Asymptotic Bethe Ansatz Research Articles

On the second-neighbour correlator in 1D XXX quantum antiferromagnetic spin chain

We have calculated the energy per site for the ground state of the antiferromagnetic quantum spin chain with variable range exchange in the framework of the asymptotic Bethe ansatz. By expanding it in powers of , we have confirmed the value of the second-neighbour correlator for the model with nearest-neighbour exchange obtained earlier in the atomic limit of the Hubbard chain.

Spectral flow in the supersymmetric t-J model with a 1/r2 interaction.

The spectral flow in the supersymmetric {\it t-J} model with $1/r^2$ interaction is studied by analyzing the exact spectrum with twisted boundary conditions. The spectral flows for the charge and spin sectors are shown to nicely fit in with the motif picture in the asymptotic Bethe ansatz. Although fractional exclusion statistics for the spin sector clearly shows up in the period of the spectral flow at half filling, such a property is generally hidden once any number of holes are doped, because the commensurability condition in the motif is not met in the metallic phase.

Ground state and excitations of the supersymmetric extended Hubbard model with long-range interaction.

We examine the ground state and excitations of the one-dimensional supersymmetric extended Hubbard model with long-range interaction. The ground state wave-function and low lying excitations are given explicitly in the form of a Jastrow product of two-body terms. This result motivates an asymptotic Bethe ansatz solution for the model. We present evidence that this solution is in fact exact and spans the complete spectrum of states. \textcopyright{} 1996 The American Physical Society.

Exact solution and spectral flow for twisted Haldane-Shastry model.

The exact solution of the spin chain model with $1/r^2$ exchange is found for twisted boundary conditions. The spectrum thus obtained can be reproduced by the asymptotic Bethe ansatz. The spectral flow of each eigenstate is determined exactly as a function of the twist angle. We find that the period $4\pi$ for the ground state nicely fits in with the notion of fractional exclusion statistics.

Critical properties of the Calogero - Sutherland model with boundaries

Critical properties of the Calogero-Sutherland model of $BC_N$-type ($BC_N$-CS model) are studied. Using the asymptotic Bethe-ansatz spectrum of the $BC_N$-CS model, we calculate finite-size corrections in the energy spectrum. Since the $BC_N$-CS model does not possess translational invariance, the finite-size spectrum acquires the contributions coming from ``boundaries''. We show that the low-energy critical behavior of the model is described by $c=1$ boundary conformal field theory. Thus the universality class of the model is identified as a chiral Tomonaga-Luttinger liquid.

Confirmation of the Asymptotic Bethe Ansatz

We show that the asymptotic Bethe ansatz gives the exact zero temperature values of all the integrals of motion for the classical one-dimensional system interacting by an inverse-sinh-squared pair potential, in the thermodynamic limit. It is remarkable that the asymptotic Bethe ansatz, using only the scattering data for finite numbers of particles in an unbounded volume, gives exact results for all density.

Asymptotic Bethe-Ansatz results for a Hubbard chain with 1/sinh-hopping

We investigate spin-1/2 electrons with local Hubbard interaction and variable range hopping amplitudes which decay like sinh(κ)/sinh(κr). Using Sutherland's Asymptotic Bethe Ansatz we derive the generalized Lieb-Wu integral equations from the two-particle phase shift. For half-filling we obtain a closed expression for the ground state energy density. Due to the nesting property there is a metal-to-insulator transition at Uc(κ> > 0) = 0+.In the singular limit κ = 0the charge gap opens when the interaction strength equals the bandwidth, U c(κ = 0) =W.

FRACTIONAL STATISTICS IN ONE DIMENSION: MODELING BY MEANS OF 1/x2 INTERACTION AND STATISTICAL MECHANICS

The equivalence of a quantum system of particles interacting with a two-body inverse square potential to a system of noninteracting particles obeying 1D fractional statistics (1D anyons), stated by Polychronakos for particles on a line, is studied for the cases where the interacting system is placed (i) into a harmonic potential on a line, and (ii) on a ring, with imposing periodic boundary conditions. In the first case, reducibility of the interacting system to the Calogero system is used to explore the statistical distribution for free 1D anyons. On a ring, the thermodynamic limit is discussed in terms of the thermodynamic (asymptotic) Bethe ansatz. Yang and Yang’s integral equation is treated in this case as describing the statistical mechanics of free 1D anyons. It gives a functional equation for the statistical distribution of 1D anyons consistent with the harmonic potential approach. We show that on a ring of a finite circumference, a system of two free 1D anyons is equivalent to a system of two particles interacting with an inverse sine square potential (the Sutherland system). We also discuss the relation to the statistical mechanics of free anyons in 2+1 dimensions.

Spectrum ofBN-Type Calogero-Sutherland-Moser Model

We explicitly construct the excited-state and derive the spectrum of the quantum Calogero-Sutherland-Moser model associated with the Weyl group B N . We also discuss the asymptotic Bethe-ansatz method for this model.

