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:1010.1301 · Physical Review A

Quantum criticality of a one-dimensional attractive Fermi gas

Xi‐Wen Guan, Tin-Lun Ho

Published Aug 9, 2011• 32 citations
arXivHTMLPDF

Abstract

We obtain an analytical equation of state for one-dimensional strongly attractive Fermi gases for all parameter regimes in current experiments. From the equation of state, we derive universal scaling functions that control whole thermodynamical properties in quantum critical regimes and illustrate the physical origin of quantum criticality. It turns out that the critical properties of the system are described by those of free fermions and those of mixtures of fermions with masses $m$ and $2m$. We also show how these critical properties of bulk systems can be revealed from the density profile of trapped Fermi gases at finite temperatures and can be used to determine the $T=0$ phase boundaries without any arbitrariness.

DOI
10.1103/physreva.84.023616

Related papers

A Unified Approach to the Thermodynamics and Quantum Scaling Functions of One-Dimensional Strongly Attractive SU(w) Fermi Gases*

Yi-Cong Yu, Xi‐Wen Guan

Abstract We present a unified derivation of the pressure equation of states, thermodynamics and scaling functions for the one-dimensional (1D) strongly attractive Fermi gases with SU(w) symmetry. These physical quantities provide a rigorous understanding on a universality class of quantum criticality characterized by the critical exponents z = 2 and correlation length exponent ν = 1/2. Such a universality class of quantum criticality can occur when the Fermi sea of one branch of charge bound states starts to fill or becomes gapped at zero temperature. The quantum critical cone can be determined by the double peaks in specific heat, which serve to mark two crossover temperatures fanning out from the critical point. Our method opens to further study on quantum phases and phase transitions in strongly interacting fermions with large SU(w) and non-SU(w) symmetries in one dimension.

arXiv:1708.07939•Chinese Physics Letters•Jun 1, 2017•1 citation

Quantum criticality of one-dimensional multicomponent Fermi gas with strongly attractive interaction

Peng He, Yuzhu Jiang, Xi‐Wen Guan +1 more

Quantum criticality of strongly attractive Fermi gas with $SU(3)$ symmetry in one dimension is studied via the thermodynamic Bethe ansatz (TBA) equations.The phase transitions driven by the chemical potential $μ$, effective magnetic field $H_1$, $H_2$ (chemical potential biases) are analyzed at the quantum criticality. The phase diagram and critical fields are analytically determined by the thermodynamic Bethe ansatz equations in zero temperature limit. High accurate equations of state, scaling functions are also obtained analytically for the strong interacting gases. The dynamic exponent $z=2$ and correlation length exponent $ν=1/2$ read off the universal scaling form. It turns out that the quantum criticality of the three-component gases involves a sudden change of density of states of one cluster state, two or three cluster states. In general, this method can be adapted to deal with the quantum criticality of multi-component Fermi gases with $SU(N)$ symmetry.

arXiv:1406.5707•Journal of Physics A Mathematical and Theoretical•Dec 2, 2014•3 citations

Quantum criticality and universal scaling of strongly attractive spin-imbalanced Fermi gases in a one-dimensional harmonic trap

Xiangguo Yin, Xi‐Wen Guan, Shu Chen +1 more

We investigate quantum criticality and universal scaling of strongly attractive Fermi gases confined in a one-dimensional harmonic trap. We demonstrate from the power-law scaling of the thermodynamic properties that current experiments on this system are capable of measuring universal features at quantum criticality, such as universal scaling and Tomonaga-Luttinger liquid physics. The results also provide insights on recent measurements of key features of the phase diagram of a spin-imbalanced atomic Fermi gas [Y. Liao et al., Nature (London) 467, 567 (2010)] and point to further study of quantum critical phenomena in ultracold atomic Fermi gases.

arXiv:1101.2494•Physical Review A•Jul 13, 2011•17 citations

Quantum criticality of a one-dimensional Bose-Fermi mixture

Xiangguo Yin, Xi‐Wen Guan, Yunbo Zhang +1 more

The one-dimensional interacting Bose-Fermi mixtures, exhibiting quantum phase transitions at zero temperature, are particularly valuable for the study of quantum critical phenomena. In the present paper, we analytically study the quantum phase diagram, equation of state, and quantum criticality of the Bose-Fermi mixture using the thermodynamic Bethe ansatz equations. We show that thermodynamical properties display universal scaling behavior at quantum criticality. Furthermore, quantum criticality of the Bose-Fermi mixture in a harmonic trap is also studied within the local-density approximation. We thus demonstrate that the phase diagram and critical properties of the bulk system provide insight into understanding the universal features of many-body critical phenomena.

arXiv:1111.3554•Physical Review A•Jan 4, 2012•15 citations

Quantum Criticality in One-dimensional Fermi Gases

Seongjoon Yi

In this thesis, we present a recent study of the one-dimensional attractively interacting two-component Fermi gas with an external magnetic field. We analytically study the quantum phase diagram, equation of state, quantum criticality, and universal scalings of the model, using the thermodynamic Bethe ansatz equations. We present a high precision equation of state from which universal scaling functions are derived; we show that the thermodynamic properties display universal scaling behaviour at quantum criticality. Expression of high-order-accuracy entropy and specific heat are also analytically derived. Moreover, we present an independent confirmation of the equation of state through an efficient numerical approach of treating the thermodynamic Bethe ansatz equations for which the contributions from the spin strings with length larger than a value of $n_c$ are calculated analytically.

