Lattice QCD at Finite Density -- An introductory review

Abstract

This is a pedagogical review of the lattice study of finite density QCD, which is intended to provide the minimum necessary contents, so that the paper may be used as the first reading for a newcomer to the field and also for those working in nonlattice communities. After a brief introduction to argue why finite density QCD can be a new attractive subject, we describe fundamental formulae which are necessary for the following sections. Then we survey lattice QCD simulations in small chemical potential regions, where several prominent works have been reported recently. Next, two-color QCD calculations are discussed, where we have a chance to glance at many new features of finite density QCD, and indeed recent simulations indicated quark pair condensation and the in-medium effect. Tables of SU(3) and SU(2) lattice simulations at finite baryon density are given. In the next section, we make a survey of several related works which may be a starting point of the new development in the future, although some works do not attract much attention now. Materials are described in a pedagogical manner. Starting from a simple 2-d model, we briefly discuss a lattice analysis of NJL model. We describe a non-perturbative analytical approach, i.e., strong coupling approximation method and some results. Canonical ensemble approach instead of usual grand canonical ensample may be another route to reach high density. We examine the density of state method and show this old idea includes recently proposed factorization method. An alternative method, complex Langevin equation and an interesting model, finite isospin model, are also discussed. In Appendix, we give several technical points which are useful in practical calculations.

50 pages, 43 Postscript figures, submitted to Prog. Theor. Phys, uses ptptex.cls and wrapft.sty

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• Color superconducting quark matter
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Cited by in corpus (160)

