Introductory lectures on lattice QCD at nonzero baryon number

Abstract

These lecture notes contain an elementary introduction to lattice QCD at nonzero chemical potential. Topics discussed include chemical potential in the continuum and on the lattice; the sign, overlap and Silver Blaze problems; the phase boundary at small chemical potential; imaginary chemical potential; and complex Langevin dynamics. An incomplete overview of other approaches is presented as well. These lectures are meant for postgraduate students and postdocs with an interest in extreme QCD. A basic knowledge of lattice QCD is assumed but not essential. Some exercises are included at the end.

45 pages, based on lectures delivered at the XIII International Workshop on Hadron Physics, Brazil, March 2015

References in corpus (28)

• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The phase boundary for the chiral transition in (2+1)-flavor QCD at small values of the chemical potential
• The QCD phase diagram at nonzero quark density
• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Lattice simulations of real-time quantum fields
• The chiral critical point of Nf=3 QCD at finite density to the order (mu/T)^4
• Stochastic quantization at finite chemical potential
• New insights into the problem with a singular drift term in the complex Langevin method
• The density of states in gauge theories
• The chiral phase transition in two-flavor QCD from imaginary chemical potential
• The lattice QCD phase diagram in and away from the strong coupling limit
• Phase of the Fermion Determinant at Nonzero Chemical Potential
• Structure of Lefschetz thimbles in simple fermionic systems
• On the existence of the critical point in finite density lattice QCD
• Some remarks on Lefschetz thimbles and complex Langevin dynamics
• The QCD Sign Problem for Small Chemical Potential
• Onset Transition to Cold Nuclear Matter from Lattice QCD with Heavy Quarks
• Simulating QCD at nonzero baryon density to all orders in the hopping parameter expansion
• Flux representation of an effective Polyakov loop model for QCD thermodynamics
• The density of states approach to dense quantum systems
• Full simulation of chiral Random Matrix Theory at non-zero chemical potential by Complex Langevin
• The Approach to the Thermodynamic Limit in Lattice QCD at μ\neq0
• U_A(1) Anomaly in Hot and Dense QCD and the Critical Surface
• Chiral Condensate at Nonzero Chemical Potential in the Microscopic Limit of QCD
• A general approach to the sign problem - the factorization method with multiple observables
• QCD in One Dimension at Nonzero Chemical Potential
• The Dirac spectrum in Complex Langevin Simulations of QCD
• Lattice gauge theory without link variables

Cited by in corpus (98)

