Eigenvalue Density of the non-Hermitian Wilson Dirac Operator

Abstract

We find the lattice spacing dependence of the eigenvalue density of the non-Hermitian Wilson Dirac operator in the $\epsilon$-domain. The starting point is the joint probability density of the corresponding random matrix theory. In addition to the density of the complex eigenvalues we also obtain the density of the real eigenvalues separately for positive and negative chiralities as well as an explicit analytical expression for the number of additional real modes.

4 pages, 6 figures, PACS: 12.38.Gc, 05.50.+q, 02.10.Yn, 11.15.Ha

References in corpus (5)

• Topological Transition in a Non-Hermitian Quantum Walk
• Matrix Models and QCD with Chemical Potential
• Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
• Discretization errors in the spectrum of the Hermitian Wilson-Dirac operator
• Staggered chiral random matrix theory

Cited by in corpus (20)

• Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model
• Complex Langevin Simulation of a Random Matrix Model at Nonzero Chemical Potential
• Spectral properties of the Wilson Dirac operator in the $\epsilon$-regime
• Phase Diagram of Dynamical Twisted Mass Wilson Fermions at Finite Isospin Chemical Potential
• Spectral Properties of the Wilson Dirac Operator and random matrix theory
• The Realization of the Sharpe-Singleton Scenario
• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• New Ways to Determine Low-Energy Constants with Wilson Fermions
• GUE-chGUE Transition preserving Chirality at finite Matrix Size
• Complex Langevin simulations of a finite density matrix model for QCD
• Microscopic Spectral Density of the Wilson Dirac Operator for One Flavor
• Non-Hermitian CP-Symmetric Dirac Hamiltonians with Real Energy Eigenvalues
• Random Matrix Models for Dirac Operators at finite Lattice Spacing
• Progress on the Microscopic Spectrum of the Dirac Operator for QCD with Wilson Fermions
• Surprising Pfaffian factorizations in Random Matrix Theory with Dyson index $\beta =2$
• Topology, Random Matrix Theory and the spectrum of the Wilson Dirac operator
• Exploring the Aoki regime
• Wilson chiral perturbation theory for dynamical twisted mass fermions vs lattice data - a case study
• Progress on Complex Langevin simulations of a finite density matrix model for QCD
• The Effect of the Low Energy Constants on the Spectral Properties of the Wilson Dirac Operator