Chiral transition as Anderson transition

Abstract

At low temperature the low-lying QCD Dirac spectrum obeys random matrix statistics. Recently we found that above T c the lowest part of the spectrum consists of localized modes that obey Poisson statistics. An interesting implication of this is that as the system crosses T c from above, the spectral statistics at λ = 0 changes from Poisson to random matrix. Here we study this transition and its possible implications for the finite temperature transition of QCD-like theories.

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

“…The scaling of low modes has been already studied in detail by Kovacs et al using staggered fermions [3,4]. We report here an example of our results as a warm-up and confirmation that the same phenomena observed in pure gauge ensembles and with different fermion discretisations [3][4][5]10] are found also with chiral fermions on dynamical configurations. In Figure 1 we illustrate the scaling of the participation ratio for a couple of ensembles at β = 4.10, 4.18 and m = 0.01 where two different volumes 16 3 × 8 and 32 3 × 8 are available.…”

“…Further study is needed to strengthen the connection and the next step would be a proper estimate of the density of the several monopole species and monopole-pairs and the dependence of these characteristics on the temperature and mass of fermions. The connection between the localisation mechanism and the chiral phase transition has been considered in [11] and in the model based approach [10,13].…”

“…The authors of [5] have shown that the scaling critical exponents for the QCD spectrum match the expectation from the three dimensional Anderson Hamiltonian model, confirming that there is an Anderson-like mechanism in action in high temperature QCD. The critical point depends on the temperature [10], an indication that the disorder is depending on the temperature too. Moreover, the low temperature phase eigenmodes exhibit a metallic behaviour, being delocalised at all energies.…”

“…There is no critical λ c in the spectrum in this regime. The interesting conjecture is whether the opening of a localised region in the spectrum is connected to the chiral phase transition [5,[10][11][12][13]]. 2 The attractive question, once we assume Anderson localisation in QCD, is what are the impurities, or the disorder, in the background gauge configurations that trigger the localisation of the eigenmodes.…”