Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1012.1828 · Physical Review A

Compressibility and entropy of cold fermions in one-dimensional optical lattices

Andrew Snyder, Iori Tanabe, Theja N. De Silva

Published Jun 28, 2011• 9 citations
arXivHTMLPDF

Abstract

We calculate several thermodynamic quantities for repulsively interacting one-dimensional fermions. We solve the Hubbard model at both zero and finite temperatures using the Bethe-ansatz method. For arbitrary values of the chemical potential, we calculate the particle number density, the double occupancy, various compressibilities, and the entropy as a function of temperature and interaction. We find that these thermodynamic quantities show a characteristic behavior so that measurements of these quantities can be used as a detection of temperature, the metal-insulator transition, and metallic and insulating phases in the trap environment. Further, we discuss an experimental scheme to extract these thermodynamic quantities from the column density profiles. The entropy and the compressibility of the entire trapped atomic cloud also reveal characteristic features indicating whether insulating and/or metallic phases coexist in the trap.

DOI
10.1103/physreva.83.063632

Related papers

Trapped Ultracold Fermions in Double-Well Optical Lattices

Atsushi Yamamoto, Makoto Yamashita, Norio Kawakami

We study the ground state properties of ultracold fermions trapped in a one-dimensional double-well optical lattice by using the density-matrix renormalization group method. The system is described by an extended Hubbard model with alternating hopping integrals and an external harmonic confining potential. We clarify the characteristic features of the metal–insulator phase transition originating from the double-well structure of the lattices. Several different types of insulating regions coexist when the number of atoms at each site is an integer or a half integer. We found that each insulating phase except for a band insulator exhibits rather large local density fluctuations, reflecting the strong dimerization of atoms within the unit cells of double-well lattices. The phase characteristics are elucidated in detail by investigating the profiles of the local density of atoms, the local density (spin) fluctuations, the double-occupancy probability and the spatially extended sp in correlations.

Journal of the Physical Society of Japan•Dec 10, 2009•1 citation

Thermodynamic properties of two-component fermionic atoms trapped in a two-dimensional optical lattice

Kensuke Inaba, Makoto Yamashita

We study the finite-temperature properties of two-component fermionic atoms trapped in a two-dimensional (2D) optical lattice. We apply the self-energy functional approach to the 2D Hubbard model with a harmonic-trapping potential, and systematically investigate the thermodynamic properties of this system. We find that entropy and grand potential provide evidence of a crossover between the Mott-insulating and the metallic phases at certain temperatures. In addition, we find that entropy exhibits a cusplike anomaly at lower temperatures, suggesting a second- or higher-order antiferromagnetic transition. We estimate the antiferromagnetic transition temperatures, and clarify how the trapping potential affects this magnetic transition.

arXiv:1005.3576•Physical Review A•Jun 9, 2010•1 citation

Polarization-induced phase separation and re-entrant transition of two-component fermions in a one-dimensional lattice

Theja N. De Silva

By investigating the compressibility of one-dimensional lattice fermions at various filling factors, we study the phase separation and re-entrant transition within the framework of the Bethe ansatz method. We model the system using the repulsive Hubbard model and calculate compressibility as a function of polarization for arbitrary values of chemical potential, temperature, and interaction strength. For filling factors $0<n<1$, compressibility is a nonmonotonic function of polarization at all thermodynamic parameters. The compressibility reveals a phase transition into a phase-separated state for both low and intermediate temperatures at intermediate interactions as one increases the polarization. For certain filling factors, we find the re-entrant transition into the mixed phase at a higher polarization.

arXiv:1505.07026•Physical Review A•May 27, 2015•1 citation

Signature of Mott-Insulator Transition with Ultracold Fermions in a One-Dimensional Optical Lattice

Xia-Ji Liu, P. D. Drummond, Hui Hu

Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultracold fermions confined in an optical lattice with a harmonic trapping potential. We determine a generic phase diagram in terms of a characteristic filling factor and a dimensionless coupling constant. The collective oscillations of the atomic mass density, a technique that is commonly used in experiments, provide a signature of the quantum phase transition from the metallic phase to the Mott-insulator phase. A detailed experimental implementation is proposed.

arXiv:cond-mat/0410433•Physical Review Letters•Apr 8, 2005•54 citations

Chemical potential-functional-theory about the properties of one-dimensional Hubbard model at finite temperature