• Review on novel methods for lattice gauge theories
• Mapping neutron star data to the equation of state using the deep neural network
• Meson condensation
• Baryon number fluctuations at finite temperature and density
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Fluctuation-induced modifications of the phase structure in (2+1)-flavor QCD
• Complex Langevin dynamics and zeroes of the fermion determinant
• Reaction rates and transport in neutron stars
• Holographic QCD in the Veneziano limit at finite Magnetic Field and Chemical Potential
• Hard-core deconfinement and soft-surface delocalization from nuclear to quark matter
• Methodology study of machine learning for the neutron star equation of state
• Inference of the sound speed and related properties of neutron stars
• Extensive Studies of the Neutron Star Equation of State from the Deep Learning Inference with the Observational Data Augmentation
• Orientation Dependence of Confinement-Deconfinement Phase Transition in Anisotropic Media
• Toward Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States
• Classically emulated digital quantum simulation for screening and confinement in the Schwinger model with a topological term
• Lefschetz thimbles decomposition for the Hubbard model on the hexagonal lattice
• Chiral matrix model of the semi-Quark Gluon Plasma in QCD
• Reconstructing the neutron star equation of state from observational data via automatic differentiation
• The QCD phase diagram in the limit of heavy quarks using complex Langevin dynamics
• Critical endpoint in the presence of a chiral chemical potential
• Applying the tempered Lefschetz thimble method to the Hubbard model away from half-filling
• Topological critical slowing down: variations on a toy model
• Physics-Driven Learning for Inverse Problems in Quantum Chromodynamics
• Criticality from Einstein-Maxwell-dilaton holography at finite temperature and density
• Translating neutron star observations to nuclear symmetry energy via artificial neural networks
• Correlated stopping, proton clusters and higher order proton cumulants
• Third-order perturbative lattice and complex Langevin analyses of the finite-temperature equation of state of non-relativistic fermions in one dimension
• Extending machine learning classification capabilities with histogram reweighting
• Dynamical stabilisation of complex Langevin simulations of QCD
• Worldvolume approach to the tempered Lefschetz thimble method
• Lattice Constraints on the QCD Chiral Phase Transition at Finite Temperature and Baryon Density
• Strangeness Neutrality and QCD Thermodynamics
• Strategies for the Determination of the Running Coupling of $(2+1)$-dimensional QED with Quantum Computing
• Pion crystals hosting topologically stable baryons
• Diffusion Models as Stochastic Quantization in Lattice Field Theory
• A simple approach towards the sign problem using path optimisation
• Primitive Quantum Gates for an SU(3) Discrete Subgroup: $\Sigma (36\times 3)$
• Fluctuations and phases in baryonic matter
• Neutron stars and phase diagram in a hard-wall AdS/QCD model
• Universality of Pattern Formation
• Hamiltonians and gauge-invariant Hilbert space for lattice Yang-Mills-like theories with finite gauge group
• $3d$ fermion-boson map with imaginary chemical potential
• Quantum computation of thermal averages in the presence of a sign problem
• Flow-based density of states for complex actions
• Fuzzy gauge theory for quantum computers
• Probing the hadron mass spectrum in dense two-color QCD with the linear sigma model
• Portable multi-node LQCD Monte Carlo simulations using OpenACC
• Renormalization group improved pressure for cold and dense QCD
• Different faces of confinement
• All order resummed leading and next-to-leading soft modes of dense QCD pressure
• Virial coefficients of 1D and 2D Fermi gases by stochastic methods and a semiclassical lattice approximation
• Pressure and speed of sound in two-flavor color-superconducting quark matter at next-to-leading order
• $\mathcal{P}T$ symmetry, pattern formation, and finite-density QCD
• Effects of Cosine Tapering Window on Quantum Phase Estimation
• Cooling Stochastic Quantization with colored noise
• Hadronic molecules with a $\bar{D}$ meson in a medium
• Fate of the topological susceptibility in two-color dense QCD
• Sound velocity peak induced by the chiral partner in dense two-color QCD
• Cold and dense perturbative QCD in a very strong magnetic background
• Hot perturbative QCD in a very strong magnetic background
• QCD pressure: renormalization group optimized perturbation theory confronts lattice
• Analytical studies of the complex Langevin equation with a Gaussian Ansatz and multiple solutions in the unstable region
• Realizing the potential of deep neural network for analyzing neutron star observables and dense matter equation of state
• Towards constraining QCD phase transitions in neutron star interiors: Bayesian Inference with TOV linear response analysis
• Distance between configurations in Markov chain Monte Carlo simulations
• Confining strings in three-dimensional gauge theories beyond the Nambu--Gotō approximation
• A complex Langevin approach to ultracold fermions
• Renormalization group improved pressure for hot and dense quark matter
• Color superconductivity under neutron-star conditions at next-to-leading order
• Stochastic quantization and diffusion models
• Renormalization group optimized $\lambda {\varphi }^4$ pressure at next-to-next-to-leading order
• A method for probing the formation of quark matter
• Chiral effective model of cold and dense two-color QCD: The linear sigma model approach
• Comparing strange and non-strange quark stars within resummed QCD at NLO
• Phases of dense matter with holographic instantons
• Time-dependent Ginzburg-Landau approach to the dynamics of inhomogeneous chiral condensates in a nonlocal Nambu--Jona-Lasinio model
• Cold Quark Matter: Renormalization Group Improvement at next-to-next-to leading order
• Advances in non-relativistic matter via complex Langevin approaches
• Nature of the chiral phase transition of two flavour QCD from imaginary chemical potential with HISQ fermions
• Equation of state of non-relativistic matter from automated perturbation theory and complex Langevin
• Low mu and imaginary mu signals of a critical point in the phase diagram of an exactly soluble chiral symmetry breaking theory
• Sign optimization and complex saddle points in one-dimensional QCD
• A quantum Monte Carlo method on asymptotic Lefschetz thimbles for quantum spin systems: An application to the Kitaev model in a magnetic field
• Relation between the continuum threshold and the Polyakov loop with the QCD deconfinement transition
• Speed of sound peak in two-color dense QCD: confronting effective models with lattice data
• Particle Projection Using a Complex Langevin Method
• The curvature of the pseudo-critical line in the QCD phase diagram from mesonic lattice correlation functions
• Heavy Quarkonium at finite temperature and chemical potential
• Resummed lattice QCD equation of state at finite baryon density: strangeness neutrality and beyond
• Roles of $U(1)$ axial anomaly effects in cold and dense two-color QCD with $2+2$ flavors
• Cosmology from Strong Interactions
• Identifying the QCD Phase Transitions via the Gravitational Wave Frequency from Supernova Explosion
• Competing color superconductivity and color Kondo effect in quark matter
• Neutron stars and phase diagram from a double hard-wall
• Combining complex Langevin dynamics with score-based and energy-based diffusion models
• Lattice QCD at nonzero temperature and density
• Stability of universal properties against perturbations of the Markov Chain Monte Carlo algorithm