Anderson localization in high temperature QCD: background configuration properties and Dirac eigenmodes

Abstract

Abstract:We investigate the properties of the background gauge field configurations that act as disorder for the Anderson localization mechanism in the Dirac spectrum of QCD at high temperatures. We compute the eigenmodes of the Möbius domain-wall fermion operator on configurations generated for the SU(3) gauge theory with two flavors of fermions, in the temperature range [0.9, 1.9]T c . We identify the source of localization of the eigenmodes with gauge configurations that are self-dual and support negative fluctuations of the Polyakov loop P L , in the high temperature sea of P L ∼ 1. The dependence of these observations on the boundary conditions of the valence operator is studied. We also investigate the spatial overlap of the left-handed and right-handed projected eigenmodes in correlation with the localization and the corresponding eigenvalue. We discuss an interpretation of the results in terms of monopole-instanton structures.

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

“…In this respect it is worth mentioning the results of ref. [11], which support a connection between localised modes and certain topological objects, namely the monopoleinstantons, which might be responsible for the deconfinement transition (see refs. [26][27][28][29] and references therein).…”

“…Further evidence has been recently obtained in ref. [11], in which a clear correlation is reported between the position of localised modes and that of the favourable "islands" of Polyakov loops. Relating deconfinement and chiral symmetry restoration is more difficult, despite the ample numerical evidence of a close relationship.…”

“…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.…”

“…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.…”

Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature

“…Given the close relation between confining and chiral properties of the theory, it is natural to wonder if confinement is somehow responsible for the accumulation of modes near the origin, and analogously if deconfinement causes the depletion of this spectral region. A similar question of course can be asked also for other gauge theories.Adding to the mistery, or possibly helping to solve it, a third phenomenon has been observed to take place in QCD around the critical temperature, namely the localisation of the lowest modes of the Dirac operator [12][13][14][15][16][17][18]. Numerical studies on the lattice have shown that while in the low-temperature phase all the Dirac modes are extended throughout the whole system, above T c the lowest modes get localised [12][13][14][15][16][17][18] on the scale of the inverse temperature [16].…”