Anderson Localization in Quark-Gluon Plasma

Abstract

At low temperature the low end of the QCD Dirac spectrum is well described by chiral random matrix theory. In contrast, at high temperature there is no similar statistical description of the spectrum. We show that at high temperature the lowest part of the spectrum consists of a band of statistically uncorrelated eigenvalues obeying essentially Poisson statistics and the corresponding eigenvectors are extremely localized. Going up in the spectrum the spectral density rapidly increases and the eigenvectors become more and more delocalized. At the same time the spectral statistics gradually crosses over to the bulk statistics expected from the corresponding random matrix ensemble. This phenomenon is reminiscent of Anderson localization in disordered conductors. Our findings are based on staggered Dirac spectra in quenched lattice simulations with the SU(2) gauge group.

Anderson transition and multifractals in the spectrum of the Dirac operator of quantum chromodynamics at high temperature

“…At low temperatures, the density of states is finite near the origin, and both low-lying and bulk eigenmodes are extended throughout the system. In contrast, at high temperatures, above T c , the density of states vanishes at the origin, and the low-lying eigenmodes are localized on the scale of the inverse temperature, while higher up in the spectrum, beyond a temperature-dependent critical "energy", E c (T ), the eigenmodes are again extended 12,13 . The temperature dependence of the "mobility edge" was investigated in Ref.…”

“…Quite surprisingly, an Anderson transition has been shown to take place also in the spectrum of the Dirac operator in Quantum Chromodynamics (QCD) at high temperature [10][11][12][13][14] (see Ref. 15 for a review).…”

Deconfinement, chiral transition and localisation in a QCD-like model

“…While at low temperatures the low-lying eigenmodes of the Dirac operator are delocalised on the entire lattice volume [35,36], above the crossover temperature, T c [2,3], they become spatially localised [4][5][6][7][8][9][10][11] on the scale of the inverse temperature [5,7,11]. From now on we focus on staggered fermions, both for simplicity and because of the larger amount of available evidence.…”

“…We finally mention that localisation of the lowest eigenmodes has been observed also in QCD-like theories, like SU(2) pure-gauge theory with staggered [5,6] or overlap fermions [6], and SU(3) pure-gauge theory [4]. In all these cases, fermions in the fundamental representation were considered.…”

“…In recent years, it has become more and more clear that the decrease in the spectral density of low modes is accompanied by a change in the localisation properties of the corresponding eigenvectors: while at low temperatures the low modes are extended throughout the whole spatial volume, above the crossover temperature the lowest modes are spatially localised on the scale of the inverse temperature. Evidence for this behaviour has been obtained by means of lattice simulations with different fermion discretisations, namely staggered [4][5][6][7][8][9], overlap [6,10] and domain wall [11] fermions.…”