# Gapped PVBS models for all species numbers and dimensions

## TL;DR

This paper establishes the existence of a spectral gap in PVBS models across all species numbers and dimensions for small anisotropy, aiding the classification of quantum phases.

## Contribution

It provides a new proof of spectral gap existence for PVBS models in any dimension and species number using a finite-size criterion, extending previous results.

## Key findings

- Spectral gap proven for all species and dimensions in PVBS models
- Uses finite-size criterion instead of martingale method
- Results support phase classification of quantum spin models

## 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.