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Physical Review B

Exactly solvable supersymmetric t−J model with boundary hoppings and fields

Igor N. Karnaukhov

Published Sep 6, 2006• 0 citations
Publisher

Abstract

The supersymmetric $t\text{\ensuremath{-}}J$ model with boundary hopping integrals and fields is proposed and solved exactly by means of the Bethe ansatz method. We find that for certain values of the boundary hopping integrals and fields the ground state contains boundary bound states, as new solutions of the Bethe ansatz equations in a charge sector called boundary charge strings. The boundary states define the thermodynamic properties of the boundary, such as the boundary charge, magnetic moment, that have been calculated numerically as a function of the magnetic field and chemical potential. We show that the boundary charge strings lead to a logarithmic divergent behavior of boundary magnetic moment in a weak magnetic field limit.

DOI
10.1103/physrevb.74.115105

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The supersymmetric t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model with boundary hopping integrals and fields is proposed and solved exactly by means of the Bethe ansatz method. We find that for certain values of the boundary hopping integrals and fields the ground state contains boundary bound states, as new solutions of the Bethe ansatz equations in a charge sector called boundary charge strings. The boundary states define the thermodynamic properties of the boundary, such as the boundary charge, magnetic moment, that have been calculated numerically as a function of the magnetic field and chemical potential. We show that the boundary charge strings lead to a logarithmic divergent behavior of boundary magnetic moment in a weak magnetic field limit.
The Hubbard model with boundary hopping integrals and fields is proposed and solved exactly by means of the Bethe ansatz method. We find that for certain values of the boundary hopping integrals and fields the ground state contains boundary bound states, these new types of states are represented as "boundary charge and spin strings". We show that the boundary bound states are realized at a strong boundary interaction for large values of the boundary hopping integrals or the boundary fields. The magnetic moment and charge of the boundary have been calculated numerically as a function of the magnetic field and band filling. It is found that the "boundary charge strings" solutions define the properties of the boundary.
The one-dimensional SU(N)-invariant t-J model consists of electrons with N spin components on a lattice with nearest-neighbour hopping and spin exchange J. The multiple occupancy of the lattice sites is excluded. The model is integrable at the supersymmetric point, t=J. The discrete Bethe ansatz equations are analysed and the solutions are classified according to the string hypothesis. The thermodynamic Bethe ansatz equations are derived for arbitrary band filling in terms of thermodynamic energy potentials for the classes of eigenstates of the Hamiltonian. These equations are solved in limiting cases, e.g., S=1/2, the ground state and the high-temperature limit. If the charge fluctuations are suppressed the Bethe ansatz equations map onto those of the SU(N)-invariant Heisenberg chain.
Starting with the known exact solution of the one-dimensional supersymmetric t-J model, the authors investigate ground-state properties of the system in the presence of an external magnetic field. By analytical calculations they find a representation of the magnetization curves and the susceptibility using the dressed charge matrix and the charge and spin densities: the dressed properties are given by a set of coupled integral equations which are derived from the Bethe ansatz equations in the thermodynamic limit. Some special results are found analytically, namely the magnetic field at which saturation occurs and the corresponding susceptibility. Furthermore they show the vanishing of the lower critical field. The dependence of magnetization and susceptibility on the magnetic field is calculated numerically for various particle densities.
In this paper, we study the surface energy of the one-dimensional supersymmetric t-J model with unparallel boundary magnetic fields, which is a typical U(1)-symmetry broken quantum integrable strongly correlated electron system. It is shown that at the ground state, the contribution of inhomogeneous term in the Bethe ansatz solution of eigenvalues of transfer matrix satisfies the finite size scaling law L^β where β<0. Based on it, the physical quantities of the system in the thermodynamic limit are calculated. We obtain the patterns of Bethe roots and the analytical expressions of density of states, ground state energy and surface energy. We also find that there exist the stable boundary bound states if the boundary fields satisfy some constraints.
An open supersymmetric t - J chain with boundary fields is studied by means of the Bethe ansatz. Ground state properties for the case of an almost half-filled band and a bulk magnetic field are determined. Boundary susceptibilities are calculated as functions of the boundary fields. The effects of the boundary on excitations are investigated by constructing the exact boundary S-matrix. From the analytic structure of the boundary S-matrices one deduces that holons can form boundary bound states for sufficiently strong boundary fields.