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physica status solidi (b)

Dynamics of Transverse Correlations in Spin-� Isotropic XY Chain with Correlated Lorentzian Disorder

Oleg Derzhko, Taras Krokhmalskii

Published Feb 1, 2000• 3 citations
Publisher

Abstract

Using a numerical approach we examine the dynamics of zz correlations for the spin-½ isotropic XY chain with random Lorentzian intersite coupling and transverse field at sites that depends linearly on the neighbouring couplings. We study in detail the wave vector and frequency-dependent zz structure factor for different values of Hamiltonian parameters and temperature. We discuss the changes in the frequency profiles of zz dynamic structure factor caused by the introduced correlated disorder.

DOI
10.1002/(sici)1521-3951(200002)217:2<927::aid-pssb927>3.0.co;2-5

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Using a numerical approach we examine the dynamics of zz correlations for the spin-½ isotropic XY chain with random Lorentzian intersite coupling and transverse field at sites that depends linearly on the neighbouring couplings. We study in detail the wave vector and frequency-dependent zz structure factor for different values of Hamiltonian parameters and temperature. We discuss the changes in the frequency profiles of zz dynamic structure factor caused by the introduced correlated disorder.
Using a numerical approach we examine the dynamics of zzzzzz correlations for the spin-121\over221​ isotropic XY chain with random Lorentzian intersite coupling and transverse field at sites that depends linearly on the neighbouring couplings. We study in detail the wave vector- and frequency-dependent zzzzzz structure factor at different values of Hamiltonian parameters and temperature. We discuss the changes in the frequency profiles of the zzzzzz dynamic structure factor caused by the introduced correlated disorder.
Dynamic xx and xy spin pair correlation functions for the isotropic spin-½ XY chain are calculated numerically for long open chains in the presence of a transverse ( z ) magnetic field at finite temperature. From these data the first numerical results for the dynamic structure factors S xx (κ,ω) and S xy (κ,ω) are obtained and compared with the known results for S zz (κ,ω). While S zz (κ,ω) is restricted to certain regions in the (κ,ω)-plane S xx (κ,ω) and S xy (κ,ω) are not. Nevertheless, the numerical results show that the latter structure factors are quite small outside the regions defined by S zz (κ,ω) and moreover, that they may in many circumstances, especially at low temperature, be approximately described by a small number of broadened excitation branches.
We have considered a numerical scheme for the calculation of the equilibrium properties of spin-1/2 XY chains. Within its frames it is necessary to solve in the last resort only the 2N\times 2N eigenvalue and eigenvector problem but not the 2^N\times 2^N one as for an arbitrary system consisting of N spins 1/2. To illustrate the approach we have presented some new results. Namely, the xx dynamic structure factor for the Ising model in transverse field, the density of states for the isotropic chain with random intersite couplings and transverse fields that linearly depend on the surrounding couplings, and the zz dynamic structure factor for the Ising model in random transverse field. The results obtained are hopped to be useful for an interpretation of observable data for one-dimensional spin-1/2 XY substances.
The zz and xx ( yy ) dynamic structure factors of the dimerized spin-½ isotropic XY chain in a transverse ( z ) field are calculated for arbitrary temperatures. The zz structure factor can be given in analytical terms, involving a single integration, whereas the xx dynamic structure factor can be evaluated completely numerically for very long chains. We compare the two structure factors and discuss in some detail how a dimerization manifests itself in the dynamic structure factors at different external fields and temperatures. We compare our results to corresponding results for the dimerized Heisenberg chain obtained by approximate techniques.
We have considered a numerical scheme for the calculation of the equilibrium properties of spin{ 1 2 XY chains.Within its frames it is necessary to solve in the last resort only the 2N 2N eigenvalue and eigenvector problem but not the 2 N 2 N one as for an arbitrary system consisting of N spins 1 2 .To illustrate the approach we have presented some new results.Namely, the xx dynamic structure factor for the Ising model in transverse eld, the density of states for the isotropic chain with random intersite couplings and transverse elds that linearly depend on the surrounding couplings, and the zz dynamic structure factor for the Ising model in the random transverse eld.The results obtained are hoped to be useful for an interpretation of observable data for one{dimensional spin{ 1 2 XY substances.