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arXiv:cond-mat/0703339 · Journal of Statistical Mechanics Theory and Experiment

Interplay between a quantum impurity and a boundary field in the SUSYt–Jmodel

Holger Frahm, Guillaume Palacios

Published May 9, 2007• 0 citations
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Abstract

We study the role of bound states appearing in different formulations of the Bethe ansatz for the supersymmetric t – J model with a boundary potential and an integrable impurity. For special values of the parameters describing the boundary and the impurity the charge fluctuations at the latter vanish. The population of the bound states selects different sectors of the impurity levels leading to integrable Kondo impurities.

DOI
10.1088/1742-5468/2007/05/p05006

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We study the role of bound states appearing in different formulations of the Bethe ansatz for the supersymmetric t – J model with a boundary potential and an integrable impurity. For special values of the parameters describing the boundary and the impurity the charge fluctuations at the latter vanish. The population of the bound states selects different sectors of the impurity levels leading to integrable Kondo impurities.
The supersymmetric $t\text{\ensuremath{-}}J$ model with boundary hopping integrals and fields is proposed and solved exactly by means of the Bethe ansatz method. We find that for certain values of the boundary hopping integrals and fields the ground state contains boundary bound states, as new solutions of the Bethe ansatz equations in a charge sector called boundary charge strings. The boundary states define the thermodynamic properties of the boundary, such as the boundary charge, magnetic moment, that have been calculated numerically as a function of the magnetic field and chemical potential. We show that the boundary charge strings lead to a logarithmic divergent behavior of boundary magnetic moment in a weak magnetic field limit.
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 study the effects of magnetic impurities in the strongly correlated electron system from the open t - J model where the two impurities are coupled to the electron system. The kinetic energy of our model is nonlinear in the momentum of the electrons and it is integratable. The interaction parameters can be changed from the ferromagnetic case to the antiferromagnetic case. We obtain the thermodynamic Bethe ansatz equations for the excitation state. The effects of the magnetic impurities on magnetization and charge fluctuation are studied. The finite-size correction of the free energy due to impurities is obtained and some special limits of the system are discussed. We find that the system has boundary bound states introduced by the impurities and formed by four imaginary modes of the rapidities.