Low temperature thermodynamics of finite spin-1/2 XX Chain with some distorted links

doi:10.26565/2222-5617-2019-31-4

O. S. Dzhenzherov V. N. Karazin Kharkiv National University, 4 Svoboda sq., Kharkiv, 61022, Ukraine
E. V. Ezerskaya V. N. Karazin Kharkiv National University, 4 Svoboda sq., Kharkiv, 61022, Ukraine http://orcid.org/0000-0002-6896-9550

DOI: https://doi.org/10.26565/2222-5617-2019-31-4

Keywords: spin, Heisenberg Hamiltonian, spin-1/2 XX-chain, energy spectrum, thermodynamic characteristics, quantum phase transition

Abstract

We present the results of our analytical and numerical study of quantum stationary states and the thermodynamics of exactly solvable finite linear spin-1/2 XX chain with one or two distorted links. The exact dispersion equations for the stationary states with one inverted spin for both cases have been derived. The corresponding spectrum consists of one quasi-continuous band and some localized impurity levels. The analytical inequalities for the values of the critical model parameters describing the appearance of local energy impurity levels above and below quasi-continuous band are obtained and analyzed. The field and the temperature dependences of the main thermodynamic characteristics of these models are studied. It is shown, that the appearance of the localized levels near the distorted links may effect significantly on the thermodynamic properties at low temperatures, leading to the additional singularities in the field and the temperature dependences of the principal thermodynamic characteristics. For example, the field dependence of z-projection of average total spin and the field dependence of the magnetization at zero temperature have the finite jumps associated with the quasi-continuous spectrum, and the impurity levels. The remnants of these jumps at rather low temperature are clearly visible. The average z-projections of the spins of distorted link(s) may decrease with the increasing of the magnetic field for some values of model parameters. The temperature dependence of the specific heat may demonstrate additional maxima at very low temperatures. The complex oscillatory pattern of the time dependence of the dynamical longitudinal pair correlation function and the autocorrelation function is associated with the finiteness of the models and the appearance of associated localized energy levels.

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