Zhanpeng Lu, Xingbo Wei, Liu Tian-Shuai +2 more

In this paper, we numerically solve the thermodynamic Bethe-ansatz coupled equations for a one-dimensional Hubbard model at finite temperature and obtain the second order thermodynamics properties, such as the specific heat, compressibility, and susceptibility. We find that these three quantities could embody the phase transitions of the system, from the vacuum state to the metallic state, from the metallic state to the Mott-insulating phase, from the Mott-insulating phase to the metallic state, and from the metallic state to the band-insulating phase. With the increase of temperature, the thermal fluctuation overwhelms the quantum fluctuations and the phase transition points disappear due to the destruction of the Mott-insulating phase. But in the case of the strong interaction strength, the Mott-insulating phase is robust, embodying the compressibility. Furthermore, we study the thermodynamic properties of the inhomogeneous Hubbard model with trapping potential. Making use of the Bethe-ansatz results from the homogeneous Hubbard model, we construct the chemical potential-functional theory (-BALDA) for the inhomogeneous Hubbard model instead of the commonly used density-functional theory, in order to solve the in-convergence problem of the Kohn-Sham equation in the case of the divergence appearing in the exchange-correlation potential. We further point out a multi-dimensional bisection method which changes the Kohn-Shan equation into a problem of finding the fixed points. Through -BALDA we numerically solve the one-dimensional homogeneous Hubbard model of trapping potential. The density profile and the local compressibility are obtained. We find that at a given interaction strength, the metallic phase and the Mott-insulating phase are destroyed and the density profile becomes a Guassian distribution with increasing temperature. To the metallic phase, Friedel oscillation caused by quantum fluctuations is still visible at low temperature. With increasing temperature, Friedel oscillation will disappear. This situation reflects the fact that the thermal fluctuation overwhelms the quantum fluctuations. For the Mott-insulating phase, the Mott-insulating plateau is robust at a certain temperature and only the boundary of the Mott-insulating plateau is destroyed. With increasing temperature, the Mott insulating plateau will be destroyed. And the change of the local compressibility provides the information about such a change. So we conclude that the thermal fluctuation destroys the original quantum phase. Through our analysis, we find that the -BALDA can be used to study the finite temperature properties for the system of the exchange-correlation potential divergence with high efficiency.

Acta Physica Sinica•Jan 1, 2017•0 citations

Quantum Monte Carlo study of confined fermions in one-dimensional optical lattices

Marcos Rigol, Alejandro Muramatsu

Using quantum Monte Carlo (QMC) simulations we study the ground-state properties of the one-dimensional fermionic Hubbard model in traps with an underlying lattice. Since due to the confining potential the density is space dependent, Mott-insulating domains always coexist with metallic regions, such that global quantities are not appropriate to describe the system. We define a local compressibility that characterizes the Mott-insulating regions and analyze other local quantities. It is shown that the momentum distribution function, a quantity that is commonly considered in experiments, fails in giving a clear signal of the Mott-insulating transition. Furthermore, we analyze a mean-field approach to these systems and compare it with the numerically exact QMC results. Finally, we determine a generic form for the phase diagram that allows us to predict the phases to be observed in the experiments.

