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Random matrix theory and critical phenomena in quantum spin chains

Research output: Contribution to journalArticle

Original languageEnglish
Article number032106
Number of pages6
JournalPhysical Review E: Statistical, Nonlinear, and Soft Matter Physics
Volume92
Issue number3
DOIs
DatePublished - 4 Sep 2015

Abstract

We compute critical properties of a general class of quantum spin chains which are quadratic in the Fermi operators and can be solved exactly under certain symmetry constraints related to the classical compact groups U(N),O(N), and Sp(2N). In particular we calculate critical exponents s,ν, and z, corresponding to the energy gap, correlation length, and dynamic exponent, respectively. We also compute the ground state correlators ⟨σxiσxi+n⟩g,⟨σyiσyi+n⟩g, and ⟨∏ni=1σzi⟩g, all of which display quasi-long-range order with a critical exponent dependent upon system parameters. Our approach establishes universality of the exponents for the class of systems in question.

Additional information

Date of Acceptance: 18/08/2015

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  • PhysRevE.92.032106

    Rights statement: ©2015 American Physical Society

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