Microscopic universality and the chiral phase transition in two flavor QCD

Farchioni, F.; Forcrand, Philippe de; Hip, Ivan; Lang, C. B.; Splittorff, K.

doi:10.1103/physrevd.62.014503

Cited by 30 publications

(40 citation statements)

References 39 publications

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“…The properties of the Dirac spectrum have been analyzed in many lattice QCD simulations [ 33,3,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48] [ 49,50,51,52,53,54] and have been found to be in complete agreement with the conclusions of the previous section. We only show three representative examples.…”

Section: Lattice Resultssupporting

confidence: 73%

Dirac Spectra and Real QCD at Nonzero Chemical Potential

Toublan¹,

Verbaarschot²

2002

Continuous Advances in QCD 2002

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We show that QCD Dirac spectra well below Λ QCD , both at zero and at nonzero chemical potential, can be obtained from a chiral Lagrangian. At nonzero chemical potential Goldstone bosons with nonzero baryon number condense beyond a critical value. Such superfluid phase transition is likely to occur in any system with a chemical potential with the quantum numbers of the Goldstone bosons. We discuss the phase diagram for one such system, QCD with two colors, and show the existence of a tricritical point in an effective potential approach.

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Section: Lattice Resultssupporting

confidence: 73%

Dirac Spectra and Real QCD at Nonzero Chemical Potential

Toublan¹,

Verbaarschot²

2002

Continuous Advances in QCD 2002

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“…[5], partly motivated by the understanding of the fate of U(1) A when SU(N F ) A is restored. The observation that low-lying eigenvalues at T T c neither obey the Airy statistics of the 'soft' band edge of classical random matrices [37,38], nor the statistics of random matrices at the (multi)critical edge [39,40], left open the issue of characterizing these eigenvalues and associated eigenstates.…”

Section: Qcd Dirac Spectra Above T Cmentioning

confidence: 99%

Critical statistics at the mobility edge of QCD Dirac spectra

Nishigaki¹,

Giordano²,

Kovács³

et al. 2014

Proceedings of 31st International Symposium on Lattice Field Theory LATTICE 2013 — PoS(LATTICE 2013)

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We examine statistical fluctuation of eigenvalues from the near-edge bulk of QCD Dirac spectra above the critical temperature. For completeness we start by reviewing on the spectral property of Anderson tight-binding Hamiltonians as described by nonlinear σ models and random matrices, and on the scale-invariant intermediate spectral statistics at the mobility edge. By fitting the level spacing distributions, deformed random matrix ensembles which model multifractality of the wave functions typical of the Anderson localization transition, are shown to provide an excellent effective description for such a critical statistics. Next we carry over the above strategy for the Anderson Hamiltonians to the Dirac spectra. For the staggered Dirac operators of QCD with 2+1 flavors of dynamical quarks at the physical point and of SU(2) quenched gauge theory, we identify the precise location of the mobility edge as the scaleinvariant fixed point of the level spacing distribution. The eigenvalues around the mobility edge are shown to obey critical statistics described by the aforementioned deformed random matrix ensembles of unitary and symplectic classes. The best-fitting deformation parameter for QCD at the physical point turns out to be consistent with the Anderson Hamiltonian in the unitary class. Finally, we propose a method of locating the mobility edge at the origin of QCD Dirac spectrum around the critical temperature, by the use of individual eigenvalue distributions of deformed chiral random matrices.

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“…Very recently a study of just the low-lying Dirac operator eigenvalues near T c has actually indicated the presence of a gap at large lattice volumes [21]. Again the statistics was rather limited, and only a small number of the lowest-lying eigenvalues could be included (varying between 8 and 10).…”

Section: Introductionmentioning

confidence: 99%

“…The present study will in many ways follow the same lines of thought as Ref. [21], but we shall have much larger statistics, and we shall also probe some different aspects. In particular, we are also interested in seeing whether quenching causes a different behavior of the smallest eigenvalues near T c compared with dynamical fermions.…”

Section: Introductionmentioning

confidence: 99%

Low-lying eigenvalues of the QCD Dirac operator at finite temperature

Damgaard¹,

Heller

Niclasen³

et al. 2000

Nuclear Physics B

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We compute the low-lying spectrum of the staggered Dirac operator above and below the finite temperature phase transition in both quenched QCD and in dynamical four flavor QCD. In both cases we find, in the high temperature phase, a density with close to square root behavior, ρ(λ) ∼ (λ − λ 0 ) 1/2 . In the quenched simulations we find, in addition, a volume independent tail of small eigenvalues extending down to zero. In the dynamical simulations we also find a tail, decreasing with decreasing mass, at the small end of the spectrum. However, the tail falls off quite quickly and does not seem to extend to zero at these couplings. We find that the distribution of the smallest Dirac operator eigenvalues provides an efficient observable for an accurate determination of the location of the chiral phase transition, as first suggested by Jackson and Verbaarschot.

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Microscopic universality and the chiral phase transition in two flavor QCD

Cited by 30 publications

References 39 publications

Dirac Spectra and Real QCD at Nonzero Chemical Potential

Dirac Spectra and Real QCD at Nonzero Chemical Potential

Critical statistics at the mobility edge of QCD Dirac spectra

Low-lying eigenvalues of the QCD Dirac operator at finite temperature

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