arXiv subjects

Shi-Jian Gu

Publications and source records attributed to Shi-Jian Gu.

68 records · Page 4Linked to original sources

arXiv2003

Local entanglement and quantum phase transition in the Hubbard model

The local entanglement $E_v$ of the one-dimensional Hubbard model is studied on the basis of its Bethe-ansatz solution. The relationship between the local entanglement and the on-site Coulomb interaction $U$ is obtained. Our results show that $E_v$ is an even analytic function of $U$ at half-filling and it reaches a maximum at the critical point U=0. The variation of the local entanglement with the filling factor shows that the ground state with maximal symmetry possesses maximal entanglement. The magnetic field makes the local entanglement to decrease and approach to zero at saturated magnetization. The on-site Coulomb interaction always suppresses the local entanglement.

quant-ph↗

arXiv2003

Phase diagram and symmetry breaking of SU(4) spin-orbital chain in a generalized external field

The ground state phases of a one-dimensional SU(4) spin-orbital Hamiltonian in a generalized external field are studied on the basis of Bethe-ansatz solution. Introducing three Landé $g$ factors for spin, orbital and their products in the SU(4) Zeeman term, we discuss systematically the various symmetry breaking. The magnetization versus external field are obtained by solving Bethe-ansatz equations numerically. The phase diagrams corresponding to distinct residual symmetries are given by means of both numerical and analytical methods.

cond-mat.str-el↗

arXiv2003

Scaling Study of the Metal-Insulator Transition in one-Dimensional Fermion Systems

We consider the Ising phase of the antiferromagnetic XXZ Heisenberg chain on a finite-size lattice with N sites.We compute the large $N$ behavior of the spin stiffness, obtaining the correlation length ξ. We use our results to discuss the scaling behavior of metal-insulator transitions in 1D systems, taking into account the mapping between the XXZ Heisenberg chain and the spinless fermion model and known results for the Hubbard model. We study the scaling properties of both the Hubbard model and the XXZ Heisenberg chain, by solving numerically the Bethe Ansatz equations. We find that for some range of values of ξ/N the scaling behavior may be observed for the Hubbard model but not for the XXZ Heisenserg chain. We show how ξcan be obtained from the scaling properties of the spin stiffness for small system sizes. This method can be applied to models having not an exact solution, illuminating their transport properties.

cond-mat.str-el↗

arXiv2003

One dimensional SU(3) bosons with $δ$ function interaction

In this paper we solve one dimensional SU(3) bosons with repulsive $δ$-function interaction by means of Bethe ansatz method. The features of ground state and low-lying excited states are studied by both numerical and analytic methods. We show that the ground state is a SU(3) color ferromagnetic state. The configurations of quantum numbers for the ground state are given explicitly. For finite $N$ system the spectra of low-lying excitations and the dispersion relations of four possible elementary particles (holon, antiholon, $σ$-coloron and $ω$-coloron) are obtained by solving Bethe-ansatz equation numerically. The thermodynamic equilibrium of the system at finite temperature is studied by using the strategy of thermodynamic Bethe ansatz, a revised Gaudin-Takahashi equation which is useful for numerical method are given . The thermodynamic quantities, such as specific heat, are obtain for some special cases. We find that the magnetic property of the model in high temperature regime is dominated by Curie's law: $χ\propto 1/T$ and the system has Fermi-liquid like specific heat in the strong coupling limit at low temperature.

cond-mat.str-el↗

arXiv2002

Numerical and Monte Carlo Bethe ansatz method: 1D Heisenberg model

In this paper we present two new numerical methods for studying thermodynamic quantities of integrable models. As an example of the effectiveness of these two approaches, results from numerical solutions of all sets of Bethe ansatz equations, for small Heisenberg chains, and Monte Carlo simulations in quasi-momentum space, for a relatively larger chains, are presented. Our results agree with those obtained by thermodynamics Bethe ansatz (TBA) and Quantum Transfer Matrix (QTM).

cond-mat.str-el↗

arXiv2002

Magnetic properties of an SU(4) spin-orbital chain

In this paper, we study the magnetic properties of the one-dimensional SU(4) spin-orbital model by solving its Bethe ansatz solution numerically. It is found that the magnetic properties of the system for the case of $g_t=1.0$ differs from that for the case of $g_t=0.0$. The magnetization curve and susceptibility are obtained for a system of 200 sites. For $0<g_t<g_s$, the phase diagram depending on the magnetic field and the ratio of Landé factors, $g_t/g_s$, is obtained. Four phases with distinct magnetic properties are found.

cond-mat.str-el↗

arXiv2002

Thermodynamics of SU(2) bosons in one dimension

On the basis of Bethe ansatz solution of two-component bosons with SU(2) symmetry and $δ$-function interaction in one dimension, we study the thermodynamics of the system at finite temperature by using the strategy of thermodynamic Bethe ansatz (TBA). It is shown that the ground state is an isospin "ferromagnetic" state by the method of TBA, and at high temperature the magnetic property is dominated by Curie's law. We obtain the exact result of specific heat and entropy in strong coupling limit which scales like $T$ at low temperature. While in weak coupling limit, it is found there is still no Bose-Einstein Condensation (BEC) in such 1D system.

