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arXiv · 1902.09678

Gapped PVBS models for all species numbers and dimensions

Marius Lemm·Bruno Nachtergaele
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Abstract

Product vacua with boundary states (PVBS) are cousins of the Heisenberg XXZ spin model and feature $n$ particle species on $\mathbb Z^d$. The PVBS models were originally introduced as toy models for the classification of ground state phases. A crucial ingredient for this classification is the existence of a spectral gap above the ground state sector. In this work, we derive a spectral gap for PVBS models at arbitrary species number $n$ and in arbitrary dimension $d$ in the perturbative regime of small anisotropy parameters. Instead of using the more common martingale method, the proof verifies a finite-size criterion in the spirit of Knabe.

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Marius Lemm, Bruno Nachtergaele. 2019-02-26. Gapped PVBS models for all species numbers and dimensions. https://doi.org/10.1142/s0129055x19500284

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