Poisson-random matrix transition in the QCD Dirac spectrum

Kovács, Tamás; Pittler, Ferenc

doi:10.1103/physrevd.86.114515

Cited by 47 publications

(111 citation statements)

References 60 publications

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“…Such a power-law behaviour has been indeed observed for staggered fermions [7]. From this it immediately follows that [10]…”

Section: Jhep02(2017)055supporting

confidence: 48%

“…Eigenmodes above λ c , on the other hand, occupy the whole lattice volume. The curve λ c (T ) reaches zero at a temperature compatible with T c [7], as determined from thermodynamic observables [2,3]. The transition in the spectrum from localised to delocalised modes, taking place at the critical point λ c , was shown to be a genuine second-order phase transition [9], analogous to the metal-insulator transition in the Anderson model [38][39][40], which describes non-interacting electrons in a disordered crystal.…”

Section: Jhep02(2017)055mentioning

confidence: 99%

“…While at low temperatures the low-lying eigenmodes of the Dirac operator are delocalised on the entire lattice volume [35,36], above the crossover temperature, T c [2,3], they become spatially localised [4][5][6][7][8][9][10][11] on the scale of the inverse temperature [5,7,11]. From now on we focus on staggered fermions, both for simplicity and because of the larger amount of available evidence.…”

Section: Jhep02(2017)055mentioning

confidence: 99%

“…In recent years, it has become more and more clear that the decrease in the spectral density of low modes is accompanied by a change in the localisation properties of the corresponding eigenvectors: while at low temperatures the low modes are extended throughout the whole spatial volume, above the crossover temperature the lowest modes are spatially localised on the scale of the inverse temperature. Evidence for this behaviour has been obtained by means of lattice simulations with different fermion discretisations, namely staggered [4][5][6][7][8][9], overlap [6,10] and domain wall [11] fermions.…”

Section: Introductionmentioning

confidence: 99%

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

Giordano¹,

Katz²,

Kovács³

et al. 2017

J. High Energ. Phys.

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Abstract: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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“…Such a power-law behaviour has been indeed observed for staggered fermions [7]. From this it immediately follows that [10]…”

Section: Jhep02(2017)055supporting

confidence: 48%

Section: Jhep02(2017)055mentioning

confidence: 99%

Section: Jhep02(2017)055mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Giordano¹,

Katz²,

Kovács³

et al. 2017

J. High Energ. Phys.

Self Cite

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show abstract

“…Above the deconfinement temperature a gap emerges in the spectrum of the Dirac operator. At the same time the statistics of the low end of the spectrum becomes Poissonian, that is, the eigenmodes become localized [1][2][3][4][5], the same is true for the quenched case [1,6]. As nonlinear sigma models share a number of properties, such as asymptotic freedom and dynamical mass generation, with QCD, we will study the localization properties of CP(N-1) models in the following.…”

Section: Introductionmentioning

confidence: 99%

Anderson localization in sigma models

Bruckmann

Wellnhofer

2018

EPJ Web Conf.

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Abstract. In QCD above the chiral restoration temperature there exists an Anderson transition in the fermion spectrum from localized to delocalized modes. We investigate whether the same holds for nonlinear sigma models which share properties like dynamical mass generation and asymptotic freedom with QCD. In particular we study the spectra of fermions coupled to (quenched) CP(N-1) configurations at high temperatures. We compare results in two and three space-time dimensions: in two dimensions the Anderson transition is absent, since all fermion modes are localized, while in three dimensions it is present. Our measurements include a more recent observable characterizing level spacings: the distribution of ratios of consecutive level spacings.

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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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Poisson-random matrix transition in the QCD Dirac spectrum

Cited by 47 publications

References 60 publications

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

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

Anderson localization in sigma models

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

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