The density in the density of states method

Abstract

It has been suggested that for QCD at finite baryon density the distribution of the phase angle, i.e. the angle defined as the imaginary part of the logarithm of the fermion determinant, has a simple Gaussian form. This distribution provides the density in the density of states approach to the sign problem. We calculate this phase angle distribution using i) the hadron resonance gas model; and ii) a combined strong coupling and hopping parameter expansion in lattice gauge theory. While the former model leads only to a Gaussian distribution, in the latter expansion we discover terms which cause the phase angle distribution to deviate, by relative amounts proportional to powers of the inverse lattice volume, from a simple Gaussian form. We show that despite the tiny inverse-volume deviation of the phase angle distribution from a simple Gaussian form, such non-Gaussian terms can have a substantial impact on observables computed in the density of states/reweighting approach to the sign problem.

43 pages, 4 figures

References in corpus (26)

• The phase diagram of dense QCD
• The QCD deconfinement transition for heavy quarks and all baryon chemical potentials
• The density of states method at non-zero chemical potential
• A new approach to the complex-action problem and its application to a nonperturbative study of superstring theory
• Phase of the Fermion Determinant at Nonzero Chemical Potential
• On the existence of the critical point in finite density lattice QCD
• Equation of State and Heavy-Quark Free Energy at Finite Temperature and Density in Two Flavor Lattice QCD with Wilson Quark Action
• Onset Transition to Cold Nuclear Matter from Lattice QCD with Heavy Quarks
• Phase diagrams of SU(N) gauge theories with fermions in various representations
• Complex Langevin dynamics and other approaches at finite chemical potential
• Lattice Monte Carlo calculations for unitary fermions in a finite box
• Centre symmetric 3d effective actions for thermal SU(N) Yang-Mills from strong coupling series
• Noise, sign problems, and statistics
• The QCD phase diagram at nonzero baryon, isospin and strangeness chemical potentials: Results from a hadron resonance gas model
• A Model for QCD at High Density and Large Quark Mass
• The pressure of strong coupling lattice QCD with heavy quarks, the hadron resonance gas model and the large N limit
• The Approach to the Thermodynamic Limit in Lattice QCD at μ\neq0
• The deconfinement transition of finite density QCD with heavy quarks from strong coupling series
• Distributions of the Phase Angle of the Fermion Determinant in QCD
• Strong coupling expansion for finite temperature Yang-Mills theory in the confined phase
• Simulating Dense Matter
• Phase structure of hot dense QCD by a histogram method
• The QCD sign problem as a total derivative
• Numerical study of QCD phase diagram at high temperature and density by a histogram method
• Histogram method in finite density QCD with phase quenched simulations
• Probability distribution functions in the finite density lattice QCD

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• Complex Langevin Dynamics for chiral Random Matrix Theory
• Comparison of complex Langevin and mean field methods applied to effective Polyakov line models
• Histograms in heavy-quark QCD at finite temperature and density
• Controlling the Sign Problem in Finite Density Quantum Field Theory
• New developments for dual methods in lattice field theory at non-zero density
• Phase Unwrapping and One-Dimensional Sign Problems
• Developments in lattice QCD for matter at high temperature and density
• Density of states method for the Z(3) spin model
• Anatomy of a strong residual sign problem on the thimbles
• Density of states techniques for lattice field theories using the functional fit approach (FFA)
• Chiral Condensation and Chiral Phase Diagram under Combined Rotation and Chemical Potential in Holographic QCD
• Preliminary QCD phase transition line for 695 MeV dynamical staggered fermions from effective Polyakov line actions
• Investigating corrections to a Gaussian distribution of the complex phase