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Ground-state phase diagram of the three-band Hubbard model from density matrix embedding theory
Authors:
Zhi-Hao Cui,
Chong Sun,
Ushnish Ray,
Bo-Xiao Zheng,
Qiming Sun,
Garnet Kin-Lic Chan
Abstract:
We determine the ground-state phase diagram of the three-band Hubbard model across a range of model parameters using density matrix embedding theory. We study the atomic-scale nature of the antiferromagnetic (AFM) and superconducting (SC) orders, explicitly including the oxygen degrees of freedom. All parametrizations of the model display AFM and SC phases, but the decay of AFM order with doping i…
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We determine the ground-state phase diagram of the three-band Hubbard model across a range of model parameters using density matrix embedding theory. We study the atomic-scale nature of the antiferromagnetic (AFM) and superconducting (SC) orders, explicitly including the oxygen degrees of freedom. All parametrizations of the model display AFM and SC phases, but the decay of AFM order with doping is too slow compared to the experimental phase diagram, and further, coexistence of AFM and SC orders occurs in all parameter sets. The local magnetic moment localizes entirely at the copper sites. The magnetic phase diagram is particularly sensitive to $Δ_{pd}$ and $t_{pp}$, and existing estimates of the charge transfer gap $Δ_{pd}$ appear too large in so-called minimal model parametrizations. The electron-doped side of the phase diagram is qualitatively distinct from hole-doped side and we find an unusual two-peak structure in the SC in the full model parametrization. Examining the SC order at the atomic scale, within the larger scale $d_{x^2 - y^2}$-wave SC pairing order between Cu-Cu and O-O, we also observe a local $p_{x (y)}$ [or $d_{xz (yz)}$]-symmetry modulation of the pair density on the Cu-O bonds. Our work highlights some of the features that arise in a three-band versus one-band picture, the role of the oxygen degrees of freedom in new kinds of atomic-scale SC orders, and the necessity of re-evaluating current parametrizations of the three-band Hubbard model.
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Submitted 30 November, 2020; v1 submitted 14 January, 2020;
originally announced January 2020.
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Finite temperature density matrix embedding theory
Authors:
Chong Sun,
Ushnish Ray,
Zhi-Hao Cui,
Miles Stoudenmire,
Michel Ferrero,
Garnet Kin-Lic Chan
Abstract:
We describe a formulation of the density matrix embedding theory at finite temperature. We present a generalization of the ground-state bath orbital construction that embeds a mean-field finite-temperature density matrix up to a given order in the Hamiltonian, or the Hamiltonian up to a given order in the density matrix. We assess the performance of the finite-temperature density matrix embedding…
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We describe a formulation of the density matrix embedding theory at finite temperature. We present a generalization of the ground-state bath orbital construction that embeds a mean-field finite-temperature density matrix up to a given order in the Hamiltonian, or the Hamiltonian up to a given order in the density matrix. We assess the performance of the finite-temperature density matrix embedding on the 1D Hubbard model both at half-filling and away from it, and the 2D Hubbard model at half-filling, comparing to exact data where available, as well as results from finite-temperature density matrix renormalization group, dynamical mean-field theory, and dynamical cluster approximations. The accuracy of finite-temperature density matrix embedding appears comparable to that of the ground-state theory, with at most a modest increase in bath size, and competitive with that of cluster dynamical mean-field theory.
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Submitted 18 November, 2019;
originally announced November 2019.
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Ground-state properties of the hydrogen chain: insulator-to-metal transition, dimerization, and magnetic phases
Authors:
Mario Motta,
Claudio Genovese,
Fengjie Ma,
Zhi-Hao Cui,
Randy Sawaya,
Garnet Kin-Lic Chan,
Natalia Chepiga,
Phillip Helms,
Carlos Jimenez-Hoyos,
Andrew J. Millis,
Ushnish Ray,
Enrico Ronca,
Hao Shi,
Sandro Sorella,
Edwin M. Stoudenmire,
Steven R. White,
Shiwei Zhang
Abstract:
Accurate and predictive computations of the quantum-mechanical behavior of many interacting electrons in realistic atomic environments are critical for the theoretical design of materials with desired properties, and require solving the grand-challenge problem of the many-electron Schrodinger equation. An infinite chain of equispaced hydrogen atoms is perhaps the simplest realistic model for a bul…
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Accurate and predictive computations of the quantum-mechanical behavior of many interacting electrons in realistic atomic environments are critical for the theoretical design of materials with desired properties, and require solving the grand-challenge problem of the many-electron Schrodinger equation. An infinite chain of equispaced hydrogen atoms is perhaps the simplest realistic model for a bulk material, embodying several central themes of modern condensed matter physics and chemistry, while retaining a connection to the paradigmatic Hubbard model. Here we report a combined application of cutting-edge computational methods to determine the properties of the hydrogen chain in its quantum-mechanical ground state. Varying the separation between the nuclei leads to a rich phase diagram, including a Mott phase with quasi long-range antiferromagnetic order, electron density dimerization with power-law correlations, an insulator-to-metal transition and an intricate set of intertwined magnetic orders.
