Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems

2021/02/14 by Nachtergaele, Bruno, Sims, Robert, Young, Amanda · 4 citations
#82B10 #82C10 #82C20 #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.2102.07209

Abstract

We prove that uniformly small short-range perturbations do not close the bulk gap above the ground state of frustration-free quantum spin systems that satisfy a standard local topological quantum order condition. In contrast with earlier results, we do not require a positive lower bound for finite-system Hamiltonians uniform in the system size. To obtain this result, we adapt the Bravyi-Hastings-Michalakis strategy to the GNS representation of the infinite-system ground state.

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• Spectral statistics and energy-gap scaling in k-local spin Hamiltonians
• The bulk spectral gap is semi-decidable: a convergent family of certified upper bounds
• On Frustration-Free Quantum Spin Models
• Dimerization in O(n)-invariant quantum spin chains

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