Dense Quarks, and the Fermion Sign Problem, in a SU(N) Matrix Model

Abstract

We study the effect of dense quarks in a SU(N) matrix model of deconfinement. For three or more colors, the quark contribution to the loop potential is complex. After adding the charge conjugate loop, the measure of the matrix integral is real, but not positive definite. In a matrix model, quarks act like a background Z(N) field; at nonzero density, the background field also has an imaginary part, proportional to the imaginary part of the loop. Consequently, while the expectation values of the loop and its complex conjugate are both real, they are not equal. These results suggest a possible approach to the fermion sign problem in lattice QCD.

9 pages, 3 figures

References in corpus (15)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Thermodynamics of Two Flavor QCD to Sixth Order in Quark Chemical Potential
• Static quark anti-quark free energy and the running coupling at finite temperature
• The critical end point of QCD
• Free energy of a static quark anti-quark pair and the renormalized Polyakov loop in three flavor QCD
• A first order deconfinement transition in large N Yang-Mills theory on a small 3-sphere
• QCD thermodynamics from an imaginary mu_B: results on the four flavor lattice model
• Black hole-black string phase transitions in thermal 1+1-dimensional supersymmetric Yang-Mills theory on a circle
• Unquenched QCD Dirac Operator Spectra at Nonzero Baryon Chemical Potential
• Finite temperature effective action, AdS_5 black holes, and 1/N expansion
• Chiral Symmetry Breaking and the Dirac Spectrum at Nonzero Chemical Potential
• Deconfinement in Matrix Models about the Gross--Witten Point
• A Pendant for Polya: The One-Loop Partition Function of N=4 SYM on R x S^3
• Study of CP(N-1) θ-Vacua by Cluster-Simulation of SU(N) Quantum Spin Ladders
• Theoretical review of diffractive phenomena

Cited by in corpus (105)

