Product vacua with boundary states and the classification of gapped phases

TL;DR

This paper introduces a new class of one-dimensional quantum spin models called PVBS, which classify gapped phases based on boundary states, extending understanding of topological phases beyond local order parameters.

Contribution

The paper defines PVBS models that classify gapped phases by boundary states and connects them to known models like AKLT, providing a new framework for phase classification.

Findings

PVBS models have unique gapped ground states with boundary states.

Phases are characterized by two integers representing boundary states.

AKLT and related models fit into the PVBS classification.

Abstract

We address the question of the classification of gapped ground states in one dimension that cannot be distinguished by a local order parameter. We introduce a family of quantum spin systems on the one-dimensional chain that have a unique gapped ground state in the thermodynamic limit that is a simple product state but which on the left and right half-infinite chains, have additional zero energy edge states. The models, which we call Product Vacua with Boundary States (PVBS), form phases that depend only on two integers corresponding to the number of edge states at each boundary. They can serve as representatives of equivalence classes of such gapped ground states phases and we show how the AKLT model and its $SO(2J+1)$-invariant generalizations fit into this classification.