Fisher–Hartwig determinants, conformal field theory and universality in generalised XX models

Joanna Hutchinson, Nick G Jones

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We discuss certain quadratic models of spinless fermions on a 1D lattice, and their corresponding spin chains. These were studied by Keating and Mezzadri in the context of their relation to the Haar measures of the classical compact groups. We show how these models correspond to translation invariant models on an infinite or semi-infinite chain, which in the simplest case reduce to the familiar XX model. We give physical context to mathematical results for the entanglement entropy, and calculate the spin–spin correlation functions using the Fisher–Hartwig conjecture. These calculations rigorously demonstrate universality in classes of these models. We show that these are in agreement with field theoretic and renormalization group arguments that we provide.
Original languageEnglish
Article number073103
Number of pages26
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue numberJuly 2016
Early online date11 Jul 2016
Publication statusPublished - Jul 2016

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