Spectral properties for a family of two-dimensional quantum antiferromagnets

TL;DR

This paper proves the existence of a spectral gap in a family of 2D quantum antiferromagnets, advancing understanding of their spectral properties and implications for quantum computation.

Contribution

It establishes a spectral gap for a subset of deformed 2D AKLT models, providing new insights into their spectral and computational properties.

Findings

Proved spectral gap existence for certain 2D antiferromagnets

Connected spectral gap to quantum computational resources

Progressed understanding of AKLT model spectral properties

Abstract

We study the spectral properties of a family of quantum antiferromagnets on two-dimensional (2D) lattices. This family of models is obtained by a deformation of the well-studied 2D quantum antiferromagnetic model of Affleck, Kennedy, Lieb and Tasaki (AKLT); they are described by two-body, frustration-free Hamiltonians on a three-colourable lattice of spins. Although the existence of a spectral gap in the 2D AKLT model remains an open question, we rigorously prove the existence of a gap for a subset of this family of quantum antiferromagnets. Along with providing new progress for the gap problem in AKLT-type antiferromagnets in 2D, this result has implications for the theory of quantum computation as it provides a family of two-body Hamiltonians for which the ground state is a resource for universal quantum computation and for which a spectral gap is proven to exist.