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Journal of Physics A Mathematical and General

Magnetic properties of the one-dimensional supersymmetric t-J model

M Quaisser, Andreas Schadschneider, J. Zittartz

Published Sep 21, 1992• 6 citations
Publisher

Abstract

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.

DOI
10.1088/0305-4470/25/18/006

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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.
The exact phase diagram and the ground-state properties of the one-dimensional Hubbard model with arbitrary on-site interaction of electrons are calculated over a wide range of magnetic field and electron concentrations by means of the Bethe-ansatz formalism. The ground-state properties, including the total energy, the average spin (magnetization) and spin (magnetic) susceptibility are investigated for both signs of the interaction strength U/t. The critical behavior near the onset of magnetization and magnetic saturation are also analyzed. At the onset of magnetization and near the magnetic saturation the spin susceptibility χ diverges at all U/t for half-filling case n=1, whereas for n≠1 it is always finite. The reverse susceptibility χ-1(U) exhibits anomalous hump, which increases with h or n, and shows discontinuity as U/t→±0 at infinitesimal h→0. The analytical results for the ground-state properties in strong and weak interaction limits are in full agreement with our numerical calculations.
The authors considers the one-dimensional SU(N)-invariant t-J model which consists of electrons with N spin components on a lattice with nearest-neighbour hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighbouring lattice sites. The model is integrable at the supersymmetric point t=J. The ground state Bethe ansatz equations are analysed and solved numerically for arbitrary band filling and several values of N. The ground state energy, the chemical potential and the spin susceptibility are obtained as a function of band filling. The elemental charge and spin excitations are derived for arbitrary N and band filling. The energy of the charge excitations vanishes at the Fermi surface. The Fermi velocity has a maximum as a function of band filling, vanishing for the empty and full bands. The spinwave velocity is inversely proportional to the susceptibility. For exactly one electron per site the charge fluctuations are suppressed and the Bethe ansatz equations map onto those of the SU(N)-invariant Heisenberg chain.
The exact phase diagrams of the one-dimensional Hubbard model, both attractive and repulsive, in the presence of an arbitrary magnetic field h for various electron concentrations n and on-site interaction strengths U <0 or U >0 are calculated and investigated. The exact ground-state properties, namely, the ground-state energy, the average spin (magnetization), the concentration of the doubly occupied sites, the kinetic energy, the chemical potential, the spin (magnetic) susceptibility and the charge compressibility, are calculated and examined over a wide range of interaction strengths U for various h and n . It is found that the spin susceptibility at half-filling is non-analytic and changes discontinuously as U →0. The exact theory shows the absence of a charge energy gap in the U ⩽0 region for all n and provides, for the chemical potential, the rigorous upper and lower bounds for half-filled and empty bands respectively. The analytical results derived for the weak-coupling limit and asymptotic expansions for strong coupling are in full agreement with the numerical calculations.
We obtain an integrable two-leg supersymmetric t - J model through the algebraic Bethe ansatz scheme in the BFF grading. In this model, the two t - J chains interact with each other via a coupling constant κ. The model reduces to a two-chain Heisenberg spin model when the bosonic degrees of freedom are turned off and to two decoupled t - J chains when κ = 0. The construction of the diagonalized Hamiltonian yields the Bethe ansatz equations. We also obtain thermodynamic Bethe ansatz equations and calculate the magnetic susceptibility at a weak magnetic field and at zero temperature.
Using results on the scaling of energies with the size of the system and the principles of conformal quantum field theory, we calculate the asymptotics of correlation functions for the one-dimensional Hubbard model in the repulsive regime in the presence of an external magnetic field. The critical exponents are given in terms of a dressed charge matrix that is defined in terms of a set of integral equations obtained from the Bethe-Ansatz solution for the Hubbard model. An interpretation of this matrix in terms of thermodynamical coefficients is given, and several limiting cases are considered.
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.