arXiv:cond-mat/0309670•Physical Review A•May 14, 2004•85 citations
We calculate several thermodynamic quantities for repulsively interacting one-dimensional fermions. We solve the Hubbard model at both zero and finite temperatures using the Bethe-ansatz method. For arbitrary values of the chemical potential, we calculate the particle number density, the double occupancy, various compressibilities, and the entropy as a function of temperature and interaction. We find that these thermodynamic quantities show a characteristic behavior so that measurements of these quantities can be used as a detection of temperature, the metal-insulator transition, and metallic and insulating phases in the trap environment. Further, we discuss an experimental scheme to extract these thermodynamic quantities from the column density profiles. The entropy and the compressibility of the entire trapped atomic cloud also reveal characteristic features indicating whether insulating and/or metallic phases coexist in the trap.
We study the ground state properties of ultracold fermions trapped in a one-dimensional double-well optical lattice by using the density-matrix renormalization group method. The system is described by an extended Hubbard model with alternating hopping integrals and an external harmonic confining potential. We clarify the characteristic features of the metal–insulator phase transition originating from the double-well structure of the lattices. Several different types of insulating regions coexist when the number of atoms at each site is an integer or a half integer. We found that each insulating phase except for a band insulator exhibits rather large local density fluctuations, reflecting the strong dimerization of atoms within the unit cells of double-well lattices. The phase characteristics are elucidated in detail by investigating the profiles of the local density of atoms, the local density (spin) fluctuations, the double-occupancy probability and the spatially extended sp in correlations.
We study the finite-temperature properties of two-component fermionic atoms trapped in a two-dimensional (2D) optical lattice. We apply the self-energy functional approach to the 2D Hubbard model with a harmonic-trapping potential, and systematically investigate the thermodynamic properties of this system. We find that entropy and grand potential provide evidence of a crossover between the Mott-insulating and the metallic phases at certain temperatures. In addition, we find that entropy exhibits a cusplike anomaly at lower temperatures, suggesting a second- or higher-order antiferromagnetic transition. We estimate the antiferromagnetic transition temperatures, and clarify how the trapping potential affects this magnetic transition.
By investigating the compressibility of one-dimensional lattice fermions at various filling factors, we study the phase separation and re-entrant transition within the framework of the Bethe ansatz method. We model the system using the repulsive Hubbard model and calculate compressibility as a function of polarization for arbitrary values of chemical potential, temperature, and interaction strength. For filling factors 0<n<10<n<10<n<1, compressibility is a nonmonotonic function of polarization at all thermodynamic parameters. The compressibility reveals a phase transition into a phase-separated state for both low and intermediate temperatures at intermediate interactions as one increases the polarization. For certain filling factors, we find the re-entrant transition into the mixed phase at a higher polarization.
Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultracold fermions confined in an optical lattice with a harmonic trapping potential. We determine a generic phase diagram in terms of a characteristic filling factor and a dimensionless coupling constant. The collective oscillations of the atomic mass density, a technique that is commonly used in experiments, provide a signature of the quantum phase transition from the metallic phase to the Mott-insulator phase. A detailed experimental implementation is proposed.
In this paper, we numerically solve the thermodynamic Bethe-ansatz coupled equations for a one-dimensional Hubbard model at finite temperature and obtain the second order thermodynamics properties, such as the specific heat, compressibility, and susceptibility. We find that these three quantities could embody the phase transitions of the system, from the vacuum state to the metallic state, from the metallic state to the Mott-insulating phase, from the Mott-insulating phase to the metallic state, and from the metallic state to the band-insulating phase. With the increase of temperature, the thermal fluctuation overwhelms the quantum fluctuations and the phase transition points disappear due to the destruction of the Mott-insulating phase. But in the case of the strong interaction strength, the Mott-insulating phase is robust, embodying the compressibility. Furthermore, we study the thermodynamic properties of the inhomogeneous Hubbard model with trapping potential. Making use of the Bethe-ansatz results from the homogeneous Hubbard model, we construct the chemical potential-functional theory (-BALDA) for the inhomogeneous Hubbard model instead of the commonly used density-functional theory, in order to solve the in-convergence problem of the Kohn-Sham equation in the case of the divergence appearing in the exchange-correlation potential. We further point out a multi-dimensional bisection method which changes the Kohn-Shan equation into a problem of finding the fixed points. Through -BALDA we numerically solve the one-dimensional homogeneous Hubbard model of trapping potential. The density profile and the local compressibility are obtained. We find that at a given interaction strength, the metallic phase and the Mott-insulating phase are destroyed and the density profile becomes a Guassian distribution with increasing temperature. To the metallic phase, Friedel oscillation caused by quantum fluctuations is still visible at low temperature. With increasing temperature, Friedel oscillation will disappear. This situation reflects the fact that the thermal fluctuation overwhelms the quantum fluctuations. For the Mott-insulating phase, the Mott-insulating plateau is robust at a certain temperature and only the boundary of the Mott-insulating plateau is destroyed. With increasing temperature, the Mott insulating plateau will be destroyed. And the change of the local compressibility provides the information about such a change. So we conclude that the thermal fluctuation destroys the original quantum phase. Through our analysis, we find that the -BALDA can be used to study the finite temperature properties for the system of the exchange-correlation potential divergence with high efficiency.
Using quantum Monte Carlo (QMC) simulations we study the ground-state properties of the one-dimensional fermionic Hubbard model in traps with an underlying lattice. Since due to the confining potential the density is space dependent, Mott-insulating domains always coexist with metallic regions, such that global quantities are not appropriate to describe the system. We define a local compressibility that characterizes the Mott-insulating regions and analyze other local quantities. It is shown that the momentum distribution function, a quantity that is commonly considered in experiments, fails in giving a clear signal of the Mott-insulating transition. Furthermore, we analyze a mean-field approach to these systems and compare it with the numerically exact QMC results. Finally, we determine a generic form for the phase diagram that allows us to predict the phases to be observed in the experiments.