arXiv subjects

Tamas G. Kovacs

Publications and source records attributed to Tamas G. Kovacs.

At least 19 recordsLinked to original sources

arXiv2026

Dirac mode localization in QCD near the crossover temperature

We study the localization properties of the low-lying Dirac eigenmodes in QCD near the crossover temperature, using stout-smeared staggered fermions and Symanzik-improved gauge action on the lattice. On $N_{\mathrm{t}}=8$ lattices we find that localized low modes, absent at low temperature, appear at a temperature $T_{\mathrm{loc}}$ in the range $150\,\mathrm{MeV}\le T_{\mathrm{loc}}\le 160\,\mathrm{MeV}$, well within the chiral crossover range as determined from the chiral condensate and from the light-quark susceptibility. Since with our choice of lattice action neither the chiral transition region nor the renormalized mobility edges change significantly above $N_{\mathrm{t}}=8$, our conclusion that $T_{\mathrm{loc}}$ is in the chiral crossover region is expected to remain valid in the continuum limit.

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arXiv2025

$U(1)_A$ Breaking in Hot QCD in the Chiral Limit

We propose a simple instanton-based random matrix model of hot QCD that in the quenched case precisely reproduces the distribution of the lowest lattice overlap Dirac eigenvalues. Even after including dynamical quarks the model can be easily simulated in volumes and for quark masses that will be out of reach for direct lattice simulations in the foreseeable future. Our simulations show that quantities connected to the $U(1)_A$ and $SU(N_f)_A$ chiral symmetry are dominated by eigenvalues in a peak of the spectral density that becomes singular at zero in the thermodynamic limit. This spectral peak turns out to be produced by an ideal instanton gas. By generalizing Banks-Casher type integrals for the singular spectral density, definite predictions can be given for physical quantities that are essential to test chiral symmetry breaking, but presently impossible to compute reliably with direct lattice simulations.

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arXiv2024

Fate of Chiral Symmetries in the Quark-Gluon Plasma from an Instanton-Based Random Matrix Model of QCD

We propose a new way of understanding how chiral symmetry is realized in the high temperature phase of QCD. Based on the finding that a simple free instanton gas precisely describes the details of the lowest part of the spectrum of the lattice overlap Dirac operator, we propose an instanton-based random matrix model of QCD with dynamical quarks. Simulations of this model reveal that even for small quark mass the Dirac spectral density has a singularity at the origin, caused by a dilute gas of free instantons. Even though the interaction, mediated by light dynamical quarks creates small instanton-antiinstanton molecules, those do not influence the singular part of the spectrum, and this singular part is shown to dominate Banks-Casher type sums in the chiral limit. By generalizing the Banks-Casher formula for the singular spectrum, we show that in the chiral limit the chiral condensate vanishes if there are at least two massless flavors. Our model also indicates a possible way of resolving a long-standing debate, as it suggests that for two massless quark flavors the $U(1)_{A}$ symmetry is likely to remain broken up to arbitrarily high finite temperatures.

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arXiv2023

High temperature $U(1)_A$ breaking in the chiral limit

We solve the long-standing problem concerning the fate of the chiral $U(1)_A$ symmetry in QCD-like theories at high temperature in the chiral limit. We introduce a simple instanton based random matrix model that precisely reproduces the properties of the lowest part of the lattice overlap Dirac spectrum. We show that in the chiral limit the instanton gas splits into a free gas component with a density proportional to $m^{N_f}$ and a gas of instanton-antiinstanton molecules. While the latter do not influence the chiral properties, for any nonzero quark mass the free gas component produces a singular spectral peak at zero that dominates Banks-Casher type spectral sums. By calculating these we show that the difference of the pion and delta susceptibility vanishes only for three or more massless flavors, however, the chiral condensate is zero already for two massless flavors

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arXiv2022

Topology and the Dirac Spectrum in Hot QCD

It is known that contrary to expectations, the order parameter of chiral symmetry breaking, the Dirac spectral density at zero virtuality does not vanish above the critical temperature of QCD. Instead, the spectral density develops a pronounced peak at zero. We show that the spectral density in the peak has large violations of the expected volume scaling. This anomalous scaling and the statistics of these eigenmodes is consistent with them being produced by mixing instanton and antiinstanton zero modes. Consequently, we show that a nonvanishing topological usceptibility implies a finite density of eigenvalues around zero, which can have implications on the restoration of chiral symmetry above the critical temperature.

