Competition and duality correspondence between inhomogeneous fermion-antifermion and fermion-fermion condensations in the NJL${}_2$ model

Abstract

We investigate the possibility of spatially homogeneous and inhomogeneous chiral fermion-antifermion condensation and superconducting fermion-fermion pairing in the (1+1)-dimensional model by Chodos {\it et al.} [ Phys. Rev. D 61, 045011 (2000)] generalized to continuous chiral invariance. The consideration is performed at nonzero values of temperature $T$, electric charge chemical potential $\mu$ and chiral charge chemical potential ${\mu }_5$. It is shown that at $G_1<G_2$, where $G_1$ and $G_2$ are the coupling constants in the fermion-antifermion and fermion-fermion channels, the $(\mu ,{\mu }_5)$-phase structure of the model is in a one-to-one correspondence with the phase structure at $G_1>G_2$ (called duality correspondence). Under the duality transformation the (inhomogeneous) chiral symmetry breaking (CSB) phase is mapped into the (inhomogeneous) superconducting (SC) phase and vice versa. If $G_1=G_2$, then the phase structure of the model is self-dual. Nevertheless, the degeneracy between the CSB and SC phases is possible in this case only when there is a spatial inhomogeneity of condensates.

arXiv comment20 pages, 3 figures; references added; discussion section extended; published version

References in corpus (35)

• Quarkyonic Chiral Spirals
• Inhomogeneous phases in the Nambu-Jona-Lasino and quark-meson model
• Chiral symmetry and density wave in quark matter
• Inhomogeneous Condensates in the Thermodynamics of the Chiral NJL_2 model
• Influence of vector interaction and Polyakov loop dynamics on inhomogeneous chiral symmetry breaking phases
• Emergence of Skyrme crystal in Gross-Neveu and 't Hooft models at finite density
• Chiral density waves in quark matter within the Nambu--Jona-Lasinio model in an external magnetic field
• Phase Diagram of the Gross-Neveu Model: Exact Results and Condensed Matter Precursors
• Hot Quark Matter with an Axial Chemical Potential
• Crystalline chiral condensates off the tricritical point in a generalized Ginzburg-Landau approach
• Phase diagram of two-color quark matter at nonzero baryon and isospin density
• An effective QCD Lagrangian in the presence of an axial chemical potential
• Inhomogeneous charged pion condensation phenomenon in the NJL${}_2$ model with quark number and isospin chemical potentials
• Non-uniform chiral phase in effective chiral quark models
• Neutral Larkin--Ovchinnikov--Fulde--Ferrell state and chromomagnetic instability in two-flavor dense QCD
• Chiral density waves in the NJL${}_2$ model with quark number and isospin chemical potentials
• A Two-dimensional Model with Chiral Condensates and Cooper Pairs having QCD-like Phase Structure
• Chemical potentials and parity breaking: the Nambu-Jona-Lasinio model
• Pion condensation in the Gross-Neveu model with nonzero baryon and isospin chemical potentials
• Inhomogeneous phases in one-dimensional mass- and spin-imbalanced Fermi gases
• Properties of the massive Gross-Neveu model with nonzero baryon and isospin chemical potentials
• No First-Order Phase Transition in the Gross-Neveu Model?
• Duality between quark-quark and quark-antiquark pairing in 1+1 dimensional large N models
• Influence of current mass on the spatially inhomogeneous chiral condensate
• Crystalline ground state in chiral Gross-Neveu and Cooper pair models at finite densities
• Chiral waves in quark matter
• Nonuniform phases in a three-flavor Nambu--Jona-Lasinio model
• Quark beta decay in the inhomogeneous chiral phase and cooling of compact stars
• Superconducting phase transitions induced by chemical potential in (2+1)-dimensional four-fermion quantum field theory
• Dual Fermion Condensates in Curved Space
• Large N solution of generalized Gross-Neveu model with two coupling constants
• Chiral Modulations in Curved Space II: Conifold Geometries
• Dimensional reduction in quantum field theories at finite temperature and density
• An Effective Field Theory Model for One-Dimensional $\mathrm{CH}$ Chains: Effects at Finite Chemical Potential, Temperature and External Zeeman Magnetic Field
• Suppression of superconductivity by inhomogeneous chiral condensation in the NJL${}_2$ model

Cited by in corpus (16)

• Dualities in dense quark matter with isospin, chiral and chiral isospin imbalance in the framework of the large-N${}_c$ limit of the NJL${}_4$ model
• Chiral imbalanced hot and dense quark matter: NJL analysis at the physical point and comparison with lattice QCD
• Inhomogeneous condensation in effective models for QCD using the finite-mode approach
• Inhomogeneous charged pion condensation in chiral asymmetric dense quark matter in the framework of NJL${}_2$ model
• Dense baryon matter with isospin and chiral imbalance in the framework of NJL${}_4$ model at large $N_c$: duality between chiral symmetry breaking and charged pion condensation
• Dualities and inhomogeneous phases in dense quark matter with chiral and isospin imbalances in framework of effective model
• Charged pion condensation and duality in dense and hot chirally and isospin asymmetric quark matter in the framework of NJL${}_2$ model
• Hybrid chiral condensate in the external magnetic field
• Competition and duality correspondence between chiral and superconducting channels in (2+1)-dimensional four-fermion models with fermion number and chiral chemical potentials
• Duality between chiral symmetry breaking and charged pion condensation at large $N_c$: Consideration of an NJL${}_2$ model with baryon-, isospin- and chiral isospin chemical potentials
• Interplay between superconductivity and chiral symmetry breaking in a (2+1)-dimensional model with compactified spatial coordinate
• QCD phase diagram with chiral imbalance in NJL model: duality and lattice QCD results
• Integrable Gross-Neveu models with fermion-fermion and fermion-antifermion pairing
• Chiral spiral in the presence of chiral imbalance
• Emergence of charge density wave and superconducting phase transitions through Lorentz-invariant interactions in the Haldane-Hubbard model
• Axial anomaly and nesting in the inhomogeneous chiral phase