Abstract
We study the localization properties of the eigenmodes of the staggered Dirac operator in finite-temperature $\mathbb{Z}_2$ pure gauge theory on the lattice in 2+1 dimensions. We find that the low modes turn from delocalized to localized as the system crosses over from the confined to the deconfined phase in the "physical" sector (positive average Polyakov loop) selected by external fermionic probes, while they remain delocalized in the "unphysical" sector (negative average Polyakov loop). This confirms that the close connection between deconfinement and localization of the low Dirac modes in the physical sector, already observed in other models, holds also in the simplest gauge theory displaying a deconfinement transition. We also observe a clear correlation of localized modes with fluctuations of the Polyakov loop away from the ordered value, as expected according to the "sea/islands" picture of localization, and with clusters of negative plaquettes. A novel finding is the presence of localized modes at the high end of the Dirac spectrum in all phases/sectors of the theory.
Highlights
In the imaginary-time functional-integral formulation of gauge theories at finite temperature, the effects of dynamical fermions are entirely encoded in the Euclidean Dirac operator in a gauge-field background
In this paper we have studied the localization properties of the eigenmodes of the staggered Dirac operator in the background of Z2 gauge field configurations on the lattice in 2 þ 1 dimensions
This is the simplest gauge theory displaying a deconfining transition at finite temperature, and so provides the most basic test of the “sea/islands” picture of localization. We have studied this theory by means of numerical simulations, producing full staggered spectra for configurations in both center sectors in order to study in detail the effects of the ordering of the Polyakov loop, Pðx⃗ Þ, throughout the whole spectrum
Summary
In the imaginary-time functional-integral formulation of gauge theories at finite temperature, the effects of dynamical fermions are entirely encoded in the Euclidean Dirac operator in a gauge-field background. In recent years it has become apparent that there is a close relation between the localization properties of the low-lying Dirac modes and the confining properties of gauge theories. It is fairly well established, by means of numerical calculations on the lattice, that in the high-temperature phase of QCD the low-lying Dirac modes become localized [6,7,8,9,10] on the scale of the inverse temperature [7,9], up to a temperature-dependent point
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