cond-mat.str-el↗

arXiv2001

Low temperature properties of one-dimensional SU(4) Hubbard-like model at low concentration

On the basis of Bethe ansatz solution of one dimensional SU(4) Hubbard-like model, we study its thermodynamics properties by means of Yang-Yang thermodynamics Bethe ansatz. The Landé $g$ factor is taken into account so as to describe electrons with orbital degeneracy. The free energy at low temperature is given and the specific heat both in strong coupling and weak coupling limits are obtained.

cond-mat.str-el↗

arXiv2001

Trapped interacting two-component bosons

In this paper we solve one dimensional trapped SU(2) bosons with repulsive $δ$-function interaction by means of Bethe-ansatz method. The features of ground state and low-lying excited states are studied by numerical and analytic methods. We show that the ground state is an isospin "ferromagnetic" state which differs from spin-1/2 fermions system. There exist three quasi-particles in the excitation spectra, and both holon-antiholon and holon-isospinon excitations are gapless for large systems. The thermodynamics equilibrium of the system at finite temperature is studied by thermodynamic Bethe ansatz. The thermodynamic quantities, such as specific heat etc. are obtained for the case of strong coupling limit.

cond-mat.str-el↗

arXiv2001

Two component interacting bosons: 1-d exact results

Motivated by the experiment of two-component Bose-Einstein condensates produced in magnetically trapped $^{87}Rb$, we study one dimensional Boson systems with repulsive $δ$-function interaction in the presence of SU(2) intrinsic degree of freedom by means of coordinate Bethe ansatz. The ground state and low-lying excitations are solved by both numerical and analytical methods. It is shown that the ground state is an isospin-ferromagnetic state and the excitations are composed of three elementary particles: holons, antiholons and isospinons. The isospinon is a triplet coupled to the ``ferromagnetic'' background antiparallelly.

cond-mat.str-el↗

arXiv2001

Symmetries in the Hubbard model with n-fold orbital degeneracy

The present paper studies the symmeries of the Hubbard model of electrons with generally $n$-fold orbital degeneracy. It's shown SU_d(2n) and SU_c(2n) symmetries hold respectively for the model with completely repulsive or attractive on-site interaction and that with partly attractive interactions. An extended Lieb-Mattis transformation is given to map these two symmetries into each other. The sub-symmetry SU_d^{(e)}(n)\otimes SU_d^{(o)}(n) is found to be shared by the two models with arbitrary chemical potential μ. By assuming at most two electrons on each site it's found that $SU_d(2n)$ and $SU_c(2n)$ both exist in each kind of the two models and consequently lead to a larger symmetry SU_d(2n)\times SU_c(2n). Another underlying symmetry SU_c^{(e)}(2)_{\cal P}\times ...\times SU_c^{(e)}(2)_{\cal P} \otimes \bigl(SU_c^{(o)}(2)_{\cal P}\times ...\times SU_c^{(o)}(2)_{\cal P}\bigr) is also revealed for the unified $U$ model under the excluding. The symmetry is valid for the partially attractive model with chemical potential $μ=-U.$

cond-mat.str-el↗

arXiv2000

Thermodynamics of trapped interacting bosons in one dimension

On the basis of Bethe ansatz solution of bosons with delta-function interaction in a one-dimensional potential well, the thermodynamics equilibrium of the system in finite temperature is studied by using the strategy of Yang and Yang. The thermodynamics quantities, such as specific heat etc. are obtained for the cases of strong coupling limit and weak coupling limit respectively.

cond-mat↗

arXiv2000

One dimensional model for doubly degenerate electrons

A Hubbard-like model with SU(4) symmetry for electrons with two-fold orbital degeneracy is studied extensively. Exact solution in one dimension is derived by means of Bethe ansatz, where the sites are supposed to be occupied by at most two electrons. The features of ground state and excited states for repulsive coupling are shown. For finite N number of electrons, the configurations of quantum numbers are given explicitly and the spectra of excitations are obtained by solving the Bethe-ansatz equation numerically. For infinite N, the ground state and various kinds of low-lying excitations are obtained on the basis of thermodynamics limit.

cond-mat.str-el↗

arXiv1999

Thermodynamics of Kondo Model with Electronic Interactions

On the basis of Bethe ansatz solution of one dimensional Kondo model with electronic interaction, the thermodynamics equilibrium of the system in finite temperature is studied in terms of the strategy of Yang and Yang. The string hypothesis in the spin rapidity is discussed extensively. The thermodynamics quantities, such as specific heat and magnetic susceptibility, are obtained.

cond-mat.str-el↗