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Physical review. B, Condensed matter

Integrable model of a one-dimensional anisotropic Kondo-like lattice

Igor N. Karnaukhov

Published Feb 15, 1998• 4 citations
Publisher

Abstract

A one-dimensional model of the modified Kondo lattice for $\ensuremath{\nu}$ degenerate conduction electrons interacting with the spin-$\frac{1}{2}$ $\mathrm{XXZ}$ Heisenberg chain is investigated. The model reduces to the $\mathrm{SU}(\ensuremath{\nu}+1)$-invariant anisotropic $t\ensuremath{-}J$ model with field splitting. The ground-state energy, the chemical potential, and the Fermi velocity of electrons have been calculated numerically for an arbitrary density of electrons. The model under consideration is characterized as a (marginal) Tomonago-Luttinger liquid described by $c=1$. We discuss the relevance of the results obtained to various theoretical treatments of the Kondo lattice model.

DOI
10.1103/physrevb.57.3863

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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.