Lieb-robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems

Bruno Nachtergaele, Robert Sims, Amanda Young

Research output: Chapter in Book/Report/Conference proceedingChapter

6 Scopus citations

Abstract

We prove Lieb-Robinson bounds for a general class of lattice fermion systems. By making use of a suitable conditional expectation onto subalgebras of the CAR algebra, we can apply the Lieb-Robinson bounds much in the same way as for quantum spin systems. We preview how to obtain the spectral flow automorphisms and to prove stability of the spectral gap for frustration-free gapped systems satisfying a Local Topological Quantum Order condition.

Original languageEnglish (US)
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages93-115
Number of pages23
DOIs
StatePublished - Jan 1 2018

Publication series

NameContemporary Mathematics
Volume717
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

ASJC Scopus subject areas

  • Mathematics(all)

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    Nachtergaele, B., Sims, R., & Young, A. (2018). Lieb-robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems. In Contemporary Mathematics (pp. 93-115). (Contemporary Mathematics; Vol. 717). American Mathematical Society. https://doi.org/10.1090/conm/717/14443