Critical Properties of Quantum Many-Body Systems with 1/r2 Interaction

We review recent results obtained for a class of one-dimensional quantum models with $1/r^2$ long-range interaction. Based on the asymptotic Bethe-ansatz solution and conformal field theory, we study critical properties of the continuum boson model, the SU($\nu$) spin chain, the OSp($\nu$,1) supersymmetric {\it t-J} model, and a new hierarchy of models related to the fractional quantum Hall effect. We further investigate the class of $1/r^2$ models with harmonic confinement by means of a newly proposed method of the renormalized-harmonic oscillator solution.

Critical Properties of Quantum Many-Body Systems with 1/r2 Interaction

We review recent results obtained for a class of one-dimensional quantum models with 1/r2 long-range interaction. Based on the asymptotic Bethe-ansatz solution and conformal field theory, we study critical properties of the continuum boson model, the SU(ν) spin chain, the OSp(ν, 1) supersymmetric t-J model and a new hierarchy of models related to the fractional quantum Hall effect. We further investigate the class of 1/r2 models with harmonic confinement by means of a newly proposed method of the renormalized-harmonic oscillator solution.

Ground-state energy corrections for antiferromagnetic s= 1/2 chains with short-range interaction

The leading finite-size effects in the description of the antiferromagnetic ground state of 1D quantum s= 1/2 chains with non-nearest-neighbour short-range exchange are calculated in the framework of the asymptotic Bethe-ansatz method under a few general assumptions on the properties of scattering phases and energies of magnons.

Unusual low-temperature thermopower in the one-dimensional Hubbard model.

The low-temperature thermoelectric power of the repulsive-interaction one-dimensional Hubbard model is calculated using an asymptotic Bethe ansatz for holons and spinons. The competition between the entropy carried by the holons and that carried by the backflow of the spinons gives rise to an unusual temperature and doping dependence of the thermopower which is qualitatively similar to that observed in the normal state of high-$T_{c}$ superconductors.

SU(N) Calogero-Sutherland Model andt-JModelwith 1/x2Interaction

The asymptotic Bethe-ansatz (ABA) solution is obtained for the one-dimensional SU( N ) Calogero-Sutherland model and the SU( N ) t - J model with 1/ x 2 long-range interaction. Bulk quantities and correlation exponents are computed. The results reproduce those obtained by Ha and Haldane using the exact Jastrow-type eigenfunctions. The ABA solution enables a simple and systematic treatment of the energy spectrum of the above models.

Novel hierarchy of the SU(N) electron models and edge states of fractional quantum Hall effect.

A novel hierarchy of the one-dimensional SU(N) electron models with 1/r 2 interaction is proposed and solved by the asymptotic Bethe ansatz both for the continuum and lattice cases. The construction of the hierarchy is closely related to that for the fractional quantum Hall effect (FQHE) of the filling factor ν c =1/[p 1 -1/(p 2 -...-1/p N )...]. Under the chiral constraint the model describes the essential properties of the edge states for the FQHE with the above filling fraction. Furthermore the matrix deduced from the excitation spectrum characterizes the topological order of the FQHE state

Bethe-ansatz solutions of 1D correlated electron systems with long-range exchange

Asymptotic Bethe-ansatz solutions are obtained for the SU( N) spin model and the supersymmetric t- J model with 1 r 2 exchange interaction in one dimension. We classify low-energy excitations and determine the critical exponents of correlation functions using conformal field theory.

Spectrum and thermodynamics of the one-dimensional supersymmetric t-J model with 1/r2 exchange and hopping.

We derive the spectrum and the thermodynamics of the one-dimensional supersymmetric t-J model with long range hopping and spin exchange using a set of maximal-spin eigenstates. This spectrum confirms the recent conjecture that the asymptotic Bethe-ansatz spectrum is exact. By empirical determining the spinon degeneracies of each state, we are able to explicitly construct the free energy.

Asymptotic Bethe-ansatz solution of multicomponent quantum systems with 1/r2 long-range interaction.

Asymptotic Bethe-ansatz solutions are obtained for one-dimensional quantum systems with a 1/r 2 long-range interaction by generalizing Sutherland's method to multicomponent quantum systems. We obtain the solutions to the supersymmetric t-J model of Kuramoto and Yokoyama, the SU(υ) Haldane-Shastry model, and the multicomponent t-J model. The excitation spectrum as well as bulk quantities are computed analytically. Conformal properties of low-energy excitations are discussed in connection with Luttinger liquid theory

Asymptotic Bethe ansatz: Application to the one-dimensional t-J model with long-range exchange and transfer.

An asymptotic Bethe-ansatz solution is obtained for the one-dimensional t-J model with the 1/${\mathit{r}}^{2}$ long-range exchange and transfer, for which the ground-state wave function was obtained exactly by Kuramoto and Yokoyama. The present approach makes it possible to study analytically the energy spectrum as well as bulk quantities. The calculated quantities reproduce the exact results known for low-temperature properties and correlation functions. This solution represents an application for the asymptotic Bethe ansatz to correlated electron systems.