Xi-Wen Guan

Fermi gases in one dimension: From Bethe ansatz to experiments

This article reviews theoretical and experimental developments for one-dimensional Fermi gases. Specifically, the experimentally realized two-component delta-function interacting Fermi gas-the Gaudin-Yang model-and its generalizations to multicomponent Fermi systems with larger spin symmetries is discussed. The exact results obtained for Bethe ansatz integrable models of this kind enable the study of the nature and microscopic origin of a wide range of quantum many-body phenomena driven by spin population imbalance, dynamical interactions, and magnetic fields. This physics includes Bardeen-Cooper-Schrieffer-like pairing, Tomonaga-Luttinger liquids, spin-charge separation, Fulde-Ferrel-Larkin-Ovchinnikov-like pair correlations, quantum criticality and scaling, polarons, and the few-body physics of the trimer state (trions). The fascinating interplay between exactly solved models and experimental developments in one dimension promises to yield further insight into the exciting and fundamental physics of interacting Fermi systems.

One-Dimensional Interacting Anyon Gas: Low-Energy Properties and Haldane Exclusion Statistics

The low-energy properties of the one-dimensional anyon gas with a delta-function interaction are discussed in the context of its Bethe ansatz solution. It is found that the anyonic statistical parameter and the dynamical coupling constant induce Haldane exclusion statistics interpolating between bosons and fermions. Moreover, the anyonic parameter may trigger statistics beyond Fermi statistics for which the exclusion parameter alpha is greater than one. The Tonks-Girardeau and the weak coupling limits are discussed in detail. The results support the universal role of alpha in the dispersion relations.

Algebraic Bethe ansatz for the one-dimensional Hubbard model with open boundaries

The one-dimensional Hubbard model with open boundary conditions is exactly solved by means of the algebraic Bethe ansatz. The eigenvalue of the transfer matrix and the energy spectrum, as well as the Bethe ansatz equations, are obtained.

Phase transitions and pairing signature in strongly attractive Fermi atomic gases

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 HHc1. A completely ferromagnetic phase without pairing occurs when the external field HHc2. In the region Hc1HHc2 ,w e 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.

Integrable Models and Quantum Spin Ladders: Comparison Between Theory and Experiment for the Strong Coupling Ladder Compounds

This article considers recent advances in the investigation of the thermal and magnetic properties of integrable spin ladder models and their applicability to the physics of strong coupling ladder compounds. For this class of compounds the rung coupling J ⊥ is much stronger than the coupling J ∥ along the ladder legs. The ground state properties of the integrable two-leg spin- and the mixed spin-( ) ladder models at zero temperature are analysed by means of the Thermodynamic Bethe Ansatz (TBA). Solving the TBA equations yields exact results for the critical fields and critical behaviour. The thermal and magnetic properties of the models are discussed in terms of the recently introduced High Temperature Expansion (HTE) method, which is reviewed in detail. In the strong coupling region the integrable spin- ladder model exhibits three quantum phases: (i) a gapped phase in the regime , (ii) a fully polarized phase for , and (iii) a Luttinger liquid magnetic phase in the regime H c1<H<H c2. The critical behaviour in the vicinity of the critical points H c1 and H c2 is of Pokrovsky-Talapov type. The temperature-dependent thermal and magnetic properties are directly evaluated from the exact free energy expression and compared to known experimental results for the strong coupling ladder compounds (5IAP)2CuBr4· 2H2O, Cu2(C5H12N2)2Cl4, (C5H12N)2CuBr4, BIP-BNO and [Cu2(C2\O 2)(C10H8N2)2)](NO3)2. Similar analysis of the mixed spin-( ) ladder model reveals a rich phase diagram, with a and a full saturation magnetization plateau within the strong antiferromagnetic rung coupling regime. For weak rung coupling, the fractional magnetization plateau is diminished and a new quantum phase transition occurs. The phase diagram can be directly deduced from the magnetization curve obtained from the exact result derived from the TBA and HTE. The results are applied to the mixed ferrimagnetic ladder compound PNNBNO. The thermodynamics of the spin-orbital model with different single-ion anisotropies is also discussed. For this model single-ion anisotropy can trigger different quantum phase transitions within the spin and orbital degrees of freedom, with magnetization plateaux arising from different spin and orbit Landé g-factors.

Ferromagnetic behavior in the strongly interacting two-component Bose gas

We investigate the low-temperature behavior of the integrable one-dimensional two-component spinor Bose gas using the thermodynamic Bethe ansatz. We find that for strong coupling the characteristics of the thermodynamics at low temperatures are quantitatively affected by the spin ferromagnetic states, which are described by an effective ferromagnetic Heisenberg chain. The free energy, specific heat, susceptibility, and local pair correlation function are calculated for various physical regimes in terms of temperature and interaction strength. These thermodynamic properties reveal spin effects which are significantly different than those of the spinless Bose gas. The zero-field susceptibility for finite strong repulsion exceeds that of a free spin paramagnet. The critical exponents of the specific heat c{sub v}{approx}T{sup 1/2} and the susceptibility {chi}{approx}T{sup -2} are indicative of the ferromagnetic signature of the two-component spinor Bose gas. Our analytic results are consistent with general arguments by Eisenberg and Lieb for polarized spinor bosons.

LAX PAIR AND BOUNDARY K-MATRICES FOR THE ONE-DIMENSIONAL HUBBARD MODEL

Abstract The Lax pair for the one-dimensional (1D) Hubbard open chain is explicitly constructed. Our construction provides an alternative and direct demonstration for the quantum integrability of the model. As a further result, we obtain its two kinds of boundary K-matrices compatible with the integrability of the model. It seems to contribute to the different boundary terms in the Hamiltonian of the model.

The Bethe ansatz for 1D interacting anyons

This paper gives a pedagogic derivation of the Bethe ansatz solution for 1D interacting anyons. This includes a demonstration of the subtle role of the anyonic phases in the Bethe ansatz arising from the anyonic commutation relations. The thermodynamic Bethe ansatz equations defining the temperature dependent properties of the model are also derived, from which some ground state properties are obtained.

Exact Results for a Tunnel-Coupled Pair of Trapped Bose-Einstein Condensates

A model describing coherent quantum tunnelling between two trapped Bose-Einstein condensates is discussed. It is not well known that the model admits an exact solution, obtained some time ago, with the energy spectrum derived through the algebraic Bethe ansatz. An asymptotic analysis of the Bethe ansatz equations leads us to explicit expressions for the energies of the ground and the first excited states in the limit of weak tunnelling and all energies for strong tunnelling. The results are used to extract the asymptotic limits of the quantum fluctuations of the boson number difference between the two Bose-Einstein condensates and to characterize the degree of coherence in the system.

Bethe ansatz study of one-dimensional Bose and Fermi gases with periodic and hard wall boundary conditions

We extend the exact periodic Bethe ansatz solution for one-dimensional bosons and fermions with δ-interaction and arbitrary internal degrees of freedom to the case of hard wall boundary conditions. We give an analysis of the ground-state properties of fermionic systems with two internal degrees of freedom, including expansions of the ground-state energy in the weak and strong coupling limits.