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

TL;DR

This paper explores quadratic fermionic models and their spin chain equivalents, demonstrating universality in entanglement and correlation behaviors through Fisher-Hartwig analysis and conformal field theory insights.

Contribution

It establishes a connection between generalized XX models and Fisher-Hartwig determinants, providing rigorous proofs of universality consistent with field theory and RG predictions.

Findings

Universality in entanglement entropy across models

Correlation functions match Fisher-Hartwig conjecture predictions

Agreement with conformal field theory and renormalization group results

Abstract

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.