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Journal of Physics A Mathematical and General

Effects of magnetic impurities in thet-Jmodel

Zhan-Ning Hu, Fu‐Cho Pu

Published Jan 1, 1999• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0305-4470/32/29/304

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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 effect of a magnetic (S=1/2) impurity coupled to a two-dimensional system of correlated electrons (described by the t-J model) is studied by exact diagonalizations. It is found that, if the exchange coupling of the impurity with the neighboring spins is ferromagnetic or weakly antiferromagnetic, an extra hole can form bound states of different spatial symmetries with the impurity extending to a few lattice spacings. The binding energy is maximum when the impurity is completely decoupled (vacancy) and vanishes for an antiferromagnetic coupling exceeding \ensuremath{\sim}0.3J. Several peaks appear in the single-hole spectral function below the lower edge of the quasiparticle band as signatures of the d-, s-, and p-wave bound states.
We consider the one-dimensional gas of electrons interacting via an attractive δ-function potential. The attractive potential leads to the formation of Cooper-pair-like bound states with a spin gap. Without destroying the integrability, we introduce a finite concentration of mixed-valence impurities with two magnetic configurations of spin S and S + {{1}/{2}}, which hybridize with the conduction states of the host. We derive the Bethe ansatz equations diagonalizing the system for the correlated host with impurities and discuss the ground-state properties as functions of the concentration of impurities and the Kondo coupling. For a sufficiently large density of electrons the spin gap is reduced by the impurities and is closed at a critical concentration which depends on the impurity spin and the coupling strength. A ferromagnetic phase of unpaired spin-polarized itinerant electrons is induced for impurity concentrations larger than the critical one. The critical behaviour of the correlation functions is studied in the gapped and gapless regions using the mesoscopic energy spectrum and conformal field theory.
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.
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+).