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Snake net and balloon force with a neural network for detecting multiple phases
Authors:
Xiaodong Sun,
Huijiong Yang,
Nan Wu,
T. C. Scott,
Jie Zhang,
Wanzhou Zhang
Abstract:
Unsupervised machine learning applied to the study of phase transitions is an ongoing and interesting research direction. The active contour model, also called the snake model, was initially proposed for target contour extraction in two-dimensional images. In order to obtain a physical phase diagram, the snake model with an artificial neural network is applied in an unsupervised learning way by th…
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Unsupervised machine learning applied to the study of phase transitions is an ongoing and interesting research direction. The active contour model, also called the snake model, was initially proposed for target contour extraction in two-dimensional images. In order to obtain a physical phase diagram, the snake model with an artificial neural network is applied in an unsupervised learning way by the authors of [Phys.Rev.Lett. 120, 176401(2018)]. It guesses the phase boundary as an initial snake and then drives the snake to convergence with forces estimated by the artificial neural network. In this paper, we extend this unsupervised learning method with one contour to a snake net with multiple contours for the purpose of obtaining several phase boundaries in a phase diagram. For the classical Blume-Capel model, the phase diagram containing three and four phases is obtained. Moreover, to overcome the limitations of the initial position and speed up the movement of the snake, the balloon force decaying with the iteration steps is introduced and applied to the snake net structure. Our method is helpful in determining the phase diagram with multiple phases, using just snapshots of configurations from cold atoms or other experiments without knowledge of the phases.
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Submitted 23 February, 2023; v1 submitted 19 May, 2022;
originally announced May 2022.
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Worm quantum Monte-Carlo study of phase diagram of extended Jaynes-Cummings-Hubbard model
Authors:
Huanhuan Wei,
Jie Zhang,
Sebastian Greschner,
Tony C Scott,
Wanzhou Zhang
Abstract:
Herein, we study the extended Jaynes-Cummings-Hubbard model mainly by the large-scale worm quantum Monte-Carlo method to check whether or not a light supersolid phase exists in various geometries, such as the one-dimensional chain, square lattices and triangular lattices. To achieve our purpose, the ground state phase diagrams are investigated. For the one-dimensional chain and square lattices, a…
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Herein, we study the extended Jaynes-Cummings-Hubbard model mainly by the large-scale worm quantum Monte-Carlo method to check whether or not a light supersolid phase exists in various geometries, such as the one-dimensional chain, square lattices and triangular lattices. To achieve our purpose, the ground state phase diagrams are investigated. For the one-dimensional chain and square lattices, a first-order transition occurs between the superfluid phase and the solid phase and therefore there is no stable supersolid phase existing in these geometries. Interestingly, soliton/beats of the local densities arise if the chemical potential is adjusted in the finite-size chain. However, this soliton-superfluid coexistence can not be considered as a supersolid in the thermodynamic limit. Searching for a light supersolid, we also studied the Jaynes-Cummings-Hubbard model on triangular lattices, and the phase diagrams are obtained. Through measurement of the structural factor, momentum distribution and superfluid stiffness for various system sizes, a supersolid phase exists stably in the triangular lattices geometry and the regime of the supersolid phase is smaller than that of the mean field results. The light supersolid in the Jaynes-Cummings-Hubbard model is attractive because it has superreliance, which is absent in the pure Bose-Hubbard model. We believe the results in this paper could help search for new novel phases in cold-atom experiments
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Submitted 5 October, 2020;
originally announced October 2020.
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Resolving the puzzle of sound propagation in liquid helium at low temperatures
Authors:
Tony C. Scott,
Konstantin G. Zloshchastiev
Abstract:
Experimental data suggests that, at temperatures below 1 K, the pressure in liquid helium has a cubic dependence on density. Thus the speed of sound scales as a cubic root of pressure. Near a critical pressure point, this speed approaches zero whereby the critical pressure is negative, thus indicating a cavitation instability regime. We demonstrate that to explain this dependence, one has to view…
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Experimental data suggests that, at temperatures below 1 K, the pressure in liquid helium has a cubic dependence on density. Thus the speed of sound scales as a cubic root of pressure. Near a critical pressure point, this speed approaches zero whereby the critical pressure is negative, thus indicating a cavitation instability regime. We demonstrate that to explain this dependence, one has to view liquid helium as a mixture of three quantum Bose liquids: dilute (Gross-Pitaevskii-type) Bose-Einstein condensate, Ginzburg-Sobyanin-type fluid, and logarithmic superfluid. Therefore, the dynamics of such a mixture is described by a quantum wave equation, which contains not only the polynomial (Gross-Pitaevskii and Ginzburg-Sobyanin) nonlinearities with respect to a condensate wavefunction, but also a non-polynomial logarithmic nonlinearity. We derive an equation of state and speed of sound in our model, and show their agreement with experiment.
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Submitted 16 June, 2020;
originally announced June 2020.
