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International Journal of Modern Physics B

Finite Temperature Correlations of the Ising Chain in a Transverse Field

Subir Sachdev A

Published Jan 20, 1997• 6 citations
Publisher

Abstract

Recent work on the finite temperature correlators of the Ising chain in a transverse field is reviewed. The crossover phase diagram in the coupling-constant and temperature plane is discussed, and various exact results and conjectures for static and dynamic correlators are presented.
DOI
10.1142/s0217979297000083

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The interplay of spin and charge fluctuations in the random transverse-field Ising spin chain on the fermionic space is investigated. The finite chemical potential, which controls the charge fluctuations, leads to the appearance of the quantum critical region in the phase diagram where the magnetic correlations are quenched by nonmagnetic sites. Regions of nonmonotonous temperature dependence of spin-spin correlation length appear at nonzero $\ensuremath{\mu}.$ The results on the one-fermion density of states of the model are discussed.
We explore short-distance static correlation functions in the infinite XXZ chain using previously derived formulae which represent the correlation functions in factorized form. We compute two-point functions ranging over 2, 3 and 4 lattice sites as functions of the temperature and the magnetic field in the massive regime ∆> 1, extending our previous results to the full parameter plane of the antiferromagnetic chain ( ∆> −1 and arbitrary field h). The factorized formulae are numerically efficient and allow for taking the isotropic limit ( ∆ = 1) and the Ising limit ( ∆ = ∞). At the critical field separating the fully polarized phase from the Néel phase, the Ising chain possesses exponentially many ground states. The residual entropy is lifted by quantum fluctuations for large but finite ∆ inducing unexpected crossover phenomena in the correlations. 1