Valence Bond States on Quantum Spin Chains as Ground States with Spectral Gap

Fannes, M., Nachtergaele, B. and Werner, R. F. (1990) Valence Bond States on Quantum Spin Chains as Ground States with Spectral Gap. (Preprint)

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Abstract

We show that every translation invariant valence bond state on a one-dimensional quantum spin chain arises as the unique ground state of a certain family of finite range interactions. For each interaction in this family we show the existence of a non-zero spectral gap above the ground state energy. A special example of this structure is a state recently studied by Affleck, Lieb, Kennedy, and Tasaki. For the Hamiltonian studied by these authors we can estimate the gap, and prove that it lies between 1/3 and 10/27.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 19 Jun 2018 14:15
Last Modified: 15 Dec 2022 02:22
URI: https://dair.dias.ie/id/eprint/764

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