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.

arXiv comment5 pages, 5 figures; v2: minor improvements, published version

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Cited by in corpus (8)

• Eigenvalues of the QCD Dirac matrix with improved staggered quarks in the continuum limit
• Super-Universality in Anderson Localization
• Deconfinement transition and localization of Dirac modes in finite-temperature ${\mathbb{Z}}_3$ gauge theory on the lattice
• 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