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arXiv2022

Localization at the quenched SU(3) phase transition

It is known that the deconfining transition of QCD is accompanied by the appearance of localized eigenmodes at the low end of the Dirac spectrum. In the quenched case localization appears exactly at the critical temperature of deconfinement. In the present work, using quenched simulations exactly at the critical temperature, we show that the localization properties of low Dirac modes change abruptly between the confined and deconfined phase. This means that in the real Polyakov loop sector, the mobility edge has a discontinuity at the critical temperature. In contrast, in the complex sector, there is no such discontinuity at $T_c$, even the lowest Dirac modes remain delocalized at the critical temperature in the deconfined phase.

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arXiv2022

Ideal topological gas in the high temperature phase of SU(3) gauge theory

We show that the nature of the topological fluctuations in $SU(3)$ gauge theory changes drastically at the finite temperature phase transition. Starting from temperatures right above the phase transition topological fluctuations come in well separated lumps of unit charge that form a non-interacting ideal gas. Our analysis is based on a novel method to count not only the net topological charge, but also separately the number of positively and negatively charged lumps in lattice configurations using the spectrum of the overlap Dirac operator. This enables us to determine the joint distribution of the number of positively and negatively charged topological objects, and we find this distribution to be consistent with that of an ideal gas of unit charged topological objects.

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arXiv2021

Localization of Dirac Fermions in Finite-Temperature Gauge Theory

It is by now well established that Dirac fermions coupled to non-Abelian gauge theories can undergo an Anderson-type localization transition. This transition affects eigenmodes in the lowest part of the Dirac spectrum, the ones most relevant to the low-energy physics of these models. Here we review several aspects of this phenomenon, mostly using the tools of lattice gauge theory. In particular, we discuss how the transition is related to the finite-temperature transitions leading to the deconfinement of fermions, as well as to the restoration of chiral symmetry that is spontaneously broken at low temperature. Other topics we touch upon are the universality of the transition, and its connection to topological excitations (instantons) of the gauge field and the associated fermionic zero modes. While the main focus is on Quantum Chromodynamics, we also discuss how the localization transition appears in other related models with different fermionic contents (including the quenched approximation), gauge groups, and in different space-time dimensions. Finally, we offer some speculations about the physical relevance of the localization transition in these models.

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arXiv2020

Localization with overlap fermions

We study the finite temperature localization transition in the spectrum of the overlap Dirac operator. Simulating the quenched approximation of QCD, we calculate the mobility edge, separating localized and delocalized modes in the spectrum. We do this at several temperatures just above the deconfining transition and by extrapolation we determine the temperature where the mobility edge vanishes and localized modes completely disappear from the spectrum. We find that this temperature, where even the lowest Dirac eigenmodes become delocalized, coincides with the critical temperature of the deconfining transition. This result, together with our previously obtained similar findings for staggered fermions shows that quark localization at the deconfining temperature is independent of the fermion discretization, suggesting that deconfinement and localization of the lowest Dirac eigenmodes are closely related phenomena.

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arXiv2019

Free caloron gas in high temperature quenched QCD

Across the finite temperature transition to the quark-gluon plasma, the QCD topological susceptibility decreases sharply. Thus in the high temperature phase the remaining topological objects (possibly calorons) form a weakly interacting dilute gas. The overlap Dirac operator, through its exact zero modes, allows one to measure the net topological charge. We show that separately the number of positively and negatively charged topological objects can also be extracted from the low end of the overlap Dirac spectrum. We find that slightly above the phase transition their number distributions are already consistent with an ideal gas of non-interacting topological objects.

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arXiv2019

Magnetic catalysis and inverse catalysis for heavy pions

We investigate the QCD phase diagram for nonzero background magnetic fields using first-principles lattice simulations. At the physical point (in terms of quark masses), the thermodynamics of this system is controlled by two opposing effects: magnetic catalysis (enhancement of the quark condensate) at low temperature and inverse magnetic catalysis (reduction of the condensate) in the transition region. While the former is known to be robust and independent of the details of the interactions, inverse catalysis arises as a result of a delicate competition, effective only for light quarks. By performing simulations at different quark masses, we determine the pion mass above which inverse catalysis does not take place in the transition region anymore. Even for pions heavier than this limiting value - where the quark condensate undergoes magnetic catalysis - our results are consistent with the notion that the transition temperature is reduced by the magnetic field. These findings will be useful to guide low-energy models and effective theories of QCD.

