Research PaperNo Access

Gapped PVBS models for all species numbers and dimensions

Department of Mathematics, Harvard University, Cambridge, MA 02138, USA

and

Department of Mathematics and Center for Quantum Mathematics and Physics, University of California, Davis, Davis, CA 95616, USA

E-mail Address: bxn@math.ucdavis.edu

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https://doi.org/10.1142/S0129055X19500284Cited by:7 (Source: Crossref)

Abstract

Product vacua with boundary states (PVBS) are cousins of the Heisenberg XXZ spin model and feature $n$ particle species on $ℤ^{d}$ . 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.

Keywords:

AMSC: 82B10, 82B20

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