scholarly journals Comparing iterative methods to compute the overlap Dirac operator at nonzero chemical potential

2009 ◽  
Author(s):  
Jacques Bloch ◽  
Tobias Breu ◽  
Tilo Wettig
Keyword(s):  
Dirac Operator ◽  
Iterative Methods ◽  
Chemical Potential

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 CHIRAL SYMMETRY BREAKING AT NONZERO CHEMICAL POTENTIAL

2006 ◽  
Vol 21 (04) ◽  
pp. 859-864 ◽  
Author(s):  
J. C. Osborn ◽  
K. Splittorff ◽  
J. J. M. Verbaarschot
Keyword(s):  
Partition Function ◽  
Symmetry Breaking ◽  
Dirac Operator ◽  
Chiral Symmetry ◽  
Chemical Potential ◽  
Chiral Symmetry Breaking ◽  
Chiral Condensate ◽  
Zero Temperature ◽  
Dirac Spectrum

We consider chiral symmetry breaking at nonzero chemical potential and discuss the relation with the spectrum of the Dirac operator. We solve the so called Silver Blaze Problem that the chiral condensate at zero temperature does not depend on the chemical potential while this is not the case for the Dirac spectrum and the weight of the partition function.

scholarly journals Selected inversion as key to a stable Langevin evolution across the QCD phase boundary

2018 ◽  
Vol 175 ◽  
pp. 07003 ◽  
Author(s):  
Jacques Bloch ◽  
Olaf Schenk
Keyword(s):  
Dirac Operator ◽  
Phase Boundary ◽  
Transition Region ◽  
Chemical Potential ◽  
Direct Solver ◽  
Drift Term ◽  
Inversion Technique

We present new results of full QCD at nonzero chemical potential. In PRD 92, 094516 (2015) the complex Langevin method was shown to break down when the inverse coupling decreases and enters the transition region from the deconfined to the confined phase. We found that the stochastic technique used to estimate the drift term can be very unstable for indefinite matrices. This may be avoided by using the full inverse of the Dirac operator, which is, however, too costly for four-dimensional lattices. The major breakthrough in this work was achieved by realizing that the inverse elements necessary for the drift term can be computed efficiently using the selected inversion technique provided by the parallel sparse direct solver package PARDISO. In our new study we show that no breakdown of the complex Langevin method is encountered and that simulations can be performed across the phase boundary.

scholarly journals Alternatives to the stochastic “noise vector” approach

2018 ◽  
Vol 175 ◽  
pp. 14022 ◽  
Author(s):  
Philippe de Forcrand ◽  
Benjamin Jäger
Keyword(s):  
Dirac Operator ◽  
Chemical Potential ◽  
Quark Condensate ◽  
Stochastic Noise ◽  
Polynomial Approximations ◽  
Taylor Coefficients ◽  
Alternative Approaches ◽  
Vector Approach

Several important observables, like the quark condensate and the Taylor coefficients of the expansion of the QCD pressure with respect to the chemical potential, are based on the trace of the inverse Dirac operator and of its powers. Such traces are traditionally estimated with “noise vectors” sandwiching the operator. We explore alternative approaches based on polynomial approximations of the inverse Dirac operator.

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

2005 ◽  
Vol 140 ◽  
pp. 568-570 ◽  
Author(s):  
Gernot Akemann ◽  
Elmar Bittner ◽  
Maria-Paola Lombardo ◽  
Harald Markum ◽  
Rainer Pullirsch
Keyword(s):  
Dirac Operator ◽  
Matrix Models ◽  
Chemical Potential ◽  
Density Profiles ◽  
Operator Eigenvalues
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