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Submitted 13 July, 2020; v1 submitted 4 November, 2019;
originally announced November 2019.
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Direct comparison of many-body methods for realistic electronic Hamiltonians
Authors:
Kiel T. Williams,
Yuan Yao,
Jia Li,
Li Chen,
Hao Shi,
Mario Motta,
Chunyao Niu,
Ushnish Ray,
Sheng Guo,
Robert J. Anderson,
Junhao Li,
Lan Nguyen Tran,
Chia-Nan Yeh,
Bastien Mussard,
Sandeep Sharma,
Fabien Bruneval,
Mark van Schilfgaarde,
George H. Booth,
Garnet Kin-Lic Chan,
Shiwei Zhang,
Emanuel Gull,
Dominika Zgid,
Andrew Millis,
Cyrus J. Umrigar,
Lucas K. Wagner
Abstract:
A large collaboration carefully benchmarks 20 first principles many-body electronic structure methods on a test set of 7 transition metal atoms, and their ions and monoxides. Good agreement is attained between the 3 systematically converged methods, resulting in experiment-free reference values. These reference values are used to assess the accuracy of modern emerging and scalable approaches to th…
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A large collaboration carefully benchmarks 20 first principles many-body electronic structure methods on a test set of 7 transition metal atoms, and their ions and monoxides. Good agreement is attained between the 3 systematically converged methods, resulting in experiment-free reference values. These reference values are used to assess the accuracy of modern emerging and scalable approaches to the many-electron problem. The most accurate methods obtain energies indistinguishable from experimental results, with the agreement mainly limited by the experimental uncertainties. Comparison between methods enables a unique perspective on calculations of many-body systems of electrons.
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Submitted 5 October, 2019; v1 submitted 30 September, 2019;
originally announced October 2019.
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Constructing Auxiliary Dynamics for Nonequilibrium Stationary States by Variance Minimization
Authors:
Ushnish Ray,
Garnet Kin-Lic Chan
Abstract:
We present a strategy to construct guiding distribution functions (GDFs) based on variance minimization. Auxiliary dynamics via GDFs mitigates the exponential growth of variance as a function of bias in Monte Carlo estimators of large deviation functions. The variance minimization technique exploits the exact properties of eigenstates of the tilted operator that defines the biased dynamics in the…
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We present a strategy to construct guiding distribution functions (GDFs) based on variance minimization. Auxiliary dynamics via GDFs mitigates the exponential growth of variance as a function of bias in Monte Carlo estimators of large deviation functions. The variance minimization technique exploits the exact properties of eigenstates of the tilted operator that defines the biased dynamics in the nonequilibrium system. We demonstrate our techniques in two classes of problems. In the continuum, we show that GDFs can be optimized to study interacting driven diffusive systems where the efficiency is systematically improved by incorporating higher correlations into the GDF. On the lattice, we use a correlator product state ansatz to study the 1D WASEP. We show that with modest resources we can capture the features of the susceptibility in large systems that marks the phase transition from uniform transport to a traveling wave state. Our work extends the repertoire of tools available to study nonequilibrium properties in realistic systems.
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Submitted 19 December, 2019; v1 submitted 25 September, 2019;
originally announced September 2019.
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Heat current fluctuations and anomalous transport in low dimensional carbon lattices
Authors:
Ushnish Ray,
David T. Limmer
Abstract:
Molecular dynamics simulations and nonequilibrium importance sampling are used to study the heat transport of low dimensional carbon lattices. For both carbon nanotubes and graphene sheets heat transport is found to be anomalous, violating Fourier's law of conduction with a system size dependent thermal conductivity and concomitant nonlinear temperature profiles. For carbon nanotubes, the thermal…
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Molecular dynamics simulations and nonequilibrium importance sampling are used to study the heat transport of low dimensional carbon lattices. For both carbon nanotubes and graphene sheets heat transport is found to be anomalous, violating Fourier's law of conduction with a system size dependent thermal conductivity and concomitant nonlinear temperature profiles. For carbon nanotubes, the thermal conductivity is found to increase as the square root of the length of the nanotube, while for graphene sheets the thermal conductivity is found to increase as the logarithm of the length of the sheet. The particular length dependence and nonlinear temperature profiles place carbon lattices into a universality class with nonlinear lattice models, and suggest that heat transport through carbon nano-structures is better described by a Levy walk rather than simple diffusion.
