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:0709.1763 · Physical Review Letters

Magnetic Phase Transitions in One-Dimensional Strongly Attractive Three-Component Ultracold Fermions

Xin Guan, Murray T. Batchelor, Chaohong Lee, Huan-Qiang Zhou

Published May 19, 2008• 45 citations
arXivHTMLPDF

Abstract

We investigate the nature of trions, pairing, and quantum phase transitions in one-dimensional strongly attractive three-component ultracold fermions in external fields. Exact results for the ground-state energy, critical fields, magnetization and phase diagrams are obtained analytically from the Bethe ansatz solutions. Driven by Zeeman splitting, the system shows exotic phases of trions, bound pairs, a normal Fermi liquid, and four mixtures of these states. Particularly, a smooth phase transition from a trionic phase into a pairing phase occurs as the highest hyperfine level separates from the two lower energy levels. In contrast, there is a smooth phase transition from the trionic phase into a normal Fermi liquid as the lowest level separates from the two higher levels.

DOI
10.1103/physrevlett.100.200401

Related papers

Phase diagrams of three-component attractive ultracold fermions in one dimension

Kuhn, Carlos Claiton Noschang, Angela Foerster

We investigate trions, paired states and quantum phase transitions in one-dimensional SU(3) attractive fermions in external fields by means of the Bethe ansatz formalism. Analytical results for the ground state energy, critical fields and complete phase diagrams are obtained for the weak coupling regime. Higher-order corrections for these physical quantities are presented in the strong attractive regime. Numerical solutions of the dressed energy equations allow us to examine how the different phase boundaries are modified by varying the intercomponent coupling throughout the whole attractive regime. The pure trionic phase existing in the strong coupling regime decreases smoothly with a decrease in this coupling, until the weak limit is reached. In this weak regime, a pure Bardeen–Cooper–Schrieffer (BCS)-like paired phase can be sustained under certain nonlinear Zeeman splittings.

•Jan 1, 2012•10 citations

Phase diagrams of three-component attractive ultracold fermions in one dimension

C C N Kuhn, Angela Foerster

We investigate trions, paired states and quantum phase transitions in one-dimensional SU(3) attractive fermions in external fields by means of the Bethe ansatz formalism. Analytical results for the ground state energy, critical fields and complete phase diagrams are obtained for the weak coupling regime. Higher-order corrections for these physical quantities are presented in the strong attractive regime. Numerical solutions of the dressed energy equations allow us to examine how the different phase boundaries are modified by varying the inter-component coupling throughout the whole attractive regime. The pure trionic phase existing in the strong coupling regime decreases smoothly with a decrease in this coupling, until the weak limit is reached. In this weak regime, a pure Bardeen–Cooper–Schrieffer (BCS)-like paired phase can be sustained under certain nonlinear Zeeman splittings.

arXiv:1003.5314•New Journal of Physics•Jan 6, 2012•12 citations

Analytical thermodynamics of a strongly attractive three-component Fermi gas in one dimension

Peng He, Xiangguo Yin, Xi‐Wen Guan +2 more

Ultracold three-component atomic Fermi gases in one dimension are expected to exhibit rich physics due to the presence of trions and different pairing states. Quantum phase transitions from the trion state into a paired phase and a normal Fermi liquid occur at zero temperature. We derive the analytical thermodynamics of strongly attractive three-component one-dimensional fermions with SU(3) symmetry via the thermodynamic Bethe ansatz method in unequal Zeeman splitting fields ${H}_{1}$ and ${H}_{2}$. We find explicitly that for low temperature the system acts like either a two-component or a three-component Tomonaga-Luttinger liquid dependent on the system parameters. The phase diagrams for the chemical potential and specific heat are presented for illustrative values of the Zeeman splitting. We also demonstrate that crossover between different Tomonaga-Luttinger-liquid phases exhibit singular behavior in specific heat and entropy as the temperature tends to zero. Beyond Tomonaga-Luttinger-liquid physics, we obtain the equation of state which provides a precise description of universal thermodynamics and quantum criticality in three-component, strongly attractive Fermi gases.

arXiv:1009.2283•Physical Review A•Nov 29, 2010•16 citations

Unified description of pairing, trionic and quarteting states for one-dimensional SU(4) attractive fermions

X. W. Guan, Murray T. Batchelor, Chaohong Lee +1 more

Paired states, trions and quarteting states in one-dimensional SU (4) attractive fermions are investigated via exact Bethe ansatz calculations. In particular, quantum phase transitions are identified and calculated from the quarteting phase into normal Fermi liquid, trionic states and spin-2 paired states which belong to the universality class of linear field-dependent magnetization in the vicinity of critical points. Moreover, unified exact results for the ground-state energy, chemical potentials and complete phase diagrams for isospin S =1/2, 1, 3/2 attractive fermions with external fields are presented. Also identified are the magnetization plateaux of m z = M s /3 and m z =2 M s /3, where M s is the magnetization saturation value. The universality of finite-size corrections and collective dispersion relations provides a further test ground for low-energy effective field theory.

arXiv:0904.2269•Europhysics Letters (EPL)•Jun 1, 2009•21 citations

Phase transitions and pairing signature in strongly attractive Fermi atomic gases

