A Nonvanishing Spectral Gap for AKLT Models on Generalized Decorated Graphs

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.

Discussion of additional results, and minor corrections

References in corpus (2)

• Propagation of Correlations in Quantum Lattice Systems
• Stability of the spectral gap and ground state indistinguishability for a decorated AKLT model

Cited by in corpus (2)

• On the critical finite-size gap scaling for frustration-free Hamiltonians
• On a bulk gap strategy for quantum lattice models