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Physical review. B, Condensed matter

Integrable multiparametric impurity model

Igor N. Karnaukhov

Published Nov 15, 1994• 0 citations
Publisher

Abstract

We present a one-dimensional model describing the interaction of spin-1/2 impurities with band electrons of a paramagnetic host metal. The model naturally describes the creation and annihilation of electron pairs localized at impurities, and the interaction between localized and band electrons. Using the Bethe-ansatz solution the thermodynamic properties of the system are calculated.

DOI
10.1103/physrevb.50.15385

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We present a one-dimensional model describing the interaction of spin-1/2 impurities with band electrons of a paramagnetic host metal. The model naturally describes the creation and annihilation of electron pairs localized at impurities, and the interaction between localized and band electrons. Using the Bethe-ansatz solution the thermodynamic properties of the system are calculated.
The one-dimensional t - J model at the supersymmetric point, J = 2t, with a magnetic impurity of arbitrary spin S is studied exactly using the Bethe ansatz technique. The impurity interacts by spin exchange with the electrons on neighbouring sites of a lattice without destroying the integrability. The discrete Bethe ansatz equations diagonalizing the model, and the thermodynamic equations are derived. The impurity free energy is obtained for arbitrary band filling as a function of temperature and external magnetic field. The impurity can localize up to one itinerant hole, and has in general mixed-valent properties.
We consider the one-dimensional t-J model, which consists of spin-1/2 electrons on a lattice with nearest neighbor hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighboring sites. The model is integrable at the supersymmetric point, J=2t. We extend the model by introducing an impurity of arbitrary spin S that interacts with the electrons on the neighboring sites without destroying the integrability. The lattice model is defined by the scattering matrices via the quantum inverse scattering method. The interaction Hamiltonian between the impurity and the itinerant electrons is only explicitly constructed in the continuum limit. The discrete Bethe ansatz equations diagonalizing the model are derived and the solutions are classified according to the string hypothesis. The thermodynamic Bethe ansatz equations are derived and the impurity free energy is obtained for arbitrary bandfilling as a function of temperature and external magnetic field. The properties of the impurity depend on one coupling parameter. The impurity can localize up to one itinerant electron and has in general mixed valent properties. The integer valent low T small H fixed point of the impurity corresponds to an asymptotically free spin S, while if either T or H (or both) become large the impurity behaves like an asymptotically free spin (S+).
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.