The Heisenberg XX spin chain and low-energy QCD

TL;DR

This paper reveals a novel connection between low-energy QCD in finite volume and the Heisenberg XX spin chain using random matrix models, predicting phase transitions and statistical laws in the spin chain.

Contribution

It establishes a new dictionary linking low-energy QCD properties with spin chain characteristics, extending the understanding of quantum field theories through integrable models.

Findings

Prediction of a third-order phase transition in the spin chain

Identification of Tracy-Widom law in the transition region

Proposed broader applicability of the QCD-spin chain correspondence

Abstract

By using random matrix models we uncover a connection between the low energy sector of four dimensional QCD at finite volume and the Heisenberg XX model in a 1d spin chain. This connection allows to relate crucial properties of QCD with physically meaningful properties of the spin chain, establishing a dictionary between both worlds. We predict for the spin chain a third-order phase transition and a Tracy-Widom law in the transition region. We postulate that this dictionary goes beyond the particular example analyzed here and can be applied to other QFT and spin chain models. We finally comment on possible numerical implications of the connection as well as on possible experimental implementations.