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Physical review. B, Condensed matter

Integrable two-parameter t−J model in one dimension

Igor N. Karnaukhov

Published Aug 1, 2000• 1 citation
Publisher

Abstract

A multicomponent anisotropic $t\ensuremath{-}J$ model with a hard-core potential is formulated and solved by the Bethe ansatz method in one dimension for an arbitrary core radius $(\ensuremath{\Delta}+1)/2.$ The ground-state Bethe equations are analyzed and solved numerically for an arbitrary band filling, several values of color components, and the coupling constants. The ground-state energy, the Fermi velocity, and the critical exponents of the correlation functions have been calculated numerically for an arbitrary density of electrons. We discuss the effect of the hard-core potential. The Fermi velocity has a maximum as a function of band filling, vanishing for the empty and full bands. In comparison to the traditional anisotropic $t\ensuremath{-}J$ model in which $\ensuremath{\Delta}=0,$ the Fermi velocity is strongly enhanced in general. In the high-density limit, there is no dynamics of charges, the model exhibits a metal-insulator phase transition, and reduces to an antiferromagnetic spin chain with a new spacing parameter $\ensuremath{\Delta}+1.$

DOI
10.1103/physrevb.62.3033

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A family of spinless fermion models with a hard core potential is formulated and solved by the Bethe ansatz method in one dimension for an arbitrary core radius. The Hamiltonian has two levels of strong interaction: the repulsive hard core potential and the kinetic energy with hopping integrals, values of which depend on the configuration of the particles. The Fermi velocity and the critical exponents describing the asymptotic behavior of the correlation functions at long distances have been calculated numerically for an arbitrary density of electrons and hard core radius. We discuss the effect of the hard core potential. The hard core potential defines an anomalous behavior of the critical exponent \ensuremath{\Theta} of the momentum distribution function. In the high-electron-density region the long-distance behavior is described by a strongly interacting Luttinger-liquid state with \ensuremath{\Theta}>1 and the residual Fermi surface disappears.
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The author considers a gas of fermions with parabolic dispersion and N spin-components (or spin S, N=2S+1) with SU(N) symmetry in one dimension interacting via a delta -function potential. The model is integrable and its solution has been obtained by Sutherland in terms of N nested Bethe ansatze. He analyses the discrete Bethe ansatz equations and classifies their solutions according to the string hypothesis. The thermodynamic Bethe-ansatz equations are derived for arbitrary band-filling for both repulsive and attractive interaction in terms of the thermodynamic energy potentials for the classes of eigenstates of the Hamiltonian. These equations are then discussed in several limiting cases, e.g. S=1/2, the ground state (T to 0), for vanishing interaction strength, for strong coupling, in the high-temperature limit, and the large-N limit.