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Submitted 17 December, 2019; v1 submitted 26 June, 2019;
originally announced June 2019.
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Dynamical phase behavior of the single- and multi-lane asymmetric simple exclusion process via matrix product states
Authors:
Phillip Helms,
Ushnish Ray,
Garnet Kin-Lic Chan
Abstract:
We analyze the dynamical phases of the current-biased 1D and multi-lane open asymmetric simple exclusion processes (ASEP), using matrix product states and the density matrix renormalization group (DMRG) algorithm. In the 1D ASEP, we present a systematic numerical study of the current cumulant generating function and its derivatives, which serve as dynamical phase order parameters. We further chara…
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We analyze the dynamical phases of the current-biased 1D and multi-lane open asymmetric simple exclusion processes (ASEP), using matrix product states and the density matrix renormalization group (DMRG) algorithm. In the 1D ASEP, we present a systematic numerical study of the current cumulant generating function and its derivatives, which serve as dynamical phase order parameters. We further characterize the microscopic structure of the phases from local observables and the entanglement spectrum. In the multi-lane ASEP, which may be viewed as finite width 2D strip, we use the same approach and find the longitudinal current-biased dynamical phase behavior to be sensitive to transverse boundary conditions. Our results serve to illustrate the potential of tensor networks in the simulation of classical nonequilibrium statistical models.
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Submitted 15 April, 2019;
originally announced April 2019.
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Properties of the Superfluid in the Disordered Bose-Hubbard Model
Authors:
Bruno R. de Abreu,
Ushnish Ray,
Silvio A. Vitiello,
David M. Ceperley
Abstract:
We investigate the properties of the superfluid phase in the three-dimensional disordered Bose-Hubbard model using Quantum Monte-Carlo simulations. The phase diagram is generated using Gaussian disorder on the on-site potential. Comparisons with box and speckle disorder show qualitative similarities leading to the re-entrant behavior of the superfluid. Quantitative differences that arise are contr…
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We investigate the properties of the superfluid phase in the three-dimensional disordered Bose-Hubbard model using Quantum Monte-Carlo simulations. The phase diagram is generated using Gaussian disorder on the on-site potential. Comparisons with box and speckle disorder show qualitative similarities leading to the re-entrant behavior of the superfluid. Quantitative differences that arise are controlled by the specific shape of the disorder. Statistics pertaining to disorder distributions are studied for a range of interaction strengths and system sizes, where strong finite-size effects are observed. Despite this, both the superfluid fraction and compressibility remain self-averaging throughout the superfluid phase. Close to the superfluid-Bose-glass phase boundary, finite-size effects dominate but still suggest that self-averaging holds. Our results are pertinent to experiments with ultracold atomic gases where a systematic disorder averaging procedure is typically not possible.
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Submitted 29 August, 2018; v1 submitted 16 April, 2018;
originally announced April 2018.
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Exact fluctuations of nonequilibrium steady states from approximate auxiliary dynamics
Authors:
Ushnish Ray,
Garnet Kin-Lic Chan,
David T. Limmer
Abstract:
We describe a framework to significantly reduce the computational effort to evaluate large deviation functions of time integrated observables within nonequilibrium steady states. We do this by incorporating an auxiliary dynamics into trajectory based Monte Carlo calculations, through a transformation of the system's propagator using an approximate guiding function. This procedure importance sample…
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We describe a framework to significantly reduce the computational effort to evaluate large deviation functions of time integrated observables within nonequilibrium steady states. We do this by incorporating an auxiliary dynamics into trajectory based Monte Carlo calculations, through a transformation of the system's propagator using an approximate guiding function. This procedure importance samples the trajectories that most contribute to the large deviation function, mitigating the exponentially complexity of such calculations. We illustrate the method by studying driven diffusions and interacting lattice models in one and two dimensions. Our work offers an avenue to calculate large deviation functions for high dimensional systems driven far from equilibrium.
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Submitted 1 May, 2018; v1 submitted 30 August, 2017;
originally announced August 2017.
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Importance sampling large deviations in nonequilibrium steady states. I
Authors:
Ushnish Ray,
Garnet Kin-Lic Chan,
David T. Limmer
Abstract:
Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states, and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult, because by construction they depend on exponentially rare events.…
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Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states, and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult, because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.
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Submitted 24 April, 2018; v1 submitted 1 August, 2017;
originally announced August 2017.
