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

Ujfalusi, László; Giordano, Matteo; Pittler, Ferenc; Kovács, Tamás; Varga, Imre

doi:10.1103/physrevd.92.094513

Cited by 39 publications

(46 citation statements)

References 55 publications

(60 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We have studied the finite temperature phase of two-flavor QCD using chiral fermions around the phase transition, T ∈ [0.9, 1.9]T c . At fixed finite temperature T , the Dirac spectrum undergoes a quantum phase transition that is in accordance with the prediction of the Anderson model for localisation [5,27]. The near-zero Dirac eigenmodes at high temperature are localised up to a critical eigenvalue λ c (T ).…”

Section: Discussionsupporting

confidence: 78%

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

Cossu

Hashimoto

2016

J. High Energ. Phys.

View full text Add to dashboard Cite

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.

show abstract

Section: Discussionsupporting

confidence: 78%

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

Cossu

Hashimoto

2016

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…In particular, it will be interesting to consider and analyze their localization/delocalization properties, in a way similar to what has been done in similar studies for the spectrum of the Dirac operator in QCD [45,46].…”

Section: Discussionmentioning

confidence: 99%

Spectrum of the Laplace-Beltrami operator and the phase structure of causal dynamical triangulations

Clemente

D’Elia

2018

Phys. Rev. D

View full text Add to dashboard Cite

We propose a new method to characterize the different phases observed in the nonperturbative numerical approach to quantum gravity known as causal dynamical triangulations. The method is based on the analysis of the eigenvalues and the eigenvectors of the Laplace-Beltrami operator computed on the triangulations: it generalizes previous works based on the analysis of diffusive processes and proves capable of providing more detailed information on the geometric properties of the triangulations. In particular, we apply the method to the analysis of spatial slices, showing that the different phases can be characterized by a new order parameter related to the presence or absence of a gap in the spectrum of the Laplace-Beltrami operator, and deriving an effective dimensionality of the slices at the different scales. We also propose quantities derived from the spectrum that could be used to monitor the running to the continuum limit around a suitable critical point in the phase diagram, if any is found.

show abstract

“…"Unitary" refers here to the symmetry class of the model in the RMT classification of random matrix ensembles [23], and the staggered Dirac operator also belongs to this class [2]. This result for the critical exponent has been recently confirmed by a study of the multifractal properties of the eigenmodes at criticality [24]. In the same paper it was also found that the multifractal exponents of the critical eigenmodes in QCD are compatible with those of the 3D unitary Anderson model [25], which further supports that the delocalisation transitions in the two models belong to the same universality class.…”

Section: Introductionmentioning

confidence: 93%

An Anderson-like model of the QCD chiral transition

Giordano

Kovács

Pittler

2016

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

Abstract:We study the problems of chiral symmetry breaking and eigenmode localisation in finite-temperature QCD by looking at the lattice Dirac operator as a random Hamiltonian. We recast the staggered Dirac operator into an unconventional three-dimensional Anderson Hamiltonian ("Dirac-Anderson Hamiltonian") carrying internal degrees of freedom, with disorder provided by the fluctuations of the gauge links. In this framework, we identify the features relevant to chiral symmetry restoration and localisation of the low-lying Dirac eigenmodes in the ordering of the local Polyakov lines, and in the related correlation between spatial links across time slices, thus tying the two phenomena to the deconfinement transition. We then build a toy model based on QCD and on the DiracAnderson approach, replacing the Polyakov lines with spin variables and simplifying the dynamics of the spatial gauge links, but preserving the above-mentioned relevant dynamical features. Our toy model successfully reproduces the main features of the QCD spectrum and of the Dirac eigenmodes concerning chiral symmetry breaking and localisation, both in the ordered (deconfined) and disordered (confined) phases. Moreover, it allows us to study separately the roles played in the two phenomena by the diagonal and the off-diagonal terms of the Dirac-Anderson Hamiltonian. Our results support our expectation that chiral symmetry restoration and localisation of the low modes are closely related, and that both are triggered by the deconfinement transition.

show abstract

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

Cited by 39 publications

References 55 publications

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

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

Spectrum of the Laplace-Beltrami operator and the phase structure of causal dynamical triangulations

An Anderson-like model of the QCD chiral transition

Contact Info

Product

Resources

About