Proceedings of the 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021) 2022
DOI: 10.22323/1.396.0265
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Localisation of Dirac modes in finite-temperature $\mathbb{Z}_2$ gauge theory on the lattice

Abstract: The low-lying Dirac modes become localised at the finite-temperature transition in QCD and in other gauge theories, suggesting a general connection between their localisation and deconfinement. The simplest model where this connection can be tested is Z 2 gauge theory in 2+1 dimensions. We show that in this model the low modes in the staggered Dirac spectrum are delocalised in the confined phase and become localised in the deconfined phase. We also show that localised modes correlate with disorder in the Polya… Show more

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Cited by 1 publication
(2 citation statements)
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“…The sea/islands picture as presented above turns out to be too simplistic, and to require a refinement involving a more prominent role for spatial gauge fields [30]. Nonetheless, Polyakov-loop fluctuations away from order still retain their role as favourable localisation centres also in the refined version of the picture.…”
Section: Localisationmentioning
confidence: 96%
See 1 more Smart Citation
“…The sea/islands picture as presented above turns out to be too simplistic, and to require a refinement involving a more prominent role for spatial gauge fields [30]. Nonetheless, Polyakov-loop fluctuations away from order still retain their role as favourable localisation centres also in the refined version of the picture.…”
Section: Localisationmentioning
confidence: 96%
“…Such predictions have been confirmed so far by all the numerical studies carried out on the lattice. These include, besides QCD, also pure gauge theories with group SU(2) in 3+1D [25], SU(3) in 3+1D [26,27] and 2+1D [28], Z 2 [29] and Z 3 [30] in 2+1D, SU(3) with trace deformation in 3+1D [31], and a toy model for QCD with N f = 3 fermions on coarse lattices [18]. Localised low modes were not found in the confined phase in any of these cases.…”
Section: Localisationmentioning
confidence: 99%