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Probing the Bose-Glass--Superfluid Transition using Quantum Quenches of Disorder
Authors:
C. Meldgin,
U. Ray,
P. Russ,
D. Ceperley,
B. DeMarco
Abstract:
We probe the transition between superfluid and Bose glass phases using quantum quenches of disorder in an ultracold atomic lattice gas that realizes the disordered Bose-Hubbard model. Measurements of excitations generated by the quench exhibit threshold behavior in the disorder strength indicative of a phase transition. Ab-initio quantum Monte Carlo simulations confirm that the appearance of excit…
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We probe the transition between superfluid and Bose glass phases using quantum quenches of disorder in an ultracold atomic lattice gas that realizes the disordered Bose-Hubbard model. Measurements of excitations generated by the quench exhibit threshold behavior in the disorder strength indicative of a phase transition. Ab-initio quantum Monte Carlo simulations confirm that the appearance of excitations coincides with the equilibrium superfluid--Bose-glass phase boundary at different lattice potential depths. By varying the quench time, we demonstrate the disappearance of an adiabatic timescale compared with microscopic parameters in the BG regime.
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Submitted 8 February, 2015;
originally announced February 2015.
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Metastable Bose-Einstein Condensation in a Strongly Correlated Optical Lattice
Authors:
David McKay,
Ushnish Ray,
Stefan Natu,
Philip Russ,
David Ceperley,
Brian DeMarco
Abstract:
We experimentally and theoretically study the peak fraction of a Bose-Einstein condensate loaded into a cubic optical lattice as the lattice potential depth and entropy per particle are varied. This system is well-described by the superfluid regime of the Bose-Hubbard model, which allows for comparison with mean-field theories and exact quantum Monte Carlo (QMC) simulations. Despite correcting for…
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We experimentally and theoretically study the peak fraction of a Bose-Einstein condensate loaded into a cubic optical lattice as the lattice potential depth and entropy per particle are varied. This system is well-described by the superfluid regime of the Bose-Hubbard model, which allows for comparison with mean-field theories and exact quantum Monte Carlo (QMC) simulations. Despite correcting for systematic discrepancies between condensate fraction and peak fraction, we discover that the experiment consistently shows the presence of a condensate at temperatures higher than the critical temperature predicted by QMC simulations. This metastability suggests that turning on the lattice potential is non-adiabatic. To confirm this behavior, we compute the timescales for relaxation in this system, and find that equilibration times are comparable with the known heating rates. The similarity of these timescales implies that turning on the lattice potential adiabatically may be impossible. Our results point to the urgent need for a better theoretical and experimental understanding of the timescales for relaxation and adiabaticity in strongly interacting quantum gases, and the importance of model-independent probes of thermometry in optical lattices.
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Submitted 25 November, 2014; v1 submitted 20 November, 2014;
originally announced November 2014.
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Revealing the Condensate and Non-Condensate Distributions in the Inhomogeneous Bose-Hubbard Model
Authors:
Ushnish Ray,
David M. Ceperley
Abstract:
We calculate the condensate fraction and the condensate and non-condensate spatial and momentum distribution of the Bose-Hubbard model in a trap. From our results, it is evident that using approximate distributions can lead to erroneous experimental estimates of the condensate. Strong interactions cause the condensate to develop pedestal-like structures around the central peak that can be mistaken…
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We calculate the condensate fraction and the condensate and non-condensate spatial and momentum distribution of the Bose-Hubbard model in a trap. From our results, it is evident that using approximate distributions can lead to erroneous experimental estimates of the condensate. Strong interactions cause the condensate to develop pedestal-like structures around the central peak that can be mistaken as non-condensate atoms. Near the transition temperature, the peak itself can include a significant non-condensate component. Using distributions generated from QMC simulations, experiments can map their measurements for higher accuracy in identifying phase transitions and temperature.
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Submitted 29 October, 2012; v1 submitted 5 September, 2012;
originally announced September 2012.
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Numerical simulation of thermal noise in Josephson circuits
Authors:
Kenneth Segall,
Dan Schult,
Ushnish Ray,
Toshiro Ohsumi
Abstract:
We present a method to numerically add thermal noise to the equations of motion for a circuit of Josephson junctions. A new noise term, which we call "linearly interpolated Gaussian noise," replaces the usual white noise process. It consists of random noise values spaced at a chosen time interval and linearly interpolated in-between. This method can be used with variable time step solvers, allowin…
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We present a method to numerically add thermal noise to the equations of motion for a circuit of Josephson junctions. A new noise term, which we call "linearly interpolated Gaussian noise," replaces the usual white noise process. It consists of random noise values spaced at a chosen time interval and linearly interpolated in-between. This method can be used with variable time step solvers, allowing more precise control over the error while ensuring that fast dynamics are not missed by the solver. We derive the spectral density of such a noise term and compare it to a white noise process. Then we demonstrate the technique by computing the switching dynamics of a circuit of two Josephson junctions and comparing the results to the traditional method.
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Submitted 18 October, 2016; v1 submitted 2 October, 2011;
originally announced October 2011.