice. We discuss the implications of these findings for optical lattice experiments. △ Less

Submitted 13 November, 2012; v1 submitted 31 May, 2012; originally announced June 2012.

Comments: 5 pages, 4 figures

Journal ref: Phys. Rev. Lett. 109, 205301 (2012)

Effect of particle statistics in strongly correlated two-dimensional Hubbard models

Authors: Ehsan Khatami, Marcos Rigol

Abstract: We study the onset of particle statistics effects as the temperature is lowered in strongly correlated two-dimensional Hubbard models. We utilize numerical linked-cluster expansions and focus on the properties of interacting lattice fermions and two-component hard-core bosons. In the weak-coupling regime, where the ground state of the bosonic system is a superfluid, the thermodynamic properties of… ▽ More We study the onset of particle statistics effects as the temperature is lowered in strongly correlated two-dimensional Hubbard models. We utilize numerical linked-cluster expansions and focus on the properties of interacting lattice fermions and two-component hard-core bosons. In the weak-coupling regime, where the ground state of the bosonic system is a superfluid, the thermodynamic properties of the two systems at half filling exhibit very large differences even at high temperatures. In the strong-coupling regime, where the low-temperature behavior is governed by a Mott insulator for either particle statistics, the agreement between the thermodynamic properties of both systems extends to regions where the antiferromagnetic (iso)spin correlations are exponentially large. We analyze how particle statistics affects adiabatic cooling in those systems. △ Less

Submitted 30 August, 2012; v1 submitted 6 April, 2012; originally announced April 2012.

Comments: 9 pages, 8 figures

Journal ref: Phys. Rev. A 86, 023633 (2012)

Thermodynamics and phase transitions for the Heisenberg model on the pinwheel distorted kagome lattice

Authors: Ehsan Khatami, Rajiv R. P. Singh, Marcos Rigol

Abstract: We study the Heisenberg model on the pinwheel distorted kagome lattice as observed in the material Rb_2Cu_3SnF_12. Experimentally relevant thermodynamic properties at finite temperatures are computed utilizing numerical linked-cluster expansions. We also develop a Lanczos-based, zero-temperature, numerical linked cluster expansion to study the approach of the pinwheel distorted lattice to the unif… ▽ More We study the Heisenberg model on the pinwheel distorted kagome lattice as observed in the material Rb_2Cu_3SnF_12. Experimentally relevant thermodynamic properties at finite temperatures are computed utilizing numerical linked-cluster expansions. We also develop a Lanczos-based, zero-temperature, numerical linked cluster expansion to study the approach of the pinwheel distorted lattice to the uniform kagome-lattice Heisenberg model. We find strong evidence for a phase transition before the uniform limit is reached, implying that the ground state of the kagome-lattice Heisenberg model is likely not pinwheel dimerized and is stable to finite pinwheel-dimerizing perturbations. △ Less

Submitted 19 December, 2011; v1 submitted 20 May, 2011; originally announced May 2011.

Comments: 6 pages, 6 figures, 1 table

Journal ref: Phys. Rev. B 84, 224411 (2011)

Thermodynamics of strongly interacting fermions in two-dimensional optical lattices

Authors: Ehsan Khatami, Marcos Rigol

Abstract: We study finite-temperature properties of strongly correlated fermions in two-dimensional optical lattices by means of numerical linked cluster expansions, a computational technique that allows one to obtain exact results in the thermodynamic limit. We focus our analysis on the strongly interacting regime, where the on-site repulsion is of the order of or greater than the band width. We compute th… ▽ More We study finite-temperature properties of strongly correlated fermions in two-dimensional optical lattices by means of numerical linked cluster expansions, a computational technique that allows one to obtain exact results in the thermodynamic limit. We focus our analysis on the strongly interacting regime, where the on-site repulsion is of the order of or greater than the band width. We compute the equation of state, double occupancy, entropy, uniform susceptibility, and spin correlations for temperatures that are similar to or below the ones achieved in current optical lattice experiments. We provide a quantitative analysis of adiabatic cooling of trapped fermions in two dimensions, by means of both flattening the trapping potential and increasing the interaction strength. △ Less

Submitted 14 November, 2011; v1 submitted 28 April, 2011; originally announced April 2011.

Comments: 7 pages, 7 figures

Journal ref: Phys. Rev. A 84, 053611 (2011)