Xin Guan, Murray T. Batchelor, Chaohong Lee +1 more

We investigate pairing and quantum phase transitions in the one-dimensional two-component Fermi atomic gas in an external field. The phase diagram, critical fields, magnetization, and local pairing correlation are obtained analytically via the exact thermodynamic Bethe ansatz solution. At zero temperature, bound pairs of fermions with opposite spin states form a singlet ground state when the external field $H<{H}_{c1}$. A completely ferromagnetic phase without pairing occurs when the external field $H>{H}_{c2}$. In the region ${H}_{c1}<H<{H}_{c2}$, we observe a mixed phase of matter in which paired and unpaired atoms coexist. The phase diagram is reminiscent of that of type II superconductors. For temperatures below the degenerate temperature and in the absence of an external field, the bound pairs of fermions form hard-core bosons obeying generalized exclusion statistics.

arXiv:cond-mat/0702191•Physical Review B•Aug 16, 2007•120 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 investigate the nature of trions, pairing, and quantum phase transitions in one-dimensional strongly attractive three-component ultracold fermions in external fields. Exact results for the ground-state energy, critical fields, magnetization and phase diagrams are obtained analytically from the Bethe ansatz solutions. Driven by Zeeman splitting, the system shows exotic phases of trions, bound pairs, a normal Fermi liquid, and four mixtures of these states. Particularly, a smooth phase transition from a trionic phase into a pairing phase occurs as the highest hyperfine level separates from the two lower energy levels. In contrast, there is a smooth phase transition from the trionic phase into a normal Fermi liquid as the lowest level separates from the two higher levels.
We investigate trions, paired states and quantum phase transitions in one-dimensional SU(3) attractive fermions in external fields by means of the Bethe ansatz formalism. Analytical results for the ground state energy, critical fields and complete phase diagrams are obtained for the weak coupling regime. Higher-order corrections for these physical quantities are presented in the strong attractive regime. Numerical solutions of the dressed energy equations allow us to examine how the different phase boundaries are modified by varying the intercomponent coupling throughout the whole attractive regime. The pure trionic phase existing in the strong coupling regime decreases smoothly with a decrease in this coupling, until the weak limit is reached. In this weak regime, a pure Bardeen–Cooper–Schrieffer (BCS)-like paired phase can be sustained under certain nonlinear Zeeman splittings.
We investigate trions, paired states and quantum phase transitions in one-dimensional SU(3) attractive fermions in external fields by means of the Bethe ansatz formalism. Analytical results for the ground state energy, critical fields and complete phase diagrams are obtained for the weak coupling regime. Higher-order corrections for these physical quantities are presented in the strong attractive regime. Numerical solutions of the dressed energy equations allow us to examine how the different phase boundaries are modified by varying the inter-component coupling throughout the whole attractive regime. The pure trionic phase existing in the strong coupling regime decreases smoothly with a decrease in this coupling, until the weak limit is reached. In this weak regime, a pure Bardeen–Cooper–Schrieffer (BCS)-like paired phase can be sustained under certain nonlinear Zeeman splittings.
Ultracold three-component atomic Fermi gases in one dimension are expected to exhibit rich physics due to the presence of trions and different pairing states. Quantum phase transitions from the trion state into a paired phase and a normal Fermi liquid occur at zero temperature. We derive the analytical thermodynamics of strongly attractive three-component one-dimensional fermions with SU(3) symmetry via the thermodynamic Bethe ansatz method in unequal Zeeman splitting fields H1{H}_{1}H1​ and H2{H}_{2}H2​. We find explicitly that for low temperature the system acts like either a two-component or a three-component Tomonaga-Luttinger liquid dependent on the system parameters. The phase diagrams for the chemical potential and specific heat are presented for illustrative values of the Zeeman splitting. We also demonstrate that crossover between different Tomonaga-Luttinger-liquid phases exhibit singular behavior in specific heat and entropy as the temperature tends to zero. Beyond Tomonaga-Luttinger-liquid physics, we obtain the equation of state which provides a precise description of universal thermodynamics and quantum criticality in three-component, strongly attractive Fermi gases.
Paired states, trions and quarteting states in one-dimensional SU (4) attractive fermions are investigated via exact Bethe ansatz calculations. In particular, quantum phase transitions are identified and calculated from the quarteting phase into normal Fermi liquid, trionic states and spin-2 paired states which belong to the universality class of linear field-dependent magnetization in the vicinity of critical points. Moreover, unified exact results for the ground-state energy, chemical potentials and complete phase diagrams for isospin S =1/2, 1, 3/2 attractive fermions with external fields are presented. Also identified are the magnetization plateaux of m z = M s /3 and m z =2 M s /3, where M s is the magnetization saturation value. The universality of finite-size corrections and collective dispersion relations provides a further test ground for low-energy effective field theory.
We investigate pairing and quantum phase transitions in the one-dimensional two-component Fermi atomic gas in an external field. The phase diagram, critical fields, magnetization, and local pairing correlation are obtained analytically via the exact thermodynamic Bethe ansatz solution. At zero temperature, bound pairs of fermions with opposite spin states form a singlet ground state when the external field H<Hc1H<{H}_{c1}H<Hc1​. A completely ferromagnetic phase without pairing occurs when the external field H>Hc2H>{H}_{c2}H>Hc2​. In the region Hc1<H<Hc2{H}_{c1}<H<{H}_{c2}Hc1​<H<Hc2​, we observe a mixed phase of matter in which paired and unpaired atoms coexist. The phase diagram is reminiscent of that of type II superconductors. For temperatures below the degenerate temperature and in the absence of an external field, the bound pairs of fermions form hard-core bosons obeying generalized exclusion statistics.
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.