• The phase diagram of dense QCD
• Critical point of QCD at finite T and μ, lattice results for physical quark masses
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• QCD phase diagram and the critical point
• Chiral magnetic effect in the PNJL model
• The ALICE experiment: a journey through QCD
• Hydrodynamical evolution near the QCD critical end point
• Finite-density lattice QCD and sign problem: current status and open problems
• QCD thermodynamics from an imaginary mu_B: results on the four flavor lattice model
• Dense Quarks, and the Fermion Sign Problem, in a SU(N) Matrix Model
• The strongly interacting Quark Gluon Plasma, and the critical behaviour of QCD at imaginary chemical potential
• Thermodynamics of two-colour QCD and the Nambu Jona-Lasinio model
• Phase structures of strong coupling lattice QCD with finite baryon and isospin density
• Anomaly matching for phase diagram of massless ${\mathbb{Z}}_N$-QCD
• Lefschetz-thimble analysis of the sign problem in one-site fermion model
• Meson condensation
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Fluctuations and the axial anomaly with three quark flavors
• Three-flavor Nambu--Jona-Lasinio model at finite isospin chemical potential
• Model study of the sign problem in the mean-field approximation
• Hard-core deconfinement and soft-surface delocalization from nuclear to quark matter
• QCD matter in extreme environments
• Study of the phase diagram of dense two-color QCD within lattice simulation
• Two-color quark matter: U(1)_A restoration, superfluidity, and quarkyonic phase
• Phase diagram of QCD at finite temperature and chemical potential from lattice simulations with dynamical Wilson quarks
• Equation of state at finite temperature and chemical potential, lattice QCD results
• Imaginary Chemical Potential Approach for the Pseudo-Critical Line in the QCD Phase Diagram with Clover-Improved Wilson Fermions
• Matrix Models and QCD with Chemical Potential
• NJL-type models in the presence of intense magnetic fields: the role of the regularization prescription
• Random matrices beyond the Cartan classification
• Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
• Finite density phase transition of QCD with $N_f=4$ and $N_f=2$ using canonical ensemble method
• Nambu-Jona-Lasinio model description of weakly interacting Bose condensate and BEC-BCS crossover in dense QCD-like theories
• Isentropic thermodynamics in the PNJL model
• Updating the Phase Diagram of the Gross-Neveu Model in 2+1 Dimensions
• Properties of hadron screening masses at small baryonic density
• The QCD phase diagram at nonzero baryon, isospin and strangeness chemical potentials: Results from a hadron resonance gas model
• Complex saddle points and the sign problem in complex Langevin simulation
• Functional renormalization group analysis of the soft mode at the QCD critical point
• Strange matter and strange stars in a thermodynamically self-consistent perturbation model with running coupling and running strange quark mass
• The Deconfinement Phase Transition in Proto-Neutron-Star Matter
• Remarks on the multi-parameter reweighting method for the study of lattice QCD at non-zero temperature and density
• Hamilton dynamics for the Lefschetz thimble integration akin to the complex Langevin method
• BEC-BCS crossover in a cold and magnetized two color NJL model
• Lattice study of thermodynamic properties of dense QC${}_2$D
• Observation of deconfinement in a cold dense quark medium
• Phase diagram at finite temperature and quark density in the strong coupling limit of lattice QCD for color SU(3)
• Cold QCD at finite isospin density: confronting effective models with recent lattice data
• Perturbative quantum Monte Carlo method for nuclear physics
• New approach to canonical partition functions computation in $N_f=2$ lattice QCD at finite baryon density
• Partial Deconfinement
• Applicability of the Linear delta Expansion for the lambda phi^4 Field Theory at Finite Temperature in the Symmetric and Broken Phases
• An improvement in complex Langevin dynamics from a view point of Lefschetz thimbles
• Gauge cooling for the singular-drift problem in the complex Langevin method --a test in Random Matrix Theory for finite density QCD
• Multi-flavor massless QED${}_2$ at finite densities via Lefschetz thimbles
• Pion crystals hosting topologically stable baryons
• Strangeness Neutrality and QCD Thermodynamics
• Thermodynamics and susceptibilities of isospin imbalanced QCD matter
• Isospin properties of quark matter from a 3-flavor NJL model
• Computing the renormalization group flow of two-dimensional ${\varphi }^4$ theory with tensor networks
• Role of mesonic fluctuations in the Polyakov loop extended quark-meson model at imaginary chemical potential
• Quark number densities at imaginary chemical potential in $N_f=2$ lattice QCD with Wilson fermions and its model analyses
• Emergent Hadrons and Diquarks
• Probing deconfinement in a chiral effective model with Polyakov loop at imaginary chemical potential
• High-Energy Phase Diagrams with Charge and Isospin Axes under Heavy-Ion Collision and Stellar Conditions
• Phase diagram evolution at finite coupling in strong coupling lattice QCD
• Effects of Dense Quark Matter on Gluon Propagators in Lattice QC${}_2$D
• Larkin-Ovchinnikov-Fulde-Ferrell state in two-color quark matter
• Primitive Quantum Gates for an SU(3) Discrete Subgroup: $\Sigma (36\times 3)$
• Hot QCD at finite isospin density: confronting SU(3) Nambu-Jona-Lasinio model with recent lattice data
• Meson Screening Mass in a Strongly Coupled Pion Superfluid
• Chiral and deconfinement transitions in strong coupling lattice QCD with finite coupling and Polyakov loop effects
• QCD phase transition at real chemical potential with canonical approach
• Fluctuations and phases in baryonic matter
• Color screening potential at finite density in two-flavor lattice QCD with Wilson fermions
• Gradient flows without blow-up for Lefschetz thimbles
• Tricritical point of lattice QCD with Wilson quarks at finite temperature and density
• QCD equation of state at finite isospin density from the linear sigma model with quarks: The cold case
• Phase diagram of hot and dense QCD constrained by the Statistical Model
