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arXiv:cond-mat/9804032 · Journal of Physics A Mathematical and General

Integrabilities of thet-Jmodel with impurities

Zhan-Ning Hu, Fu-Cho Pu, Yupeng Wang

Published Jun 12, 1998• 36 citations
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Abstract

The Hamiltonian with magnetic impurities coupled to the strongly correlated electron system is constructed from the t - J model. It is diagonalized exactly by using the Bethe ansatz method. Our boundary matrices depend on the spins of the electrons. The Kondo problem in this system is discussed in detail. The integral equations are derived with complex rapidities which describe the bound states in the system. The finite-size corrections for the ground-state energies are obtained.

DOI
10.1088/0305-4470/31/23/007

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The Hamiltonian with magnetic impurities coupled to the strongly correlated electron system is constructed from the t - J model. It is diagonalized exactly by using the Bethe ansatz method. Our boundary matrices depend on the spins of the electrons. The Kondo problem in this system is discussed in detail. The integral equations are derived with complex rapidities which describe the bound states in the system. The finite-size corrections for the ground-state energies are obtained.
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.
The Kondo problem of two impurities in a 1D strongly correlated electron system within the framework of the open boundary Hubbard chain is solved and the impurities, coupled to the ends of the electron system, are introduced by their scattering matrices with electrons so that the boundary matrices satisfy the reflecting integrability condition. The finite-size correction of the ground-state energy is obtained due to the impurities. Exact expressions for the low-temperature specific heat contributed by the charge and spin parts of the magnetic impurities are derived. The Pauli susceptibility and the Kondo temperature are given explicitly. The Kondo temperature is inversely proportional to the density of electrons.
In this paper, the Kondo magnetic effect is studied for the XXZ\mathrm{XXZ}XXZ spin chain where the impurities are coupled to the edges of the system. The Hamiltonian of our model can be constructed from the transfer matrix. It is exactly solvable and the exchange constants between the bulk and the boundary impurities are arbitrary. The finite-size corrections to the ground-state energy are obtained for the magnetic impurities and the boundary condition. The specific heat and the susceptibility contributed by the impurities are derived and the Kondo temperature is given explicitly by the use of the Luttinger-Fermi liquid picture and the Bethe ansatz method.
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 propose an integrable Kondo problem in a one-dimensional $t\ensuremath{-}J$ model. With the open boundary condition of the wave functions at the impurity sites, the model can be exactly solved via Bethe ansatz for a set of JL,R{J}_{L,R}JL,R​ (Kondo coupling constants) and VL,R{V}_{L,R}VL,R​ (impurity potentials) parametrized by a single parameter ccc. The integrable value of JL,R{J}_{L,R}JL,R​ runs from negative infinity to positive infinity, which allows us to study both the ferromagnetic Kondo problem and the antiferromagnetic Kondo problem in a strongly correlated electron system. Generally, there is a residual entropy for the ground state, which indicates a typical non-Fermi liquid behavior.
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+).