•Jan 1, 2013•0 citations

Exactly solvable models and ultracold Fermi gases

M T Batchelor, Angela Foerster, X-W Guan +1 more

Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirms that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.

arXiv:1011.3259•Journal of Statistical Mechanics Theory and Experiment•Dec 6, 2010•17 citations
We obtain an analytical equation of state for one-dimensional strongly attractive Fermi gases for all parameter regimes in current experiments. From the equation of state, we derive universal scaling functions that control whole thermodynamical properties in quantum critical regimes and illustrate the physical origin of quantum criticality. It turns out that the critical properties of the system are described by those of free fermions and those of mixtures of fermions with masses mmm and 2m2m2m. We also show how these critical properties of bulk systems can be revealed from the density profile of trapped Fermi gases at finite temperatures and can be used to determine the T=0T=0T=0 phase boundaries without any arbitrariness.
Abstract We present a unified derivation of the pressure equation of states, thermodynamics and scaling functions for the one-dimensional (1D) strongly attractive Fermi gases with SU(w) symmetry. These physical quantities provide a rigorous understanding on a universality class of quantum criticality characterized by the critical exponents z = 2 and correlation length exponent ν = 1/2. Such a universality class of quantum criticality can occur when the Fermi sea of one branch of charge bound states starts to fill or becomes gapped at zero temperature. The quantum critical cone can be determined by the double peaks in specific heat, which serve to mark two crossover temperatures fanning out from the critical point. Our method opens to further study on quantum phases and phase transitions in strongly interacting fermions with large SU(w) and non-SU(w) symmetries in one dimension.
Quantum criticality of strongly attractive Fermi gas with SU(3)SU(3)SU(3) symmetry in one dimension is studied via the thermodynamic Bethe ansatz (TBA) equations.The phase transitions driven by the chemical potential μμμ, effective magnetic field H1H_1H1​, H2H_2H2​ (chemical potential biases) are analyzed at the quantum criticality. The phase diagram and critical fields are analytically determined by the thermodynamic Bethe ansatz equations in zero temperature limit. High accurate equations of state, scaling functions are also obtained analytically for the strong interacting gases. The dynamic exponent z=2z=2z=2 and correlation length exponent ν=1/2ν=1/2ν=1/2 read off the universal scaling form. It turns out that the quantum criticality of the three-component gases involves a sudden change of density of states of one cluster state, two or three cluster states. In general, this method can be adapted to deal with the quantum criticality of multi-component Fermi gases with SU(N)SU(N)SU(N) symmetry.
We investigate quantum criticality and universal scaling of strongly attractive Fermi gases confined in a one-dimensional harmonic trap. We demonstrate from the power-law scaling of the thermodynamic properties that current experiments on this system are capable of measuring universal features at quantum criticality, such as universal scaling and Tomonaga-Luttinger liquid physics. The results also provide insights on recent measurements of key features of the phase diagram of a spin-imbalanced atomic Fermi gas [Y. Liao et al., Nature (London) 467, 567 (2010)] and point to further study of quantum critical phenomena in ultracold atomic Fermi gases.
The one-dimensional interacting Bose-Fermi mixtures, exhibiting quantum phase transitions at zero temperature, are particularly valuable for the study of quantum critical phenomena. In the present paper, we analytically study the quantum phase diagram, equation of state, and quantum criticality of the Bose-Fermi mixture using the thermodynamic Bethe ansatz equations. We show that thermodynamical properties display universal scaling behavior at quantum criticality. Furthermore, quantum criticality of the Bose-Fermi mixture in a harmonic trap is also studied within the local-density approximation. We thus demonstrate that the phase diagram and critical properties of the bulk system provide insight into understanding the universal features of many-body critical phenomena.
In this thesis, we present a recent study of the one-dimensional attractively interacting two-component Fermi gas with an external magnetic field. We analytically study the quantum phase diagram, equation of state, quantum criticality, and universal scalings of the model, using the thermodynamic Bethe ansatz equations. We present a high precision equation of state from which universal scaling functions are derived; we show that the thermodynamic properties display universal scaling behaviour at quantum criticality. Expression of high-order-accuracy entropy and specific heat are also analytically derived. Moreover, we present an independent confirmation of the equation of state through an efficient numerical approach of treating the thermodynamic Bethe ansatz equations for which the contributions from the spin strings with length larger than a value of ncn_cnc​ are calculated analytically.
Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirms that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.