Density profiles of small Dirac operator eigenvalues for two color QCD at nonzero chemical potential compared to matrix models

Akemann, Gernot; Bittner, Elmar; Lombardo, Maria-Paola; Markum, H.; Pullirsch, Rainer

doi:10.1016/j.nuclphysbps.2004.11.301

Cited by 7 publications

(15 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As the symmetry-violating effect of µ in the two-color QCD is inherent in its low-energy effective theory and is well under control, one can predict the fluctuation of the Dirac eigenvalues in the ε regime (i.e., below the Thouless energy) from its zero-momentum part. This, in turn, is equivalent to the chiral Gaussian orthogonal or symplectic ensemble (chGOE, chGSE) [15,16] in its non-Hermitian extended form by the introduction of schematic (real) µ component [17,18].…”

Section: Introductionmentioning

confidence: 99%

Universality crossover between chiral random matrix ensembles and twisted SU(2) lattice Dirac spectra

Nishigaki¹

2012

Phys. Rev. D

View full text Add to dashboard Cite

Motivated by the statistical fluctuation of Dirac spectrum of QCD-like theories subjected to (pseudo)reality-violating perturbations and in the ε regime, we compute the smallest eigenvalue distribution and the level spacing distribution of chiral and nonchiral parametric random matrix ensembles of Dyson-Mehta-Pandey type. To this end we employ the Nyström-type method to numerically evaluate the Fredholm Pfaffian of the integral kernel for the chG(O,S)E-chGUE and G(O,S)E-GUE crossover. We confirm the validity and universality of our results by comparing them with several lattice models, namely fundamental and adjoint staggered Dirac spectra of SU(2) quenched lattice gauge theory under the twisted boundary condition (imaginary chemical potential) or perturbed by phase noise. Both in the zero-virtuality region and in the spectral bulk, excellent one-parameter fitting is achieved already on a small 4 4 lattice. Anticipated scaling of the fitting parameter with the twisting phase, mean level spacing, and the system size allows for precise determination of the pion decay (diffusion) constant F in the low-energy effective Lagrangian.2 boundary condition or imaginary chemical potential) [19][20][21]. These cases are distinct from the previously mentioned case in that the Dirac eigenvalues stay real even after the inclusion of symmetry violations and their statistical behavior exhibits crossover, rather than develops into the complex plane. In terms of the effective σ-model description, these two cases are almost identical, save for the difference of the sign of trBQ †B Q term (µ 2 F 2 or (iµ) 2 F 2 , see Sec. IV.).Crossover between universality classes of Hermitian random matrix ensembles [22][23][24], namely GOE-GUE and GSE-GUE, is extensively studied in the context of disordered [25,26] and quantum-chaotic Hamiltonians [27][28][29] with its time-reversal invariance slightly broken by weak magnetic field or AB flux applied [30]. On the other hand, the chiral or superconducting variant of universality crossover appears to be a relatively unexplored field so far. Previous attempts in this area either focused on the level number variance and the spectral form factor (both of which are integral transforms of the two-level correlator and insensitive to chiralness) of two-color QCD with AB fluxes versus GOE-GUE crossover [19], or have fruited in a series of tours de force by Damgaard and collaborators [31,32] devoted to the analytical computation of the level density and individual small eigenvalue distributions for the spectral crossover within the chiral Gaussian unitary ensemble (chGUE) class, due to the imaginary isospin chemical potential. Despite that analytic results for the microscopic spectral correlation functions are known for some time for chGOE-chGUE and chGSE-chGUE crossover [33,34], 1 they are yet to encounter with physical application. To the best of our knowledge, the only example of the crossover involving different Hermitian chiral universality classes discussed in a physical setting is the CI-C transition ...

show abstract

Section: Introductionmentioning

confidence: 99%

Universality crossover between chiral random matrix ensembles and twisted SU(2) lattice Dirac spectra

Nishigaki¹

2012

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…It is given by a two-MM generalising the chiral Symplectic Ensemble (chSE) [11] and was solved for two-fold degenerate quark masses [5]. Its predictions were compared to quenched [12] and unquenched Lattice simulations [13] 1 for 2-colour QCD using staggered fermions. Because of this success we expect that this MM is equivalent to the corresponding chiral Lagrangian in the epsilon-regime [15].…”

Section: Introductionmentioning

confidence: 99%

Massive partition functions and complex eigenvalue correlations in matrix models with symplectic symmetry

Akemann

Basile

2007

Nuclear Physics B

View full text Add to dashboard Cite

We compute all massive partition functions or characteristic polynomials and their complex eigenvalue correlation functions for non-Hermitean extensions of the symplectic and chiral symplectic ensemble of random matrices. Our results are valid for general weight functions without degeneracies of the mass parameters. The expressions we derive are given in terms of the Pfaffian of skew orthogonal polynomials in the complex plane and their kernel. They are much simpler than the corresponding expressions for symplectic matrix models with real eigenvalues, and we explicitly show how to recover these in the Hermitean limit. This explains the appearance of three different kernels as quaternion matrix elements there in terms of derivatives of a single kernel here.

show abstract

“…Away from the edge Fig. 2 is already very close to 1, to which we compared our preliminary data [14].…”

mentioning

confidence: 71%

“…Unquenching is seen only for small m depending on the particular size of the system. Our preliminary results for SU2 have been presented in [14], compared to SU2 at 0 [15] and quenched QCD at Þ 0 [16,17].…”

mentioning

confidence: 99%

Unquenched Complex Dirac Spectra at Nonzero Chemical Potential: Two-Color QCD Lattice Data versus Matrix Model

Akemann

Bittner

2006

Phys. Rev. Lett.

Self Cite

View full text Add to dashboard Cite

We compare analytic predictions of non-Hermitian chiral random matrix theory with the complex Dirac operator eigenvalue spectrum of two-color lattice gauge theory with dynamical fermions at nonzero chemical potential. The Dirac eigenvalues come in complex conjugate pairs, making the action of this theory real and positive for our choice of two staggered flavors. This enables us to use standard Monte Carlo simulations in testing the influence of the chemical potential and quark mass on complex eigenvalues close to the origin. We find excellent agreement between the analytic predictions and our data for two different volumes over a range of chemical potentials below the chiral phase transition. In particular, we detect the effect of unquenching when going to very small quark masses.

show abstract

Density profiles of small Dirac operator eigenvalues for two color QCD at nonzero chemical potential compared to matrix models

Cited by 7 publications

References 16 publications

Universality crossover between chiral random matrix ensembles and twisted SU(2) lattice Dirac spectra

Universality crossover between chiral random matrix ensembles and twisted SU(2) lattice Dirac spectra

Massive partition functions and complex eigenvalue correlations in matrix models with symplectic symmetry

Unquenched Complex Dirac Spectra at Nonzero Chemical Potential: Two-Color QCD Lattice Data versus Matrix Model

Contact Info

Product

Resources

About