A Nonvanishing Spectral Gap for AKLT Models on Generalized Decorated Graphs
Mathematical Physics
2023-04-19 v2 Statistical Mechanics
math.MP
Quantum Physics
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 with a chain of 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.
Cite
@article{arxiv.2212.11872,
title = {A Nonvanishing Spectral Gap for AKLT Models on Generalized Decorated Graphs},
author = {Angelo Lucia and Amanda Young},
journal= {arXiv preprint arXiv:2212.11872},
year = {2023}
}
Comments
Discussion of additional results, and minor corrections