Critical Behaviour of One-particle Spectral Weights in the Transverse Ising Model

TL;DR

This paper studies the critical behavior of quasiparticle spectral weights in the transverse Ising model across different lattice structures, providing new series expansion results and confirming theoretical predictions.

Contribution

It introduces series expansions for spectral weights in the transverse Ising model on various lattices and verifies critical exponents against theoretical predictions.

Findings

Exact result for the chain model's spectral weight.

Estimated critical exponents for square and cubic lattices.

Agreement with Sachdev's theoretical predictions.

Abstract

We investigate the critical behaviour of the spectral weight of a single quasiparticle, one of the key observables in experiment, for the particular case of the transverse Ising model.Series expansions are calculated for the linear chain and the square and simple cubic lattices. For the chain model, a conjectured exact result is discovered. For the square and simple cubic lattices, series analyses are used to estimate the critical exponents. The results agree with the general predictions of Sachdev.