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

Giordano, Matteo; Katz, Sándor D.; Kovács, Tamás; Pittler, Ferenc

doi:10.1007/jhep02(2017)055

Cited by 25 publications

(40 citation statements)

References 70 publications

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Section: Contentssupporting

confidence: 72%

“…The mobility edge, λ c , vanishes at a temperature compatible with T c [16], suggesting that localisation of the low Dirac modes is closely related to deconfinement and chiral restoration. This is further supported by a similar coincidence of the three phenomena in other theories and models, like SU(3) pure gauge theory in 3+1 dimensions [22], the N f = 3 unimproved staggered fermion model mentioned above [23], and also in a toy model for QCD [24], devised in Ref.[25] precisely to study the issue of localisation.A qualitative understanding of the relation between deconfinement and localisation is provided by what in this paper will be referred to as the "sea/islands" picture of localisation [26,27]. The idea is that the local Polyakov lines provide a sort of local potential for the Dirac modes via the effective boundary condition that they impose on the eigenmodes.…”

supporting

confidence: 64%

“…Localisation in the high-temperature, deconfined phase has been observed also in other gauge theories (see Ref. [36] for a recent review), namely SU(2) [15] and SU(3) pure gauge theory [22], and SU(3) with N f = 3 flavours of unimproved rooted staggered fermions on N t = 4 lattices [23]. In these models the finite-temperature transition is a genuine phase transition, which provides a clean-cut setting for investigating the possible coincidence of deconfinement, chiral-symmetry restoration and localisation of the low Dirac modes.…”

Section: Localisation In Lattice Gauge Theoriesmentioning

confidence: 73%

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Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature

Giordano

2019

J. High Energ. Phys.

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I study the localisation properties of low Dirac eigenmodes in 2+1 dimensional SU(3) pure gauge theory, both in the low-temperature, confined and chirally-broken phase and in the high-temperature, deconfined and chirally-restored phase, by means of numerical lattice simulations. While these modes are delocalised at low temperature, they become localised at high temperature, up to a critical point in the Dirac spectrum where a BKT-type Anderson transition takes place. All results point to localisation appearing at the deconfinement temperature, and support previous expectations about the close relation between deconfinement, chiral symmetry breaking, and localisation. Contents1 Introduction 1 2 Localisation in lattice gauge theories 4 3 Lattice SU(3) pure gauge theory in 2+1 dimensions 7 4 Numerical results 9 4.1 Participation ratio 10 4.2 Spectral statistics 16 5 Conclusions and outlook 28with N f = 2 flavours of adjoint fermions [9] on the lattice: 2 here two phase transitions are present, a deconfining one at T dec and a chiral-symmetry-restoring one at T χ with T dec < T χ . Nonetheless, at T dec the chiral condensate jumps downwards, and a partial restoration of chiral symmetry happens via a first-order phase transition. It is also well known that the fate of chiral symmetry is determined by the spectrum of the Dirac operator near the origin. In fact, the celebrated Banks-Casher relation [11] establishes that the chiral condensate in the chiral limit is proportional to the spectral density of the Dirac operator near the origin. For finite but small quark masses, an accumulation of eigenmodes near the origin is still expected at low temperatures, leading to light pions and all the other phenomenological consequences for QCD due to its being close to a theory with spontaneously broken symmetry. At high temperatures, instead, the spectral density is expected to vanish near the origin, reflecting the restoration of chiral symmetry in the massless case. Given the close relation between confining and chiral properties of the theory, it is natural to wonder if confinement is somehow responsible for the accumulation of modes near the origin, and analogously if deconfinement causes the depletion of this spectral region. A similar question of course can be asked also for other gauge theories.Adding to the mistery, or possibly helping to solve it, a third phenomenon has been observed to take place in QCD around the critical temperature, namely the localisation of the lowest modes of the Dirac operator [12][13][14][15][16][17][18]. Numerical studies on the lattice have shown that while in the low-temperature phase all the Dirac modes are extended throughout the whole system, above T c the lowest modes get localised [12][13][14][15][16][17][18] on the scale of the inverse temperature [16]. More precisely, modes are localised up to a temperature-dependent critical point in the spectrum, λ c = λ c (T ). 3 At λ c , a second-order phase transition takes place in the spectrum [19], and modes become delocalised. This type of tr...

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Section: Contentssupporting

confidence: 72%

supporting

confidence: 64%

Section: Localisation In Lattice Gauge Theoriesmentioning

confidence: 73%

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Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature

Giordano

2019

J. High Energ. Phys.

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“…The interested reader can find a full description of our methodology and results in the published paper [1]. Analogous investigations were reported at this conference [6] and in recent papers [7,8].…”

Section: Introductionsupporting

confidence: 53%

Anderson localisation of Dirac eigenmodes in high temperature QCD

Cossu¹,

Hashimoto²

2017

Proceedings of 34th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2016)

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We investigate the properties of background gauge field configurations that act as disorder for the Anderson localization mechanism in the Dirac spectrum of QCD at high temperatures. We compute the eigenmodes of the Möbius domain-wall fermion operator on configurations generated for the SU(3) gauge theory with two flavors of fermions. We identify the source of localization of the eigenmodes with gauge configurations that are approximately self-dual and support local negative fluctuations of the Polyakov loop P L (x), in the bulk of P L ∼ 1. We investigate the dependence of these observations on the boundary conditions of the valence operator and interpret the results in terms of monopole-instanton structures. The results presented here are from [1], where we describe more details on the methods and conclusions.

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“…This system possesses a genuine phase transition in the thermodynamic limit, as the spatial box size goes to infinity while the temporal size is kept fixed at N t = 4 [9]. Here it was shown that the disappearance of localized modes at the low-end of the Dirac spectrum precisely coincides with the chiral phase transition [10]. However, the chiral phase transition of N t = 4 staggered quarks does not survive in the continuum limit.…”

Section: Introductionmentioning

confidence: 88%

Localization transition in SU(3) gauge theory

Kovács

Vig

2018

Phys. Rev. D

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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.I.

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

Cited by 25 publications

References 70 publications

Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature

Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature

Anderson localisation of Dirac eigenmodes in high temperature QCD

Localization transition in SU(3) gauge theory

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