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arXiv · 1709.02756

Knabe's spectral gap method for open boundary conditions

Marius Lemm
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Abstract

In 1988, Knabe found a "finite-size criterion" to determine whether a frustration-free quantum spin chain with periodic boundary conditions is uniformly gapped in the thermodynamic limit. The criterion provides a threshold for the spectral gap at a finite system size such that, if the threshold is exceeded for a fixed system size, then the chain with periodic boundary conditions is uniformly gapped. We extend Knabe's result to frustration-free spin chains equipped with open boundary conditions. We now obtain two finite-size criteria: The first one is identical to Knabe's criterion and we interpret it as a bulk criterion. The second one controls the spectral gaps at smaller system sizes and can be interpreted as a new edge criterion. Heuristically, it excludes the presence of thermodynamically gapless excitations living near the edge.

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Marius Lemm. 2017-09-08. Knabe's spectral gap method for open boundary conditions. https://arxiv.org/abs/1709.02756

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