Product vacua with boundary states

TL;DR

This paper introduces a family of quantum spin chains called PVBS models, which clarify the classification of gapped quantum phases by characterizing ground states with boundary-bound particles and connecting to known models like AKLT.

Contribution

The paper defines PVBS models with boundary states, describes their ground states as Matrix Product States, and connects them to existing models, refining phase classification.

Findings

PVBS models characterized by boundary-bound particles.

Connection established between PVBS and AKLT models.

Examples provided for models with arbitrary boundary particle numbers.

Abstract

We introduce a family of quantum spin chains with nearest-neighbor interactions that can serve to clarify and refine the classification of gapped quantum phases of such systems. The gapped ground states of these models can be described as a product vacuum with a finite number of particles bound to the edges. The numbers of particles, n_L and n_R, that can bind to the left and right edges of the finite chains serve as indices of the particular phase a model belongs to. All these ground states, which we call Product Vacua with Boundary States (PVBS) can be described as Matrix Product States (MPS). We present a curve of gapped Hamiltonians connecting the AKLT model to its representative PVBS model, which has indices n_L=n_R=1. We also present examples with n_L=n_R=J, for any integer J\geq 1, that are related to a recently introduced class of SO(2J+1)-invariant quantum spin chains.