Localization and topology in high temperature QCD Tam as G. Kov - - PowerPoint PPT Presentation

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Localization and topology in high temperature QCD Tam as G. Kov acs Institute for Nuclear Research, Debrecen, Hungary and E otv os University, Budapest, Hungary with eka R A. Vig University of Debrecen, Hungary Lattice

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Localization and topology in high temperature QCD

Tam´ as G. Kov´ acs

Institute for Nuclear Research, Debrecen, Hungary and E¨

tv¨
s University, Budapest, Hungary

with

R´ eka ´

A. Vig

University of Debrecen, Hungary Lattice 2018, July 24, 2018 Tam´ as G. Kov´ acs Localization and topology in high temperature QCD 1

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Above Tc low Dirac eigenmodes are localized

Below Tc

Chiral symmetry broken All eigenmodes delocalized spectral density eigenvalue

Tam´ as G. Kov´ acs Localization and topology in high temperature QCD 2

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Above Tc low Dirac eigenmodes are localized

Below Tc

Chiral symmetry broken All eigenmodes delocalized spectral density eigenvalue

Above Tc

Chiral symmetry restored Lowest eigenmodes localized spectral density eigenvalue

Tam´ as G. Kov´ acs Localization and topology in high temperature QCD 2

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Low Dirac modes are related to topology

Instanton − → quark zero mode Instanton + antiinstanton − → two cmplx conj. modes QCD at T < Tc : rI ≈ dIA instanton liquid Zero-mode zone − → finite density of modes at 0 (SχSB)

Tam´ as G. Kov´ acs Localization and topology in high temperature QCD 3

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Above Tc dilute instanton gas

Instanton density falls sharply with increasing T Zero modes exponentially localized rI,rA ≪ dIA ⇒ |λIA| small Can the zero-mode zone explain localized modes? Is this the ZMZ?

spectral density eigenvalue

Tam´ as G. Kov´ acs Localization and topology in high temperature QCD 4

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Above Tc dilute instanton gas

Instanton density falls sharply with increasing T Zero modes exponentially localized rI,rA ≪ dIA ⇒ |λIA| small Can the zero-mode zone explain localized modes? Is this the ZMZ?

spectral density eigenvalue

How to count modes in the zero-mode zone?

Tam´ as G. Kov´ acs Localization and topology in high temperature QCD 4

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Above Tc the ZMZ separates from bulk spectrum

Overlap spectral density

quenched Nt = 6, T = 1.06Tc zero modes removed rI,rA ≪ dIA ⇒ |λIA| small Already seen by

Edwards, Heller, Kiskis, Narayanan, PRD (1999)

Is this really the full ZMZ? Count topological charge: Q2 − → density of top. obj.-s (Assume non-interacting gas.)

Tam´ as G. Kov´ acs Localization and topology in high temperature QCD 5

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Instanton gas is non-interacting

The topological charge distribution at 1.06Tc

Simulation data compared with non-interacting instanton gas with the same topological susceptibility

Tam´ as G. Kov´ acs Localization and topology in high temperature QCD 6

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Peak at zero in the density is the ZMZ

The zero-mode zone in the overlap spectrum

Tam´ as G. Kov´ acs Localization and topology in high temperature QCD 7

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Localization extends beyond the ZMZ

The ZMZ and localized part in the overlap spectral density

Tam´ as G. Kov´ acs Localization and topology in high temperature QCD 8

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ZMZ ⊂ localized part of the spectrum

Fraction of localized modes contained in the ZMZ

Tam´ as G. Kov´ acs Localization and topology in high temperature QCD 9

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Staggered ZMZ also separates from bulk sectrum

Staggered spectral density

staggered + 2 stout Nt = 6,10 T = 1.06Tc zero modes included

Zero-mode zone can be identified Finer lattice − → better precision

Tam´ as G. Kov´ acs Localization and topology in high temperature QCD 10

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ZMZ accounts for tiny fraction of localized modes

Fraction of localized modes contained in the ZMZ

Tam´ as G. Kov´ acs Localization and topology in high temperature QCD 11

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Conclusions and outlook

“Good” chiral action − → ZMZ separates from bulk spectrum (staggered + 2 stout Nt = 6 already good). Zero-mode zone consists of localized modes. Only a small fraction of localized modes are in the ZMZ (falls sharply with icreasing T). Quark modes related to topology cannot explain localization. Dynamical quarks? (See talk by Holicki, Friday).

Tam´ as G. Kov´ acs Localization and topology in high temperature QCD 12

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Conclusions and outlook

“Good” chiral action − → ZMZ separates from bulk spectrum (staggered + 2 stout Nt = 6 already good). Zero-mode zone consists of localized modes. Only a small fraction of localized modes are in the ZMZ (falls sharply with icreasing T). Quark modes related to topology cannot explain localization. Dynamical quarks? (See talk by Holicki, Friday). interesting structure in locality properties of lowest modes. − → maybe connected to chiral polarization? (see

Alexandru and Horvath Lattice 2014 ) Tam´ as G. Kov´ acs Localization and topology in high temperature QCD 12

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Participation ratio for different volumes

fraction of volume occupied by eigenmode

Tam´ as G. Kov´ acs Localization and topology in high temperature QCD 13

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Participation ratio for different volumes

Lowest part of the spectrum

Tam´ as G. Kov´ acs Localization and topology in high temperature QCD 14