Nambu-Jona-Lasinio model description of weakly interacting Bose condensate and BEC-BCS crossover in dense QCD-like theories

Abstract

QCD-like theories possess a positively definite fermion determinant at finite baryon chemical potential ${\mu }_{\text{B}}$ and the lattice simulation can be successfully performed. While the chiral perturbation theories are sufficient to describe the Bose condensate at low density, to describe the crossover from Bose-Einstein condensation (BEC) to BCS superfluidity at moderate density we should use some fermionic effective model of QCD, such as the Nambu-Jona-Lasinio model. In this paper, using two-color two-flavor QCD as an example, we examine how the Nambu-Jona-Lasinio model describes the weakly interacting Bose condensate at low density and the BEC-BCS crossover at moderate density. Near the quantum phase transition point ${\mu }_{\text{B}}=m_{\pi }$ ($m_{\pi }$ is the mass of pion/diquark multiplet), the Ginzburg-Landau free energy at the mean-field level can be reduced to the Gross-Pitaevskii free energy describing a weakly repulsive Bose condensate with a diquark-diquark scattering length identical to that predicted by the chiral perturbation theories. The Goldstone mode recovers the Bogoliubov excitation in weakly interacting Bose condensates. The results of in-medium chiral and diquark condensates predicted by chiral perturbation theories are analytically recovered. The BEC-BCS crossover and meson Mott transition at moderate baryon chemical potential as well as the beyond-mean-field corrections are studied. Part of our results can also be applied to real QCD at finite baryon or isospin chemical potential.

29 pages + 9 figures. Published version in PRD

References in corpus (75)

• QCD Phenomenology based on a Chiral Effective Lagrangian
• Color superconductivity in dense quark matter
• NJL-model analysis of dense quark matter
• QCD at Finite Baryon Density: Nucleon Droplets and Color Superconductivity
• Vortices and Superfluidity in a Strongly Interacting Fermi Gas
• Diquark Bose Condensates in High Density Matter and Instantons
• BCS-BEC Crossover: From High Temperature Superconductors to Ultracold Superfluids
• Weakly bound dimers of fermionic atoms
• QCD at finite isospin density
• Color superconducting quark matter
• Superconductivity by long-range color magnetic interaction in high-density quark matter
• Theory of the Weakly Interacting Bose Gas
• The Quark-Gluon Plasma in Equilibrium
• Thermodynamics of the BCS-BEC crossover
• QCD-like Theories at Finite Baryon Density
• Superconductivity from perturbative one-gluon exchange in high density quark matter
• Lattice QCD at finite isospin density at zero and finite temperature
• On two-color QCD with baryon chemical potential
• Lattice QCD at Finite Density -- An introductory review
• Pion Superfluidity and Meson Properties at Finite Isospin Density
• Quantum Fluctuations in the Superfluid State of the BCS-BEC Crossover
• Color superconductivity in weak coupling
• Pseudogap and spectral function from superconducting fluctuations to the bosonic limit
• QCD at finite isospin density: from pion to quark-antiquark condensation
• QCD-like Theories at Finite Baryon and Isospin Density
• QCD Sum Rules and Applications to Nuclear Physics
• Two lectures on color superconductivity
• Equation of state of a superfluid Fermi gas in the BCS-BEC crossover
• Gaps and Critical Temperature for Color Superconductivity
• Numerical Study of Dense Adjoint Matter in Two Color QCD
• The finite temperature transition for 2-flavour lattice QCD at finite isospin density
• Flavor-Mixing Effects on the QCD Phase Diagram at non-vanishing Isospin Chemical Potential: One or Two Phase Transitions?
• BEC-BCS Crossover in the Nambu--Jona-Lasinio Model of QCD
• Isospin Chemical Potential and the QCD Phase Diagram at Nonzero Temperature and Baryon Chemical Potential
• Two-colour QCD at non-zero quark-number density
• Deconfinement in dense 2-color QCD
• QCD at small non-zero quark chemical potentials
• Universal thermodynamics of strongly interacting Fermi gases
• Quenched lattice QCD at finite isospin density and related theories
• BCS-BEC crossover at finite temperature in the broken-symmetry phase
• A calculation of the QCD phase diagram at finite temperature, and baryon and isospin chemical potentials
• Phase diagram of a cold polarized Fermi gas
• Thermal Pions at Finite Isospin Chemical Potential
• Thermodynamics of two-colour QCD and the Nambu Jona-Lasinio model
• A Quarkyonic Phase in Dense Two Color Matter?
• Color Superconductivity at Moderate Baryon Density
• Diquark Condensate in QCD with Two Colors at Next-to-Leading Order
• Phase Structure of Nambu-Jona-Lasinio Model at Finite Isospin Density
• Thermodynamics of chiral symmetry at low densities
• BCS-BEC crossover in a relativistic superfluid and its significance to quark matter
• Pion Condensation in Baryonic Matter: from Sarma Phase to Larkin-Ovchinnikov-Fudde-Ferrell Phase
• Two-color quark matter: U(1)_A restoration, superfluidity, and quarkyonic phase
• Diquark Condensation at Nonzero Chemical Potential and Temperature
• Massive Quark Propagator in the Color-superconducting Phase
• Massive quark propagator and competition between chiral and diquark condensate
• Pion and Kaon Condensation at Finite Temperature and Density
• BCS/BEC crossover in Quark Matter and Evolution of its Static and Dynamic properties
• The Superfluid and Conformal Phase Transitions of Two-Color QCD
• Coupling of pion condensate, chiral condensate and Polyakov loop in an extended NJL model
• Pion and kaon condensation in a 3-flavor NJL model
• Phase diagram of two-color quark matter at nonzero baryon and isospin density
• Color superconductivity vs. pseudoscalar condensation in a three-flavor NJL model
• Chiral Lagrangian and spectral sum rules for dense two-color QCD
• Diquark condensation in dense adjoint matter
• Pion, sigma-meson and diquarks in the 2SC phase of dense cold quark matter
• Relativistic BCS-BEC Crossover at Zero Temperature
• Bound diquarks and their Bose-Einstein condensation in strongly coupled quark matter
• Relativistic BCS-BEC Crossover at Finite Temperature and Its Application to Color Superconductivity
• QCD-like theories at nonzero temperature and density
• BCS-BEC crossover in dense relativistic matter: Collective excitations
• Superfluid equation of state of dilute composite bosons
• On the chiral perturbation theory for two-flavor two-color QCD at finite chemical potential
• Confinement-Deconfinement Phase Transition at Nonzero Chemical Potential
• Pions in the quark matter phase diagram
• Quark and Gluon Condensates in Isospin Matter

