Finitely Correlated States on Quantum Spin Chains

Fannes, M., Nachtergaele, B. and Werner, R. F. (1990) Finitely Correlated States on Quantum Spin Chains. (Preprint)

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Abstract

We study a construction, which yields a class of translation invariant states on quantum spin chains, characterised by the property that the correlations across any bond can be modelled on a finite dimensional vector space. These states, which are dense in the set of all translation invariant states, can be considered as generalised valence bond states. We develop a complete theory of the ergodic decomposition of such states, including the decomposition into periodic "Néel ordered" states. Ergodic finitely correlated states have exponential decay of correlations. All states considered can be considered as "functions" of states of a special kind, so-called "purely generated states", which are shown to be ground states for suitably chosen interactions. We show that all these states have a spectral gap. Our theory does not require symmetry of the state with respect to a local gauge group, but the isotropic ground states of some one-dimensional antiferromagnets, recently studied by Affleck, Kennedy, Lieb, and Tasaki fall in this class.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 10 Jul 2018 14:56
Last Modified: 16 Dec 2022 01:08
Identification Number: DIAS-STP-90-11
URI: https://dair.dias.ie/id/eprint/895

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