The Heisenberg XX spin chain and low-energy QCD

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.

12 pages. v3 Final version to appear in Phys. Rev. X; discussion on experimental accessibility extended; title modified in journal

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• Multiple phases in a generalized Gross-Witten-Wadia matrix model
• Limit shape phase transitions: a merger of arctic circles
• Emptiness formation probability of the six-vertex model and the sixth Painlevé equation
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• Dynamical quantum phase transitions from random matrix theory
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• Spin correlation functions, Ramus-like identities, and enumeration of constrained lattice walks and plane partitions