Rokhsar-Kivelson Models of Bosonic Symmetry-Protected Topological States

TL;DR

This paper introduces a class of frustration-free Rokhsar-Kivelson models that construct bosonic symmetry-protected topological states by leveraging a classical-quantum mapping, enabling the design of models with universal SPT properties.

Contribution

It presents a novel approach to building microscopic Hamiltonians for bosonic SPT states using Rokhsar-Kivelson models and classical stochastic systems.

Findings

Constructed models exhibit non-degenerate gapped symmetric ground states.

Demonstrated the approach with 1D and 2D SPT state examples.

Established a classical-quantum correspondence for SPT state construction.

Abstract

A platform for constructing microscopic Hamiltonians describing bosonic symmetry-protected topological (SPT) states is presented. The Hamiltonians we consider are examples of frustration-free Rokhsar-Kivelson models, which are known to be in one-to-one correspondence with classical stochastic systems in the same spatial dimensionality. By exploring this classical-quantum mapping, we are able to construct a large class of microscopic models which, in a closed manifold, have a non-degenerate gapped symmetric ground state describing the universal properties of SPT states. Examples of one and two dimensional SPT states which illustrate our approach are discussed.