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Low Temperature Physics

Low-temperature properties of two XY spin chains with a point contact

E. V. Ezerskaya

Published May 1, 1998• 1 citation
Publisher

Abstract

The energy spectrum of a one-dimensional, exactly solvable spin model formed by two semi-infinite XY spin chains with spin s=1/2 with a point-contact interaction in a longitudinal magnetic field is calculated. It is shown that the spectrum of such a system can contain one or two local energy levels apart from two bands overlapping in weak fields. Local thermodynamic parameters of the chains can have singularities at zero temperature.

DOI
10.1063/1.593600

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The energy spectrum of a one-dimensional, exactly solvable spin model formed by two semi-infinite XY spin chains with spin s=1/2 with a point-contact interaction in a longitudinal magnetic field is calculated. It is shown that the spectrum of such a system can contain one or two local energy levels apart from two bands overlapping in weak fields. Local thermodynamic parameters of the chains can have singularities at zero temperature.
The exact energy spectrum in a longitudinal magnetic field is found for an infinite XY chain (s=1∕2) with an impurity fragment. It is shown that, in addition to a continuum band and a discrete set of levels, the existence of from one to four bound states, localized at the boundaries of the impurity fragment with the main chain, is possible. The critical behavior of the local static thermodynamic characteristics and time dependence of the longitudinal dynamic correlation functions for different temperatures are studied. It is shown that local thermodynamic characteristics of the model can be influenced significantly by both the discrete levels and the bound states.
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.
We study the energy spectrum of a dual spin chain with an XY interaction among nearest neighbors. This model is applicable in particular to the description of the magnetic properties of the compound Cu(NO3)2 · 2.5H2O. We obtain exact expressions for the energy and wave functions of the one- and two- magnon states. Analysis of the stationary states with a large number of excitations is carried out in terms of perturbation theory under the condition that the exchange interaction J1 between the members of a spin pair significantly exceeds the interaction between pairs, J2. For small ratios J2/J1 the curves of the thermodynamic functions obtained as functions of magnetic field indicate the presence of two critical fields at low temperatures (T≪J2), in agreement with the experimental data.
This is a theoretical study of quantum stationary states and thermodynamics of two exactly solvable quantum models: a finite XX-chain with an “offshoot” that is connected via ZZ-interaction (Ising) to one of the chain nodes, and two different finite XX-chains joined through an additional ZZ-spin. It is shown that the spectrum can have impurity levels localized near the impurity spin, and the conditions for their manifestation are determined. The field and temperature dependences of the main thermodynamic characteristics of the models are investigated.
We consider an exactly solvable two-chain quantum spin- model in a generalized form with enhanced spin frustration. This model is exactly diagonalized via Bethe's ansatz. The low-temperature specific heat of the system is obtained with and without a magnetic field, using the thermodynamic Bethe ansatz equations. We also calculate the magnetic susceptibility in a sufficiently weak field, yielding typical logarithmic corrections. The spin frustration affects only the amplitudes in the magnetic susceptibility and the specific heat. This extends the previous results for a simple two-chain quantum spin model to the generalized one.