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Ground State Properties of the One-Dimensional Unconstrained Pseudo-Anyon Hubbard Model
Authors:
Wanzhou Zhang,
Sebastian Greschner,
Ernv Fan,
Tony C Scott,
Yunbo Zhang
Abstract:
We study the (pseudo-) anyon Hubbard model on a one-dimensional lattice without the presence of a three-body hardcore constraint. In particular, for the pseudo-fermion limit of a large statistical angle $θ\approxπ$, we observe a wealth of exotic properties including {a first order transition} between different superfluid phases and a {two-component} partially paired phase for large fillings withou…
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We study the (pseudo-) anyon Hubbard model on a one-dimensional lattice without the presence of a three-body hardcore constraint. In particular, for the pseudo-fermion limit of a large statistical angle $θ\approxπ$, we observe a wealth of exotic properties including {a first order transition} between different superfluid phases and a {two-component} partially paired phase for large fillings without need of an additional three-body hardcore constraint.In this limit, we analyze the effect of an induced hardcore constraint, which leads to the stabilization of superfluid {ground states} for vanishing or even small attractive on-site interactions. For finite statistical angles, we study the unconventional broken-symmetry superfluid peaked at a finite momentum, resulting in an interesting beat phenomenon of single particle correlation functions.We show how some features of various ground state phases, including an analog of the partially paired phase in the pseudo-fermion limit, may be reproduced in a naive mean field frame.
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Submitted 28 May, 2017; v1 submitted 8 September, 2016;
originally announced September 2016.
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Beats, broken-symmetry superfluid on a one dimensional anyon Hubbard model
Authors:
Wanzhou Zhang,
Ernv Fan,
Tony C Scott,
Yunbo Zhang
Abstract:
By using the density matrix renormalization group and mean field methods, the anyon Hubbard model is studied systematically on a one dimensional lattice. The model can be expressed as a Bose-Hubbard model with a density-dependent-phase term. When the phase angle is $θ=0$ or $θ=π$, the model will be equivalent to boson and pseudo fermion models, respectively. In the mean field frame, we find a brok…
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By using the density matrix renormalization group and mean field methods, the anyon Hubbard model is studied systematically on a one dimensional lattice. The model can be expressed as a Bose-Hubbard model with a density-dependent-phase term. When the phase angle is $θ=0$ or $θ=π$, the model will be equivalent to boson and pseudo fermion models, respectively. In the mean field frame, we find a broken-symmetry superfluid (BSF), in which the $b^{\dagger}(b)$ operators on the nearest neighborhood sites have exactly opposite directions and behave like a directed oscillation pattern. By the density matrix reorganization group method, in the broken-symmetry superfluid, both the real and imaginary parts of the correlation $b^{\dagger}_ib_{i+r}$ behave according to a {\it beat phenomenon} with $0<θ<π$ in the form $C_0e^{i k r}(-1)^{r}$ or behave like waves with different wavelengths in the form $C_0e^{i k r}$. The distributions of the broken-symmetry superfluid phase and other phases are shown in the phase diagrams with different values of $θ$ and the direct phase transition between the two types of superfluid is observed. The beats phenomenon is explained by double peaks of momentum distribution with two wave numbers ${k}_1$ and ${k}_2$ satisfying the condition $\frac{{k}_1-{k}_2}{{k}_1+{k}_2}<\frac{1}{3}$, which are expected to be observed in the optical experiments.
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Submitted 10 March, 2016; v1 submitted 5 November, 2015;
originally announced November 2015.
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Trimer superfluid and supersolid on two-dimensional optical lattices
Authors:
Wanzhou Zhang,
Yuan Yang,
Lijuan Guo,
Chengxiang Ding,
Tony C. Scott
Abstract:
By the photoassociation method, the trimer superfluid phase disappears in the one dimensional state-dependent optical lattice if the ratio of the three-body interaction $W$ to the trimer tunneling $J$is kept at $W/J=12$ [Phys Rev A. {\bf 90}, 033622(2014)]. To search for a trimer superfluid and trimer supersolid, we load the cold atom into two-dimensional lattices, whose coordinate number $z$ and…
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By the photoassociation method, the trimer superfluid phase disappears in the one dimensional state-dependent optical lattice if the ratio of the three-body interaction $W$ to the trimer tunneling $J$is kept at $W/J=12$ [Phys Rev A. {\bf 90}, 033622(2014)]. To search for a trimer superfluid and trimer supersolid, we load the cold atom into two-dimensional lattices, whose coordinate number $z$ and kinetic energy $-zJ$ are respectively larger and lower than those of a one dimensional lattice. Herein, we study the Bose-Hubbard model, which has an additional trimer tunneling term, a three-body interaction and a next-nearest repulsion. The on-site trimer and trimer superfluid exist if the on-site two-body repulsion and three-body repulsion are smaller than some thresholds. With atom-tunneling terms, the phase transitions from trimer superfluid phase to both atom superfluid and atom supersolid phases are first order. With $W/J=12$, in a one dimensional lattice, the trimer superfluid phase does not exist at all. In contrast, the trimer superfluid phase, exists in the lower density regions $0 \textless ρ\textless2$ on the square lattice if $J$ is not very large. The trimer superfluid phase emerges in a wider range $0 \textless ρ\textless3$ in the triangular lattice, or in the cubic lattice ($z=6$). When the three-body interaction is turned on, a trimer supersolid phase emerges due to the classical degeneracy between the quasi trimer solid and the trimer solid being broken by the quantum fluctuation. The phase transitions from the trimer supersolid phase to quasi trimer solid are first order and the phase transition from the trimer supersolid phase to trimer solid is continuous. Our results, obtained by mean-field and quantum Monte Carlo methods, will be helpful in realizing the trimer superfluid and supersolid by cold atom experiments.
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Submitted 10 July, 2015; v1 submitted 22 December, 2014;
originally announced December 2014.