The supersymmetric transfer matrix for linear chains with nondiagonal disorder

Constantinescu, Florin

doi:10.1007/bf01019159

Cited by 18 publications

(35 citation statements)

References 12 publications

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“…However this general situation is quite non-trivial to verify. It goes back to Cauchy-like integrals of superfunctions invariant under supersymmetric groups [48,[54][55][56][57][58] which were first derived in a general form by Wegner [59]. Indeed the integrand in Eq.…”

Section: A Discussion Of the Partition Function At Finite Amentioning

confidence: 99%

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Dirac spectrum of the Wilson-Dirac operator for QCD with two colors

2015

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We study the lattice artefacts of the Wilson Dirac operator for QCD with two colors and fermions in the fundamental representation from the viewpoint of chiral perturbation theory. These effects are studied with the help of the following spectral observables: the level density of the Hermitian Wilson Dirac operator, the distribution of chirality over the real eigenvalues, and the chiral condensate for the quenched as well as for the unquenched theory. We provide analytical expressions for all these quantities. Moreover we derive constraints for the level density of the real eigenvalues of the non-Hermitian Wilson Dirac operator and the number of additional real modes. The latter is a good measure for the strength of lattice artefacts. All computations are confirmed by Monte Carlo simulations of the corresponding random matrix theory which agrees with chiral perturbation theory of two color QCD with Wilson fermions.

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Section: A Discussion Of the Partition Function At Finite Amentioning

confidence: 99%

“…(56). To calculate the inverse of U and its traces thereof we split U into a numerical part U 0 which is a diagonal matrix and a nilpotent part G,…”

Section: Integration Over the Grassmann Variablesmentioning

confidence: 99%

Dirac spectrum of the Wilson-Dirac operator for QCD with two colors

2015

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“…[45,46,47] for slightly modified versions. Let l ∈ N be a positive integer and f be an integrable and smooth superfunction on the set of supermatrices Herm…”

Section: Projection Formula For Dyson's Threefold Waymentioning

confidence: 99%

The supersymmetry method for chiral random matrix theory with arbitrary rotation-invariant weights

Kaymak¹,

Kieburg²,

Guhr³

2014

J. Phys. A: Math. Theor.

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Abstract. In the past few years, the supersymmetry method was generalized to real-symmetric, Hermitean, and Hermitean self-dual random matrices drawn from ensembles invariant under the orthogonal, unitary, and unitary symplectic group, respectively. We extend this supersymmetry approach to chiral random matrix theory invariant under the three chiral unitary groups in a unifying way. Thereby we generalize a projection formula providing a direct link and, hence, a 'short cut' between the probability density in ordinary space and the one in superspace. We emphasize that this point was one of the main problems and critiques of the supersymmetry method since only implicit dualities between ordinary and superspace were known before. As examples we apply this approach to the calculation of the supersymmetric analogue of a Lorentzian (Cauchy) ensemble and an ensemble with a quartic potential. Moreover we consider the partially quenched partition function of the three chiral Gaussian ensembles corresponding to four-dimensional continuum QCD. We identify a natural splitting of the chiral Lagrangian in its lowest order into a part of the physical mesons and a part associated to source terms generating the observables, e.g. the level density of the Dirac operator.

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“…The b-dependence is indeed only apparent because of the Cauchy-like integration theorems in superspaces [50][51][52][53][54][55].…”

Section: Asymptotics Of the Level Densitymentioning

confidence: 99%

“…The normalization has been calculated by choosing b 1 = b±ıε where Cauchy-like integral theorems [50][51][52][53][54][55] apply. In the parametrization of σ, the variables a, b, c, σ 2 are real commuting whereas α, β are complex Grassmann variables.…”

Section: Eigenvalue Density In the Real Ensemblementioning

confidence: 99%

The Correlated Jacobi and the Correlated Cauchy–Lorentz Ensembles

et al. 2015

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We calculate the k-point generating function of the correlated Jacobi ensemble using supersymmetric methods. We use the result for complex matrices for k = 1 to derive a closed-form expression for eigenvalue density. For real matrices we obtain the density in terms of a twofold integral that we evaluate numerically. For both expressions we find agreement when comparing with Monte Carlo simulations. Relations between these quantities for the Jacobi and the Cauchy-Lorentz ensemble are derived.

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The supersymmetric transfer matrix for linear chains with nondiagonal disorder

Cited by 18 publications

References 12 publications

Dirac spectrum of the Wilson-Dirac operator for QCD with two colors

Dirac spectrum of the Wilson-Dirac operator for QCD with two colors

The supersymmetry method for chiral random matrix theory with arbitrary rotation-invariant weights

The Correlated Jacobi and the Correlated Cauchy–Lorentz Ensembles

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