Gaplessness is not generic for translation-invariant spin chains

2019/02/28 by Marius Lemm · 1 voice · 2 citations
#quant-ph #cond-mat.stat-mech #math-ph

paper · pdf · doi:10.1103/physrevb.100.035113

Abstract

The existence of a spectral gap above the ground state has far-reaching consequences for the low-energy physics of a quantum many-body system. A recent work of Movassagh [R. Movassagh, PRL 119 (2017), 220504] shows that a spatially random local quantum Hamiltonian is generically gapless. Here we observe that a gap is more common for translation-invariant quantum spin chains, more specifically, that these are gapped with a positive probability if the interaction is of small rank. This is in line with a previous analysis of the spin-1/2 case by Bravyi and Gosset. The Hamiltonians are constructed by selecting a single projection of sufficiently small rank at random, and then translating it across the entire chain. By the rank assumption, the resulting Hamiltonians are automatically frustration-free and this fact plays a key role in our analysis.

Cited by

• Spectral statistics and energy-gap scaling in k-local spin Hamiltonians
• Two classes of quantum spin systems that are gapped on any bounded-degree graph

Discussions

• To the extent we can ignore finite-size gaps (that is, gaps due to finite system size rather than gaps necessarily present in the thermodynamic limit), it may make more sense to think of gapless Hamil [stackexchange, 6 points]

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