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arXiv:1009.2283 · Physical Review A

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

Peng He, Xiangguo Yin, Xi‐Wen Guan, Murray T. Batchelor, Yupeng Wang

Published Nov 29, 2010• 16 citations
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Abstract

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.

DOI
10.1103/physreva.82.053633

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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.
A simple set of algebraic equations is derived for the exact low-temperature thermodynamics of one-dimensional multicomponent strongly attractive fermionic atoms with enlarged SU(N)(N)(N) spin symmetry and Zeeman splitting. Universal multicomponent Tomonaga-Luttinger liquid (TLL) phases are thus determined. For linear Zeeman splitting, the physics of the gapless phase at low temperatures belongs to the universality class of a two-component asymmetric TLL corresponding to spin-neutral NNN-atom composites and spin-$(N\ensuremath{-}1)/2$ single atoms. The equation of state which we obtained provides a precise description of multicomponent composite fermions and opens up the study of quantum criticality in one-dimensional systems of NNN-component Fermi gases with population imbalance.
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 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 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.
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.
Abstract It has been shown (Yang and You 2011 Chin. Phys. Lett. 28 020503 ) that at zero temperature the ground state of the one-dimensional (1D) w -component Fermi gas coincides with that of the spinless Bose gas in the limit . This behavior was experimentally evidenced through quasi-1D tightly trapping ultracold 173 Yb atoms in a recent paper (Pagano et al 2014 Nat. Phys. 10 198 ). However, understanding of low-temperature behavior of Fermi gases with a repulsive interaction requires spin-charge separated conformal field theories of an effective Tomonaga–Luttinger liquid and an antiferromagnetic SU ( w ) Heisenberg spin chain. Here we analytically derive universal thermodynamics of 1D strongly repulsive fermionic gases with SU ( w ) symmetry via the Yang–Yang thermodynamic Bethe ansatz method. The analytical free energy and magnetic properties of the systems at low temperature in a weak magnetic field are obtained through the Wiener–Hopf method. In particular, the free energy essentially manifests the spin-charge separated conformal field theories for high-symmetry systems with arbitrary repulsive interaction strength. We also find that the sound velocity of the Fermi gases in the large w limit coincides with that for the spinless Bose gas, whereas the spin velocity vanishes quickly as w becomes large. This indicates strong suppression of the Fermi exclusion statistics by the commutativity feature among the w -component fermions with different spin states in the Tomonaga–Luttinger liquid phase. Moreover, the equations of state and critical behavior of physical quantities at finite temperature are analytically derived in terms of the polylogarithm functions in the quantum critical region.