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Low Temperature Physics

Spin-orbit interaction in the supersymmetric antiferromagnetict-Jchain with a magnetic impurity

Andrei A. Zvyagin

Published Jan 1, 2014• 1 citation
Publisher

Abstract

The effect of spin-orbit interaction in the strongly correlated exactly solvable electron model with magnetic impurity is studied. The considered magnetic impurity reveals the property of a “mobile” one. It is shown that the asymptotics of correlation functions, calculated in the framework of the conformal field theory and finite size corrections of the Bethe ansatz exact solution, are strongly affected by both, the spin-orbit coupling, and by the magnetic impurity.

DOI
10.1063/1.4850535

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The effect of spin-orbit interaction in the strongly correlated exactly solvable electron model with magnetic impurity is studied. The considered magnetic impurity reveals the property of a “mobile” one. It is shown that the asymptotics of correlation functions, calculated in the framework of the conformal field theory and finite size corrections of the Bethe ansatz exact solution, are strongly affected by both, the spin-orbit coupling, and by the magnetic impurity.
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Motivated by recent experiments on ultracold fermions we study the effect of the spin-orbit interaction in an exactly solvable one-dimensional model with strong local attractive correlations between the fermions. We show that the asymptotes of correlation functions, calculated in the framework of the conformal field theory and finite size corrections of the Bethe ansatz exact solution, are strongly affected by the spin-orbit coupling. In the mixed phase, the correlation functions consist of terms that are the product of a power law of the distance and an oscillating function of the distance. We obtain the critical exponents for superfluidity and density waves. The leading exponents decrease as a function of spin-orbit coupling. In particular, the exponent for superfluidity is the smallest one signaling an instability to a phase where a weak interchain coupling can produce superfluidity of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type. The spatial oscillation of the order parameter is also modified by the spin-orbit parameter, i.e., its modulation is not just given by the spin imbalance.
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+).
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 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.