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Mapping between the Heisenberg XX Spin Chain and Low-Energy QCD

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Pérez García, David and Tierz, Miguel (2014) Mapping between the Heisenberg XX Spin Chain and Low-Energy QCD. Physical Review X, 4 (2). ISSN 2160-3308

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Official URL: http://journals.aps.org/prx/pdf/10.1103/PhysRevX.4.021050


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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 us to relate crucial properties of QCD with physically meaningful properties of the spin chain, establishing a dictionary between both worlds. For the spin chain, we predict a third-order phase transition and a Tracy-Widom law in the transition region. We also comment on possible numerical implications of the connection as well as on possible experimental implementations.


Item Type:Article
Uncontrolled Keywords:Lattice gauge-theories; Atomic Mott insulator; Optical lattices; Phase-transition; Dirac operator; Random-walks; Expansions; Spectrum; Systems; Physics
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:26441
Deposited On:29 Jul 2014 08:15
Last Modified:24 Nov 2014 08:47

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