From relativistic quantum fields to condensed matter and back again: Updating the Gross-Neveu phase diagram

Abstract

During the last few years, the phase diagram of the large N Gross-Neveu model in 1+1 dimensions at finite temperature and chemical potential has undergone a major revision. Here we present a streamlined account of this development, collecting the most important results. Quasi-one-dimensional condensed matter systems like conducting polymers provide real physical systems which can be approximately described by the Gross-Neveu model and have played some role in establishing its phase structure. The kink-antikink phase found at low temperatures is closely related to inhomogeneous superconductors in the Larkin-Ovchinnikov-Fulde-Ferrell phase. With the complete phase diagram at hand, the Gross-Neveu model can now serve as a firm testing ground for new algorithms and theoretical ideas.

33 pages, 12 figures; invited contribution to a special issue of Journal of Physics A on "QFT in lower dimensions and its applications"

Cited by in corpus (114)

• The QCD phase structure at finite temperature and density
• Inhomogeneous chiral condensates
• Inhomogeneous phases in the Nambu-Jona-Lasino and quark-meson model
• Inhomogeneous Condensates in the Thermodynamics of the Chiral NJL_2 model
• Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems
• How many phases meet at the chiral critical point?
• Influence of vector interaction and Polyakov loop dynamics on inhomogeneous chiral symmetry breaking phases
• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• A Twisted Kink Crystal in the Chiral Gross-Neveu model
• Chiral density waves in quark matter within the Nambu--Jona-Lasinio model in an external magnetic field
• Interweaving Chiral Spirals
• Functional Determinants in Quantum Field Theory
• QCD at finite temperature and density within the fRG approach: An overview
• Phonons, pions and quasi-long-range order in spatially modulated chiral condensates
• Phase structure of the massive chiral Gross-Neveu model from Hartree-Fock
• Emergence of Tricritical Point and Liquid-Gas Phase in the Massless 2+1 Dimensional Gross-Neveu Model
• Ultracold atoms and the Functional Renormalization Group
• Landau-Peierls instability in a Fulde-Ferrell type inhomogeneous chiral condensed phase
• Quantum field theory on toroidal topology: algebraic structure and applications
• Solitonic ground states in (color-) superconductivity
• Higgs Mass Bounds from Renormalization Flow for a Higgs-top-bottom model
• The Bogoliubov/de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry
• How to get from imaginary to real chemical potential
• Inhomogeneous charged pion condensation phenomenon in the NJL${}_2$ model with quark number and isospin chemical potentials
• Phase structure of mass- and spin-imbalanced unitary Fermi gases
• Finite size effects in the Gross-Neveu model with isospin chemical potential
• How transverse thermal fluctuations disorder a condensate of chiral spirals into a quantum spin liquid
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Self-consistent multiple complex-kink solutions in Bogoliubov-de Gennes and chiral Gross-Neveu systems
• Sign Flip in the Casimir Force for Interacting Fermion Systems
• Chiral density waves in the NJL${}_2$ model with quark number and isospin chemical potentials
• Two-dimensional chiral crystals in the NJL model
• Exotic supersymmetry of the kink-antikink crystal, and the infinite period limit
• Inhomogeneous charged pion condensation in chiral asymmetric dense quark matter in the framework of NJL${}_2$ model
• Strongly Interacting Fermions and Phases of the Casimir Effect
• Regulator dependence of inhomogeneous phases in the 2+1-dimensional Gross-Neveu model
• Fluctuations in cool quark matter and the phase diagram of Quantum Chromodynamics
• Critical and Tricritical Points for the Massless 2d Gross-Neveu Model Beyond Large N
• Time-Dependent Hartree-Fock Solution of Gross-Neveu models: Twisted Kink Constituents of Baryons and Breathers
• Crystals of superconducting Baryonic tubes in the low energy limit of QCD at finite density
• Critical Dopant Concentration in Polyacetylene and Phase Diagram from a Continuous Four-Fermi Model
• Tricritical behavior of the massive chiral Gross-Neveu model
• Interacting Fermions, Boundaries, and Finite Size Effects
• Properties of the massive Gross-Neveu model with nonzero baryon and isospin chemical potentials
