A Nonvanishing Spectral Gap for AKLT Models on Generalized Decorated Graphs

TL;DR

This paper proves that AKLT models on decorated graphs maintain a nonzero spectral gap if the decoration length exceeds a certain linear threshold related to the graph's maximum degree, ensuring stability of the quantum phase.

Contribution

It establishes a condition on the decoration parameter that guarantees a nonvanishing spectral gap for AKLT models on generalized decorated graphs.

Findings

Spectral gap remains nonzero for decorations above a linear threshold.

Applicable to decorated multi-dimensional lattices.

Uses Tensor Network States approach for proof.

Abstract

We consider the spectral gap question for AKLT models defined on decorated versions of simple, connected graphs G. This class of decorated graphs, which are defined by replacing all edges of $G$ with a chain of $n$ sites, in particular includes any decorated multi-dimensional lattice. Using the Tensor Network States (TNS) approach from a work by Abdul-Rahman et. al. 2020, we prove that if the decoration parameter is larger than a linear function of the maximal vertex degree, then the decorated model has a nonvanishing spectral gap above the ground state energy.