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arXiv2019

Localization and topology in high temperature QCD

At high temperature part of the spectrum of the quark Dirac operator is known to consist of localized states. This comes about because around the crossover temperature to the quark-gluon plasma localized states start to appear at the low end of the spectrum and as the system is further heated, states higher up in the spectrum also get localized. Since localization and the crossover to the chirally restored phase happen around the same temperature, the question of how the two phenomena are connected naturally arises. Here we speculate on the nature of possible gauge configurations that could support localized quark eigenmodes. In particular, by analyzing eigenmodes of the staggerd and overlap Dirac operator we show that the dilute gas of calorons in the high temperature phase is very unlikely to play a major role in localization.

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arXiv2019

The localization transition in SU(3) gauge theory

We study the Anderson-like localization transition in the spectrum of the Dirac operator of quenched QCD. Above the deconfining transition we determine the temperature dependence of the mobility edge separating localized and delocalized eigenmodes in the spectrum. We show that the temperature where the mobility edge vanishes and localized modes disappear from the spectrum, coincides with the critical temperature of the deconfining transition. We also identify topological charge related close to zero modes in the Dirac spectrum and show that they account for only a small fraction of localized modes, a fraction that is rapidly falling as the temperature increases.

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arXiv2018

Localization in SU(3) gauge theory

In this paper we study the localization transition of Dirac eigenmodes in quenched QCD. We determined the temperature dependence of the mobility edge in the quark-gluon plasma phase near the deconfining critical temperature. We calculated the critical temperature where all of the localized modes disappear from the spectrum and compared it with the critical temperature of the deconfining transition. We found that the localization transition happens at the same temperature as the deconfining transition which indicates a strong relation between the two phenomena.

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arXiv2017

Landau levels in QCD in an external magnetic field

We will discuss the issue of Landau levels of quarks in lattice QCD in an external magnetic field. We will show that in the two-dimensional case the lowest Landau level can be identified unambiguously even if the strong interactions are turned on. Starting from this observation, we will then show how one can define a "lowest Landau level" in the four-dimensional case, and discuss how much of the observed effects of a magnetic field can be explained in terms of it. Our results can be used to test the validity of low-energy models of QCD that make use of the lowest-Landau-level approximation.

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arXiv2017

Temperature-dependence of the QCD topological susceptibility

We recently obtained an estimate of the axion mass based on the hypothesis that axions make up most of the dark matter in the universe. A key ingredient for this calculation was the temperature-dependence of the topological susceptibility of full QCD. Here we summarize the calculation of the susceptibility in a range of temperatures from well below the finite temperature cross-over to around 2 GeV. The two main difficulties of the calculation are the unexpectedly slow convergence of the susceptibility to its continuum limit and the poor sampling of nonzero topological sectors at high temperature. We discuss how these problems can be solved by two new techniques, the first one with reweighting using the quark zero modes and the second one with the integration method.

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arXiv2017

Localization and chiral properties near the ordering transition of an Anderson-like toy model for QCD

The Dirac operator in finite temperature QCD is equivalent to the Hamiltonian of an unconventional Anderson model, with on-site noise provided by the fluctuations of the Polyakov lines. The main features of its spectrum and eigenvectors, concerning the density of low modes and their localization properties, are qualitatively reproduced by a toy-model random Hamiltonian, based on an Ising-type spin model mimicking the dynamics of the Polyakov lines. Here we study the low modes of this toy model in the vicinity of the ordering transition of the spin model, and show that at the critical point the spectral density at the origin has a singularity, and the localization properties of the lowest modes change. This provides further evidence of the close relation between deconfinement, chiral transition and localization of the low modes.

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arXiv2017

Deconfinement, chiral transition and localisation in a QCD-like model

We study the problems of deconfinement, chiral symmetry restoration and localisation of the low Dirac eigenmodes in a toy model of QCD, namely unimproved staggered fermions on lattices of temporal extension $N_T=4$. This model displays a genuine deconfining and chirally-restoring first-order phase transition at some critical value of the gauge coupling. Our results indicate that the onset of localisation of the lowest Dirac eigenmodes takes place at the same critical coupling where the system undergoes the first-order phase transition. This provides further evidence of the close relation between deconfinement, chiral symmetry restoration and localisation of the low modes of the Dirac operator on the lattice.

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