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

Bruno Nachtergaele, Robert J Sims, Amanda Young

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

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
Volume717
DOIs
StatePublished - Jan 1 2018

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Spectral Flow
Spectral Stability
Spectral Gap
Fermions
Quantum Spin System
Frustration
Order Conditions
Conditional Expectation
Subalgebra
Automorphisms
Algebra
Class

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

Lieb-robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems. / Nachtergaele, Bruno; Sims, Robert J; Young, Amanda.

Contemporary Mathematics. Vol. 717 American Mathematical Society, 2018. p. 93-115.

Research output: Chapter in Book/Report/Conference proceedingChapter

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