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Physical review. B, Condensed matter

Integrable narrow-band model with possible relevance to heavy-fermion systems

P. Schlottmann

Published Oct 1, 1987• 308 citations
Publisher

Abstract

A lattice model consisting of a single narrow band is introduced to describe some aspects of heavy electrons. The model excludes double occupancy of the sites and electrons on nearest-neighbor sites interact via a charge interaction and spin exchange. The model is integrable in one dimension for some special values of the coupling constants. These cases are related to the SU(3) invariance. The Bethe-ansatz equations are obtained and ground-state and thermodynamic properties are discussed and solved in some limiting cases.

DOI
10.1103/physrevb.36.5177

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A lattice model consisting of a single narrow band is introduced to describe some aspects of heavy electrons. The model excludes double occupancy of the sites and electrons on nearest-neighbor sites interact via a charge interaction and spin exchange. The model is integrable in one dimension for some special values of the coupling constants. These cases are related to the SU(3) invariance. The Bethe-ansatz equations are obtained and ground-state and thermodynamic properties are discussed and solved in some limiting cases.
A lattice model consisting of a single narrow band is introduced to describe some aspects of heavy electrons. The model excludes double occupancy of the sites and electrons on nearest-neighbor sites interact via a charge interaction and spin exchange. The model is integrable in one dimension for some special values of the coupling constants. These cases are related to the SU(3) invariance. The Bethe-ansatz equations are obtained and ground-state and thermodynamic properties are discussed and solved in some limiting cases.
A one-dimensional-lattice model consisting of a single narrow band and excluded double occupancy of the sites is considered. The electrons on nearest-neighbor sites interact via a charge interaction and spin exchange. In a previous paper we discussed the exact solution of the model for special values of the coupling constants [related to SU(3) invariance]. Here we construct an asymptotically exact solution in the low-electron-density limit for coupling parameters deviating from SU(3) symmetry. The results are compared to those obtained via multiplicative renormalization for the model in the continuum limit and used to discuss the phase diagram.
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 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.
We consider a one-dimensional supersymmetric t−J model and introduce a finite concentration of impurities of arbitrary spin S without destroying the integrability. Using the Bethe ansatz equations diagonalizing the correlated host with impurities, we discuss the ground state properties as a function of magnetic field H and the Kondo exchange coupling. While an isolated impurity of spin S>1/2 has a magnetic ground state of effective spin (S−12), a finite concentration introduces a heavy impurity band and yields a singlet ground state with antiferromagnetically correlated impurities. A field H first polarizes the narrow impurity band. The impurities have mixed valent properties induced in part by correlations in the host. Some aspects of the model are related to heavy fermion alloys.