Statistics of spectra of disordered systems near the metal-insulator transition

Osborn

2006

Nuclear Physics A

We study the spectrum and eigenmodes of the QCD Dirac operator in a gauge background given by an Instanton Liquid Model (ILM) at temperatures around the chiral phase transition. Generically we find the Dirac eigenvectors become more localized as the temperature is increased. At the chiral phase transition, both the low lying eigenmodes and the spectrum of the QCD Dirac operator undergo a transition to localization similar to the one observed in a disordered conductor. This suggests that Anderson localization is the fundamental mechanism driving the chiral phase transition. We also find an additional temperature dependent mobility edge (separating delocalized from localized eigenstates) in the bulk of the spectrum which moves toward lower eigenvalues as the temperature is increased. In both regions, the origin and the bulk, the transition to localization exhibits features of a 3D Anderson transition including multifractal eigenstates and spectral properties that are well described by critical statistics. Similar results are obtained in both the quenched and the unquenched case though the critical temperature in the unquenched case is lower. Finally we argue that our findings are not in principle restricted to the ILM approximation and may also be found in lattice simulations.

Section: The Bulkmentioning

confidence: 99%

Section: Anderson Transition: Description and Signaturesmentioning

confidence: 99%

Section: A Technical Details Of the Numerical Simulationmentioning

confidence: 99%

See 1 more Smart Citation

Chiral phase transition and Anderson localization in the instanton liquid model for QCD

Osborn

2006

Nuclear Physics A

“…A similar picture holds for d > 3. The spectral correlations at the Anderson transition, usually referred to as critical statistics [16,17], are scale invariant and intermediate between the prediction for a metal and for an insulator [17,18]. By scale invariant we mean that any spectral correlator utilized to describe the spectral properties of the disordered Hamiltonian does not depend on the system size.…”

Section: Introductionmentioning

confidence: 99%

Anderson Localization in Quantum Chaos: Scaling and Universality

Wang

2007

Acta Phys. Pol. A

The one-parameter scaling theory is a powerful tool to investigate Anderson localization effects in disordered systems. In this paper we show that this theory can be adapted to the context of quantum chaos provided that the classical phase space is homogeneous, not mixed. The localization problem in this case is defined in momentum, not in real space. We then employ the one-parameter scaling theory to: (a) propose a precise characterization of the type of classical dynamics related to the Wigner-Dyson and Poisson statistics which also predicts in which situations Anderson localization corrections invalidate the relation between classical chaos and random matrix theory encoded in the Bohigas-Giannoni-Schmit conjecture, (b) to identify the universality class associated with the metal-insulator transition in quantum chaos. In low dimensions it is characterized by classical superdiffusion, in higher dimensions it has in general a quantum origin as in the case of disordered systems. We illustrate these two cases by studying 1d kicked rotors with non-analytical potentials and a 3d kicked rotor with a smooth potential.

“…Spectral fluctuations at the Anderson transition (commonly referred as 'critical statistics' [19]) are intermediate between WD and Poisson statistics. Typical features include: scale invariant spectrum [20], level repulsion, and sub-Poisson number variance [21]. Different generalized random matrix model (gRMM) have been successfully employed to describe critical statistics [22,23].…”

Section: Introductionmentioning

confidence: 99%

Long range disorder and Anderson transition in systems with chiral symmetry

Takahashi

2004

Nuclear Physics B

We study the spectral properties of a chiral random banded matrix (chRBM) with elements decaying as a power-law Hij ∼ |i−j| −α . This model is equivalent to a chiral 1D Anderson Hamiltonian with long range power-law hopping. In the weak disorder limit we obtain explicit nonperturbative analytical results for the density of states (DoS) and the two-level correlation function (TLCF) by mapping the chRBM onto a nonlinear σ model. We also put forward, by exploiting the relation between the chRBM at α = 1 and a generalized chiral random matrix model, an exact expression for the above correlation functions. We give compelling analytical and numerical evidence that for this value the chRBM reproduces all the features of an Anderson transition. Finally we discuss possible applications of our results to quantum chromodynamics (QCD).