Cited by in corpus (35)

• Quark-meson-diquark model for two-color QCD
• Quantum fluctuations in the BCS-BEC crossover of two-dimensional Fermi gases
• Scrutinizing the pion condensed phase
• Three-flavor Nambu--Jona-Lasinio model at finite isospin chemical potential
• Study of the phase diagram of dense two-color QCD within lattice simulation
• Singular values of the Dirac operator in dense QCD-like theories
• Universal Aspects of QCD-like Theories
• Phase transitions and gluodynamics in 2-colour matter at high density
• Dense 2-color QCD towards continuum and chiral limits
• Peaks of sound velocity in two color dense QCD: quark saturation effects and semishort range correlations
• Two-colour QCD phases and the topology at low temperature and high density
• BEC-BCS crossover in a cold and magnetized two color NJL model
• Equation of state of imbalanced cold matter from chiral perturbation theory
• Bose-Einstein condensate strings
• Continuum Goldstone spectrum of two-color QCD at finite density with staggered quarks
• BCS-BEC crossover in three-dimensional Fermi gases with spherical spin-orbit coupling
• Thin accretion disks around cold Bose-Einstein Condensate stars
• Dense two-color QCD from Dyson-Schwinger equations
• Quark-Hadron Matter at Finite Temperature and Density in a Two-Color PNJL model
• Effects of Dense Quark Matter on Gluon Propagators in Lattice QC${}_2$D
• Holographic Floquet states II: Floquet condensation of vector mesons in nonequilibrium phase diagram
• Thermal quarks and gluon propagators in two-color dense QCD
• BCS-BEC crossover in relativistic Fermi systems
• Multicomponent meson superfluids in chiral perturbation theory
• Probing the hadron mass spectrum in dense two-color QCD with the linear sigma model
• Non-Hermitian BCS-BEC crossover of Dirac fermions
• Optimized perturbation theory applied to the study of the thermodynamics and BEC-BCS crossover in the three-color Nambu--Jona-Lasinio model
• A quarksonic matter at high isospin density
• Delineating chiral separation effect in two-color dense QCD
• Phases of circle-compactified QCD with adjoint fermions at finite density
• BCS-BEC Crossover and Stability in a Nambu-Jona-Lasinio Model with Diquark-Diquark Repulsion
• Chiral effective model of cold and dense two-color QCD: The linear sigma model approach
• Chiral random matrix theory for single-flavor spin-one Cooper pairing
• Response functions of hot and dense matter in the Nambu-Jona-Lasino model
• Pairing fluctuation effects in a strongly coupled color superfluid/superconductor