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arXiv:cond-mat/9806129 · Journal of Physics A Mathematical and General

Integrability of atJmodel with impurities

Jon Links, Angela Foerster

Published Jan 1, 1999• 41 citations
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Abstract

A t-J model for correlated electrons with impurities is proposed. The impurities are introduced in such a way that integrability of the model in one dimension is not violated. The algebraic Bethe ansatz solution of the model is also given and it is shown that the Bethe states are highest weight states with respect to the supersymmetry algebra .

DOI
10.1088/0305-4470/32/1/016

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Physical review. B, Condensed matter•Feb 15, 1997•56 citations
A t-J model for correlated electrons with impurities is proposed. The impurities are introduced in such a way that integrability of the model in one dimension is not violated. The algebraic Bethe ansatz solution of the model is also given and it is shown that the Bethe states are highest weight states with respect to the supersymmetry algebra .
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.
Integrable Kondo impurities in the one-dimensional supersymmetric U model of strongly correlated electrons are studied by means of the boundary graded quantum inverse scattering method. The boundary K -matrices depending on the local magnetic moments of the impurities are presented as non-trivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, the model Hamiltonian is diagonalized and the Bethe ansatz equations are derived. It is interesting to note that our model exhibits a free parameter in the bulk Hamiltonian but no free parameter exists on the boundaries. This is in sharp contrast to the impurity models arising from the supersymmetric t-J and extended Hubbard models where there is no free parameter in the bulk but there is a free parameter on each boundary.
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+).