• Phases of QCD: lattice thermodynamics and a field theoretical model
• Phases of Dense Quarks at Large N_c
• Polyakov loop, diquarks and the two-flavour phase diagram
• Phase diagrams in the three-flavor Nambu--Jona-Lasinio model with the Polyakov loop
• Phase diagram of hot QCD in an external magnetic field: possible splitting of deconfinement and chiral transitions
• Susceptibilities and the Phase Structure of a Chiral Model with Polyakov Loops
• Hadron Production in Ultra-relativistic Nuclear Collisions: Quarkyonic Matter and a Triple Point in the Phase Diagram of QCD
• The chiral and deconfinement crossover transitions: PNJL model beyond mean field
• Thermodynamics of the PNJL model
• Renormalized Polyakov loops in many representations
• Thermodynamics of the PNJL model with nonzero baryon and isospin chemical potentials
• The hadronic SU(3) Parity Doublet Model for Dense Matter, its extension to quarks and the strange equation of state
• Polyakov loop modeling for hot QCD
• An effective chiral Hadron-Quark Equation of State
• Effective Theory of Wilson Lines and Deconfinement
• Three flavor Nambu-Jona Lasinio model with Polyakov loop and competition with nuclear matter
• Entanglement between deconfinement transition and chiral symmetry restoration
• The strongly interacting Quark Gluon Plasma, and the critical behaviour of QCD at imaginary chemical potential
• Quark number susceptibilities: lattice QCD versus PNJL model
• Equation of state for hot QCD and compact stars from a mean field approach
• Polyakov loop extended NJL model with imaginary chemical potential
• Lefschetz-thimble analysis of the sign problem in one-site fermion model
• PNJL model with a Van der Monde term
• How Wide is the Transition to Deconfinement?
• Phase diagram and surface tension in the three-flavor Polyakov-quark-meson model
• Thermal entropy of a quark-antiquark pair above and below deconfinement from a dynamical holographic QCD model
• Model study of the sign problem in the mean-field approximation
• Nonlocal SU(3) chiral quark models at finite temperature: the role of the Polyakov loop
• Hybrid Stars in an SU(3) Parity Doublet Model
• QCD matter in extreme environments
• Nonlocal Polyakov-Nambu-Jona-Lasinio model with wavefunction renormalization at finite temperature and chemical potential
• Determination of QCD phase diagram from the imaginary chemical potential region
• Phase diagram in the imaginary chemical potential region and extended Z3 symmetry
• Higher-order baryon number susceptibilities: interplay between the chiral and the nuclear liquid-gas transitions
• Meson properties at finite temperature in a three flavor nonlocal chiral quark model with Polyakov loop
• Chiral and deconfinement transitions in a magnetic background using the functional renormalization group with the Polyakov loop
• Small shear viscosity in the semi quark gluon plasma
• Gauge dynamics in the PNJL model: Color neutrality and Casimir scaling
• Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
• Roberge-Weiss phase transition and its endpoint
• Isentropic thermodynamics in the PNJL model
• Chiral matrix model of the semi-Quark Gluon Plasma in QCD
• Hard thermal loops, to quadratic order, in the background of a spatial 't Hooft loop
• A perturbative study of the QCD phase diagram for heavy quarks at nonzero chemical potential: two-loop corrections
• Vector-type four-quark interaction and its impact on QCD phase structure
• Enforced neutrality and color-flavor unlocking in the three-flavor Polyakov-loop NJL model
• Confinement and Z_3 symmetry in three-flavor QCD
• Deconfinement and chiral restoration in nonlocal SU(3) chiral quark models
• Universal aspects of the phase diagram of QCD with heavy quarks
• Equation of state of a quark-meson mixture in the improved-PNJL model at finite chemical potential
• Differences and similarities between fundamental and adjoint matters in SU(N) gauge theories
• Multi-flavor massless QED${}_2$ at finite densities via Lefschetz thimbles
• Polyakov loop fluctuations and deconfinement in the limit of heavy quarks
• Strangeness Neutrality and QCD Thermodynamics
• The thermodynamics for a hadronic gas of fireballs with internal color structures and chiral fields
• Color neutrality effects in the phase diagram of the PNJL model
• The quarkynic phase and the Z_{Nc} symmetry
• SU(3) Polyakov linear-sigma model: Conductivity and viscous properties of QCD matter in thermal medium
• Understanding of QCD at high density from Z3-symmetric QCD-like theory
• Correlations among discontinuities in QCD phase diagram
• Strong magnetic fields in nonlocal chiral quark models
• Crystalline Ground States in Polyakov-loop extended Nambu--Jona-Lasinio Models
• Mean field theory of effective spin models as a baryon fugacity expansion
• Meson mass at real and imaginary chemical potentials
• Thermodynamics and phase diagrams of Polyakov-loop extended chiral models
• Chiral and deconfinement transitions in strong coupling lattice QCD with finite coupling and Polyakov loop effects
• Supporting the search for the CEP location with nonlocal PNJL models constrained by Lattice QCD
• Isospin symmetry breaking and baryon-isospin correlations from Polyakov$-$Nambu$-$Jona-Lasinio model
• The Heavy Quark Free Energy in QCD and in Gauge Theories with Gravity Duals
• On the neutrality issue in the Polyakov-loop NJL model
• Finite-temperature phase transitions of third and higher order in gauge theories at large $N$
• Strong-interaction matter under extreme conditions from chiral quark models with nonlocal separable interactions
• The Polyakov loop in various representations in the confined phase of QCD
• Free energy of a Holonomous Plasma
• Violations of parity and charge conjugation in the theta vacuum with imaginary chemical potential
• Effective models of a semi-quark gluon plasma
• Themodynamics for pure SU($2$) gauge theory using gradient flow
• Mean eigenvalues for simple, simply connected, compact Lie groups
• In medium properties of axion within a Polyakov loop enhanced Nambu-Jona-Lasinio model
• Langevin dynamics of the pure SU(2) deconfining transition
• Interplay between sign problem and Z_3 symmetry in three-dimensional Potts model
• Spontaneous parity and charge-conjugation violations at real isospin and imaginary baryon chemical potentials
• Comparison between the continuum threshold and the Polyakov loop as deconfinement order parameters
• Spontaneous Parity Violation
• Sign problem in $Z_3$-symmetric effective Polyakov-line model
• Phase diagram for strongly interacting matter in the presence of a magnetic field using the Polyakov-Nambu-Jona-Lasinio model with magnetic field dependent coupling strengths
• Perturbative aspects of the deconfinement transition -- Physics beyond the Faddeev-Popov model
• Sign problem and the chiral spiral on the finite-density lattice
• Dissipation and memory effects in pure glue deconfinement
• Polyakov-Nambu-Jona Lasinio model and Color-Flavor-Locked phase of QCD
• Effective potential for Polyakov loops from a center symmetric effective theory in three dimensions
• Magnetic susceptibility of the QCD vacuum in a nonlocal SU(3) PNJL model
• $Z_3$ meta-stable states in PNJL model
• Color superconductivity in the Nambu Jona-Lasinio model complemented by a Polyakov loop
• Vector meson spectral function and dilepton rate in the presence of strong entanglement effect between the chiral and the Polyakov loop dynamics
• Shear and bulk viscosity for a pure glue theory using an effective matrix model
• Wilson loops in the Hamiltonian formalism
• Inhomogeneous Polyakov loop induced by inhomogeneous chiral condensates
• Lattice simulation of a center symmetric three-dimensional effective theory for SU(2) Yang-Mills
• Nonlocal chiral quark models with Polyakov loop at finite temperature and chemical potential
• Non-local quark models for description of dense matter in the cores of neutron stars
• Quark matter phase diagram under the influence of strong magnetic fields with a nonlocal chiral model
• Gluon condensate from the Polyakov loop
• Mesons and diquarks in a color superconducting regime
• Baryons in the Nambu Jona-Lasinio models