The Approach to the Thermodynamic Limit in Lattice QCD at μ\neq0

Abstract

The expectation value of the complex phase factor of the fermion determinant is computed to leading order in the $p$-expansion of the chiral Lagrangian. The computation is valid for $\mu <m_{\pi }/2$ and determines the dependence of the sign problem on the volume and on the geometric shape of the volume. In the thermodynamic limit with $L_i\to \infty$ at fixed temperature $1/L_0$, the average phase factor vanishes. In the low temperature limit where $L_i/L_0$ is fixed as $L_i$ becomes large the average phase factor approaches one. The results for a finite volume compare well with lattice results obtained by Allton {\it et al}.. After taking appropriate limits, we reproduce previously derived results for the $\epsilon$-regime and for 1-dimensional QCD. The distribution of the phase itself is also computed.

arXiv comment9 pages, 5 figures

References in corpus (40)

• Critical point of QCD at finite T and μ, lattice results for physical quark masses
• The QCD phase diagram for small densities from imaginary chemical potential
• Lattice determination of the critical point of QCD at finite T and μ
• The QCD thermal phase transition in the presence of a small chemical potential
• Finite density QCD via imaginary chemical potential
• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• Quark Mass and Flavour Dependence of the QCD Phase Transition
• Thermodynamics of Two Flavor QCD to Sixth Order in Quark Chemical Potential
• The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way
• The Equation of State for Two Flavor QCD at Non-zero Chemical Potential
• Random matrix model of QCD at finite density and the nature of the quenched limit
• The QCD Phase Diagram for Three Degenerate Flavors and Small Baryon Density
• Imaginary chemical potential and finite fermion density on the lattice
• Pressure and non-linear susceptibilities in QCD at finite chemical potentials
• The pressure of QCD at finite temperatures and chemical potentials
• Universal results from an alternate random matrix model for QCD with a baryon chemical potential
• Results on Finite Density QCD
• Quark number susceptibilities from HTL-resummed thermodynamics
• The density of states method at non-zero chemical potential
• Lattice QCD at finite density via a new canonical approach
• The strongly interacting Quark Gluon Plasma, and the critical behaviour of QCD at imaginary chemical potential
• Factorization of Correlation Functions and the Replica Limit of the Toda Lattice Equation
• Unquenched QCD Dirac Operator Spectra at Nonzero Baryon Chemical Potential
• Partially Quenched Chiral Perturbation Theory and the Replica Method
• Phase of the Fermion Determinant at Nonzero Chemical Potential
• Diquark Condensate in QCD with Two Colors at Next-to-Leading Order
• Chiral Symmetry Breaking and the Dirac Spectrum at Nonzero Chemical Potential
• The QCD Sign Problem for Small Chemical Potential
• Thermodynamics of chiral symmetry at low densities
• What do lattice baryonic susceptibilities tell us about quarks, diquarks and baryons at $T>Tc$?
• The factorization method for systems with a complex action -a test in Random Matrix Theory for finite density QCD-
• Lee-Yang zero analysis for the study of QCD phase structure
• Remarks on the multi-parameter reweighting method for the study of lattice QCD at non-zero temperature and density
• Microscopic correlation functions for the QCD Dirac operator with chemical potential
• The solution of a chiral random matrix model with complex eigenvalues
• Instantons and the Chiral Phase Transition at non-zero Baryon Density
• Imaginary chemical potentials and the phase of the fermionic determinant
• The role of the Polyakov loop in finite density QCD
• Phase Fluctuation of Fermion Determinant in Lattice QCD at Finite Density
• The Sign Problem via Imaginary Chemical Potential

Cited by in corpus (29)

• The phase diagram of dense QCD
• Canonical partition function and finite density phase transition in lattice QCD
• Introductory lectures on lattice QCD at nonzero baryon number
• Thermodynamics of two flavor QCD from imaginary chemical potentials
• Complex Langevin Dynamics for chiral Random Matrix Theory
• Full simulation of chiral Random Matrix Theory at non-zero chemical potential by Complex Langevin
• A Random Matrix Study of the QCD Sign Problem
• Histograms in heavy-quark QCD at finite temperature and density
• Lattice QCD at finite temperature and density in the phase-quenched approximation
• Phase Diagram of Dynamical Twisted Mass Wilson Fermions at Finite Isospin Chemical Potential
• Distributions of the Phase Angle of the Fermion Determinant in QCD
• Phase structure of hot dense QCD by a histogram method
• Average phase factor in the PNJL model
• The density in the density of states method
• On the sign problem in dense QCD
• A study of the sign problem for lattice QCD with chemical potential
• The QCD sign problem as a total derivative
• Distribution of Canonical Determinants in QCD
• On the phase of quark determinant in lattice QCD with finite chemical potential
• The sign problem across the QCD phase transition
• Simple QED- and QCD-like Models at Finite Density
• Lessons from Random Matrix Theory for QCD at Finite Density
• Developments in lattice QCD for matter at high temperature and density
• Towards extremely dense matter on the lattice
• The Fluctuations of the Quark Number and of the Chiral Condensate
• Advances in non-relativistic matter via complex Langevin approaches
• Triage of the Sign Problem
• How the Quark Number fluctuates in QCD at small chemical potential
• Investigating corrections to a Gaussian distribution of the complex phase