Random matrices and quantum spin chains

Jon P Keating, Noah Linden, Huw J Wells

Research output: Contribution to journalArticle (Academic Journal)peer-review

7 Citations (Scopus)
117 Downloads (Pure)

Abstract

Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of n distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the density of states when n → ∞, giving explicit bounds on the rate of approach to the limit. Universality within a class of probability measures and the extension to more general interaction geometries are established. The level spacing distributions of the Gaussian Orthogonal, Unitary and Symplectic Ensembles are observed numerically for the energy levels in these ensembles.

Original languageEnglish
Pages (from-to)537-555
Number of pages19
JournalMarkov Processes and Related Fields
Volume21
Issue number3
Publication statusPublished - Sep 2015

Keywords

  • Density of states
  • Quantum spin chains
  • Random matrix theory
  • Spectral statistics

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