Product Vacua and Boundary State Models in d Dimensions

TL;DR

This paper introduces a class of quantum spin models called PVBS in d dimensions, analyzing their ground states, excitation spectrum, and boundary effects, revealing conditions for gapless and gapped phases and boundary sensitivity.

Contribution

It defines PVBS models, characterizes their ground states, and analyzes their spectral properties and boundary effects in arbitrary dimensions.

Findings

Models have a gapped spectrum except at critical parameters.

Boundary orientation affects the excitation spectrum.

Edge states can be gapless while the bulk remains gapped.

Abstract

We introduce and analyze a class of quantum spin models defined on d-dimensional lattices Lambda subset of Z^d, which we call `Product Vacua with Boundary States' (PVBS). We characterize their ground state spaces on arbitrary finite volumes and study the thermodynamic limit. Using the martingale method, we prove that the models have a gapped excitation spectrum on Z^d except for critical values of the parameters. For special values of the parameters we show that the excitation spectrum is gapless. We demonstrate the sensitivity of the spectrum to the existence and orientation of boundaries. This sensitivity can be explained by the presence or absence of edge excitations. In particular, we study a PVBS models on a slanted half-plane and show that it has gapless edge states but a gapped excitation spectrum in the bulk.