Dirac eigenmodes at the QCD Anderson transition

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

doi:10.48550/arxiv.1410.8308

Cited by 1 publication

(1 citation statement)

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“…We have not considered yet the information which can be gained by inspecting the eigenvectors of the LB operator, that will be done in a forthcoming study. 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

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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.

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Section: Discussionmentioning

confidence: 99%