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Ferroelectrics

Density of states in 1D S=1/2 anisotropic XY model with random parameters

Oleg Derzhko, Taras Krokhmaiskii

Published Mar 1, 1994• 6 citations
Publisher

Abstract

The determination of the spectrum of the Hamiltonian for 1D s= 1/2 anisotropic nonuniform XY model in transverse field reduces to the determination of the eigenvalues of dynamical matrix for 1D nonuniform chain within harmonic approximation taking into account the interactions between nearest and next nearest neighbours. Therefore Dean's method may be used for finding the density of states. The obtained in such a manner result for isotropic XY model in lorentzian random transverse field, for which an exact result is known, is discussed.

DOI
10.1080/00150199408016542

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The determination of the spectrum of the Hamiltonian for 1D s= 1/2 anisotropic nonuniform XY model in transverse field reduces to the determination of the eigenvalues of dynamical matrix for 1D nonuniform chain within harmonic approximation taking into account the interactions between nearest and next nearest neighbours. Therefore Dean's method may be used for finding the density of states. The obtained in such a manner result for isotropic XY model in lorentzian random transverse field, for which an exact result is known, is discussed.
The anisotropic XY-model in a transverse field (s=1/2) on the one-dimensional alternating superlattice (closed chain) is considered. The solution of the model is obtained by introducing a generalized Jordan-Wigner transformation which maps the system onto a non-interacting fermion gas. The exact excitation spectrum is determined by reducing the problem to a diagonalization of a block matrix, and it is shown that it is numerically identical to the one obtained by using the approximate transfer matrix method . The induced magnetization and the susceptibility χzzχ^{zz}χzz are determined as a function of the transverse field, and it is shown that, at T=0, the susceptibility presents multiple singularities. It is also shown, as expected, that this critical behaviour driven by transverse field belongs to the same universality class of the model on the alternating chain.
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.