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Localization in lattice QCD (with emphasis on practical implications)

Maarten Golterman·Yigal Shamir
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Abstract

When Anderson localization takes place in a quenched disordered system, a continuous symmetry can be broken spontaneously without accompanying Goldstone bosons. Elaborating on this observation we propose a unified, microscopic physical picture of the phase diagram of both quenched and unquenched QCD with two flavors of Wilson fermions. The phase with Goldstone bosons -- by definition the Aoki phase -- is always identified as the region where the mobility edge of the (hermitian) Wilson operator is zero. We then discuss the implications for domain-wall and overlap fermions. We conclude that both formulations are valid only well outside the Aoki phase of the associated Wilson-operator kernel, because this is where locality and chirality can be both maintained.

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Maarten Golterman, Yigal Shamir. 2003-09-09. Localization in lattice QCD (with emphasis on practical implications). https://doi.org/10.1016/s0920-5632(03)02516-7

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