Anderson Metal-to-Critical Transition in QCD

Abstract

A picture of thermal QCD phase change based on the analogy with metal-to-insulator transition of Anderson type was proposed in the past. In this picture, a low-$T$ thermal state is akin to a metal with deeply infrared (IR) Dirac modes abundant and extended, while a high-$T$ state is akin to an insulator with IR modes depleted and localized below a mobility edge ${\lambda }_{\text{A}}>0$. Here we argue that, while ${\lambda }_{\text{A}}$ exists in QCD, a high-$T$ state is not an insulator in such an analogy. Rather, it is a critical state arising due to a new singular mobility edge at ${\lambda }_{\text{I}R}=0$. This new mobility edge appears upon the transition into the recently proposed IR phase. As a key part of such a metal-to-critical scenario, we present evidence using pure-glue QCD that deeply infrared Dirac modes in the IR phase extend to arbitrarily long distances. This is consistent with our previous suggestion that the IR phase supports scale invariance in the infrared. We discuss the role of Anderson-like aspects in this thermal regime and emphasize that the combination of gauge field topology and disorder plays a key role in shaping its IR physics. Our conclusions are conveyed by the structure of Dirac spectral non-analyticities.

5 pages, 5 figures; v2: minor improvements, published version

References in corpus (4)

• Chiral phase transition in lattice QCD as a metal-insulator transition
• Anderson Localization in Quark-Gluon Plasma
• Chiral Symmetry Breaking and Chiral Polarization: Tests for Finite Temperature and Many Flavors
• Thermal monopole condensation in QCD with physical quark masses

Cited by in corpus (8)

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• Super-Universality in Anderson Localization
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• Localisation of Dirac modes in gauge theories and Goldstone's theorem at finite temperature
• QCD Anderson transition with overlap valence quarks on a twisted-mass sea
• Topological Dimensions from Disorder and Quantum Mechanics?
• Understanding the approach to thermalization from the eigenspectrum of non-Abelian gauge theories
• Gluon Condensate via Dirac Spectral Density: IR Phase, Scale Anomaly and IR Decoupling