scholarly journals Erratum: QCD Dirac Operator at Nonzero Chemical Potential: Lattice Data and Matrix Model [Phys. Rev. Lett.92, 102002 (2004)]

2006 ◽  
Vol 96 (2) ◽  
Author(s):  
Gernot Akemann ◽  
Tilo Wettig
Keyword(s):  
Dirac Operator ◽  
Matrix Model ◽  
Chemical Potential ◽  
Lattice Data

scholarly journals MATRIX MODELS AND QCD WITH CHEMICAL POTENTIAL

2007 ◽  
Vol 22 (06) ◽  
pp. 1077-1122 ◽  
Author(s):  
G. AKEMANN
Keyword(s):  
Dirac Operator ◽  
Matrix Models ◽  
Matrix Model ◽  
Chemical Potential ◽  
General Concept ◽  
Real Plane ◽  
Random Matrix Model ◽  
Symmetry Classes ◽  
Spectrum Matching ◽  
Model Approach

The random matrix model approach to quantum chromodynamics (QCD) with nonvanishing chemical potential is reviewed. The general concept using global symmetries is introduced, as well as its relation to field theory, the so-called epsilon regime of chiral perturbation theory (∊χPT). Two types of matrix model results are distinguished: phenomenological applications leading to phase diagrams, and an exact limit of the QCD Dirac operator spectrum matching with ∊χPT. All known analytic results for the spectrum of complex and symplectic matrix models with chemical potential are summarised for the symmetry classes of ordinary and adjoint QCD, respectively. These include correlation functions of Dirac operator eigenvalues in the complex plane for real chemical potential, and in the real plane for imaginary isospin chemical potential. Comparisons of these predictions to recent lattice simulations are also discussed.

scholarly journals Comparative studies of the deformation techniques for the singular-drift problem in the complex Langevin method

2018 ◽  
Vol 175 ◽  
pp. 07019 ◽  
Author(s):  
Yuta Ito ◽  
Jun Nishimura
Keyword(s):  
Low Temperature ◽  
Dirac Operator ◽  
Matrix Model ◽  
Comparative Studies ◽  
Deformation Parameter ◽  
High Density ◽  
Large N ◽  
Singular Drift ◽  
Different Types ◽  
Data Points

In application of the complex Langevin method to QCD at high density and low temperature, the singular-drift problem occurs due to the appearance of near-zero eigenvalues of the Dirac operator. In order to avoid this problem, we proposed to de-form the Dirac operator in such a way that the near-zero eigenvalues do not appear and to extrapolate the deformation parameter to zero from the available data points. Here we test three different types of deformation in a simple large-N matrix model, which under-goes an SSB due to the phase of the fermion determinant, and compare them to see the consistency with one another.

Quantum chromodynamics

2018 ◽  
Author(s):  
Marcos Marino
Keyword(s):  
Symmetry Breaking ◽  
Dirac Operator ◽  
Global Symmetries ◽  
Quantum Chromodynamics ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Matrix Theory ◽  
Global Symmetry

This article focuses on chiral random matrix theories with the global symmetries of quantum chromodynamics (QCD). In particular, it explains how random matrix theory (RMT) can be applied to the spectra of the Dirac operator both at zero chemical potential, when the Dirac operator is Hermitian, and at non-zero chemical potential, when the Dirac operator is non-Hermitian. Before discussing the spectra of these Dirac operators at non-zero chemical potential, the article considers spontaneous symmetry breaking in RMT and the QCD partition function. It then examines the global symmetries of QCD, taking into account the Dirac operator for a finite chiral basis, as well as the global symmetry breaking pattern and the Goldstone manifold in chiral random matrix theory (chRMT). It also describes the generating function for the Dirac spectrum and applications of chRMT to QCD to gauge degrees of freedom.

scholarly journals Complex Langevin simulation of a random matrix model at nonzero chemical potential

2018 ◽  
Vol 2018 (3) ◽  
Author(s):  
J. Bloch ◽  
J. Glesaaen ◽  
J. J. M. Verbaarschot ◽  
S. Zafeiropoulos
Keyword(s):  
Matrix Model ◽  
Random Matrix ◽  
Chemical Potential ◽  
Random Matrix Model ◽  
Langevin Simulation
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