Knabe's spectral gap method for open boundary conditions

Abstract

In 1988, Knabe found a "finite-size criterion" to determine whether a frustration-free quantum spin chain with periodic boundary conditions is uniformly gapped in the thermodynamic limit. The criterion provides a threshold for the spectral gap at a finite system size such that, if the threshold is exceeded for a fixed system size, then the chain with periodic boundary conditions is uniformly gapped. We extend Knabe's result to frustration-free spin chains equipped with open boundary conditions. We now obtain two finite-size criteria: The first one is identical to Knabe's criterion and we interpret it as a bulk criterion. The second one controls the spectral gaps at smaller system sizes and can be interpreted as a new edge criterion. Heuristically, it excludes the presence of thermodynamically gapless excitations living near the edge.

This paper is superseded by arXiv:1801.08915

References in corpus (5)

• Stochastic Error Cancellation in Analog Quantum Simulation
• Quantum phase transition from bounded to extensive entanglement entropy in a frustration-free spin chain
• Deformed Fredkin Spin Chain with Extensive Entanglement
• Local gap threshold for frustration-free spin systems
• Spectral Gap and Edge Excitations of $d$-dimensional PVBS models on half-spaces