• Unquenched complex Dirac spectra at nonzero chemical potential: two-colour QCD lattice data versus matrix model
• Spatial modulation and topological current in holographic QCD matter
• BCS-BEC crossover in relativistic Fermi systems
• Influence of chiral asymmetry on phase structure of the two-color quark matter
• Anisotropic pressure of magnetized quark matter with anomalous magnetic moment
• Study of QCD critical point using canonical ensemble method
• Fuzzy gauge theory for quantum computers
• Breaking of universal relationships of axial wI-modes in hybrid stars: rapid and slow hadron-quark conversion scenarios
• Fourier coefficients of the net-baryon number density and chiral criticality
• Probing the hadron mass spectrum in dense two-color QCD with the linear sigma model
• Masses of vector bosons in two-color dense QCD based on the hidden local symmetry
• Effects of finite volume and magnetic fields on thermodynamic properties of quark matter and fluctuations of conserved charges
• Complex Langevin Dynamics in Large $N$ Unitary Matrix Models
• Existence of positive representations for complex weights
• QCD Equation of State at nonzero baryon density in external magnetic field
• Fate of the topological susceptibility in two-color dense QCD
• Two-color QCD at high density
• Multipoint reweighting method and its applications to lattice QCD
• PNJL model at zero temperature: three-flavor case
• Thermodynamical phases in a PNJL model at zero temperature
• Modern nuclear and astrophysical constraints of dense matter in a renormalized chiral approach
• EoS of finite density QCD with Wilson fermions by Multi-Parameter Reweighting and Taylor expansion
• Chiral condensate thermal evolution at finite baryon chemical potential within Chiral Perturbation Theory
• Insignificance of the anomalous magnetic moment of the quarks in presence of chiral imbalance
• Sound velocity peak induced by the chiral partner in dense two-color QCD
• Thermodynamics of an exactly solvable confining quark model
• 3-dimensional QCD phase diagram with pion condensate in the NJL model
• Restricted phase-space approximation in real-time stochastic quantization
• Non-Commutativity of the Zero Chemical Potential Limit and the Thermodynamic Limit in Finite Density Systems
• Schwinger Mechanism with Stochastic Quantization
• Schwinger mechanism in the SU(3) Nambu--Jona-Lasinio model with an electric field
• Polyakov loop effects on the phase diagram in strong-coupling lattice QCD
• Analytical studies of the complex Langevin equation with a Gaussian Ansatz and multiple solutions in the unstable region
• Dyons and Roberge - Weiss transition in lattice QCD
• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly
• Describing the speed of sound peak of isospin-asymmetric cold strongly interacting matter using effective models
• Meson Scattering in a Pion Superfluid
• Magnetized pole-mass of neutral $\rho$ meson within full RPA evaluation
• Liquid Phases in SU(3) Chiral Perturbation Theory: Drops of Strange Chiral Nucleon Liquid & Ordinary Chiral Heavy Nuclear Liquid
• Gluon Propagators in $2+1$ Lattice QCD with Nonzero Isospin Chemical Potential
• Perturbative quantum Monte Carlo calculation with high-fidelity nuclear forces
• Sign-Problem-Free Nuclear Quantum Monte Carlo Simulation
• Isospin effect on baryon and charge fluctuations from the pNJL model
• Sign problem and the chiral spiral on the finite-density lattice
• Universality crossover between chiral random matrix ensembles and twisted SU(2) lattice Dirac spectra
• Effective Model Approach to the Dense State of QCD Matter
• Heavy-quark spin polarization induced by the Kondo effect in a magnetic field
• Complex Langevin study for polarons in an attractively interacting one-dimensional two-component Fermi gas
• The BEST framework for the search for the QCD critical point and the chiral magnetic effect
• A method for probing the formation of quark matter
• A Multi-Purpose Platform for Analog Quantum Simulation
• Lattice QCD at finite baryon density using analytic continuation
• Towards extremely dense matter on the lattice
• Chiral effective model of cold and dense two-color QCD: The linear sigma model approach
• Stochastic quantization and diffusion models
• Stable Yang-Lee zeros in truncated fugacity series from net-baryon number multiplicity distribution
• Complex singularities around the QCD critical point at finite densities
• Density of States Method at Finite Isospin Density
• The mass and spectral function of scalar and pseudoscalar mesons in a hot and chirally imbalanced medium using the two-flavor NJL model
• Strongly interacting matter in extreme magnetic fields
• Hadronic property at finite density
• Gluons in Two-Color QCD at High Baryon Density
• Regularization of Complex Langevin Method
• In-medium electromagnetic form factors of pseudoscalar mesons from the quark model
• Towards sampling complex actions
• Testing the equivalence between the planar Gross-Neveu and Thirring models at $N=1$
• Generalized Nambu-Goldstone pion in dense matter: a schematic NJL model
• Building imaginary-time thermal field theory with artificial neural networks
• Semi-classical analysis of non self-adjoint transfer matrices in statistical mechanics. I
• Effect of chiral imbalance on the electrical conductivity of hot and dense quark matter using Green-Kubo Method within the 2-flavour gauged NJL model
• Response functions of hot and dense matter in the Nambu-Jona-Lasino model
• Silver Blaze Puzzle in 1/Nc Expansions of Cold and Dense QCD Matter
• Renormalized dual basis for scalable simulations of 2+1D compact quantum electrodynamics
• Quantum lattice models that preserve continuous translation symmetry
• Roles of $U(1)$ axial anomaly effects in cold and dense two-color QCD with $2+2$ flavors
• Non-local quark models for description of dense matter in the cores of neutron stars
• Langevin Simulation of the Chirally Decomposed Sine-Gordon Model
• Study of lattice QCD at finite baryon density using the canonical approach
• Study of lattice QCD at finite chemical potential using canonical ensemble approach
• Taming the pion condensation in QCD at finite baryon density
• Phase transitions at high and low densities for a rotating QCD matter from holography