Dynamic properties of spin-1/2 XY chains

TL;DR

This paper introduces a numerical method for efficiently calculating equilibrium properties of spin-1/2 XY chains, enabling analysis of dynamic structure factors and density of states with reduced computational complexity.

Contribution

A new numerical scheme that simplifies the calculation of equilibrium properties of spin-1/2 XY chains by reducing eigenvalue problem size, with applications to various models.

Findings

Calculated xx dynamic structure factor for the Ising model in transverse field.

Determined density of states for the isotropic chain with random couplings.

Computed zz dynamic structure factor for the Ising model in random transverse field.

Abstract

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.