• Charged pion condensation and duality in dense and hot chirally and isospin asymmetric quark matter in the framework of NJL${}_2$ model
• Pion condensation in the Gross-Neveu model with nonzero baryon and isospin chemical potentials
• Supersymmetric twisting of carbon nanotubes
• 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
• Baryons in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Crystalline Ground States in Polyakov-loop extended Nambu--Jona-Lasinio Models
• The Chiral Magnetic Effect and Axial Anomalies
• Transmutations of supersymmetry through soliton scattering, and self-consistent condensates
• Inhomogeneities in the $2$-Flavor Chiral Gross-Neveu Model
• Analytic SU(N) Skyrmions at finite Baryon density
• Competition of inhomogeneous chiral phases and two-flavor color superconductivity in the NJL model
• Worldline Monte Carlo for fermion models at large N_f
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. III. Shock and rarefaction waves in RG flows reveal limitations of the $N\to \infty$ limit in $O(N)$-type models
• Soliton defects in one-gap periodic system and exotic supersymmetry
• Full time-dependent Hartree-Fock solution of large N Gross-Neveu models
• Inhomogeneous phases in the chirally imbalanced $2+1$-dimensional Gross-Neveu model and their absence in the continuum limit
• Baryons in the large N limit of the massive two-dimensional Nambu-Jona-Lasinio model
• Spontaneous Non-Hermiticity in Nambu-Jona-Lasinio model
• Dirac field in the background of a planar defect
• Phase transition in the massive Gross-Neveu model in toroidal topologies
• Absence of inhomogeneous chiral phases in 2+1-dimensional four-fermion and Yukawa models
• Extended supersymmetry of the self-isospectral crystalline and soliton chains
• Exact solution of N baryon problem in the Gross-Neveu model
• Divergence of the axial current and fermion density in Gross-Neveu models
• Strong-interaction matter under extreme conditions from chiral quark models with nonlocal separable interactions
• Fermion in a multi-kink-antikink soliton background, and exotic supersymmetry
• Kink dynamics, sinh-Gordon solitons and strings in AdS(3) from the Gross-Neveu model
• Beyond the constant-mass Dirac physics: Solitons, charge fractionization, and the emergence of topological insulators in graphene rings
• Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model
• Integrating out the Dirac sea: Effective field theory approach to exactly solvable four-fermion models
• Collective modes of a soliton train in a Fermi superfluid
• Bogoliubov-de Gennes Soliton Dynamics in Unconventional Fermi Superfluids
• Phase transition in the 3-D massive Gross-Neveu model
• Large N solution of generalized Gross-Neveu model with two coupling constants
• Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions $1\le d<3$. II. Nonzero temperature and chemical potential
• Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions $1\le d<3$
• Stability of homogeneous chiral phases against inhomogeneous perturbations in 2+1 dimensions
• Fermion bound states in geometrically deformed backgrounds
• Chiral density wave versus pion condensation in the 1+1 dimensional NJL model
• Consistent regularization and renormalization in models with inhomogeneous phases
• The connection between nonzero density and spontaneous symmetry breaking for interacting scalars
• Dimensional reduction in quantum field theories at finite temperature and density
• Covariant boost and structure functions of baryons in Gross-Neveu models
• An Effective Field Theory Model for One-Dimensional $\mathrm{CH}$ Chains: Effects at Finite Chemical Potential, Temperature and External Zeeman Magnetic Field
• Crystals of gauged solitons, force free plasma and resurgence
• Speeding up Pontus-Mpemba effects via dynamical phase transitions
• Self-consistent Analytic Solutions in Twisted $\mathbb{C}{P}^{N-1}$ Model in the Large-$N$ Limit
• An Investigation of the Casimir Energy for a Fermion Coupled to the Sine-Gordon Soliton with Parity Decomposition
• Finite-gap twists of carbon nanotubes and an emergent hidden supersymmetry
• Spatially oscillating correlation functions in $\left(2+1\right)$-dimensional four-fermion models: The mixing of scalar and vector modes at finite density
• Excitonic insulators and Gross-Neveu models
• Non-Abelian twisted kinks in chiral Gross-Neveu model with isospin
• Evidence for factorized scattering of composite states in the Gross-Neveu model
• Remnants of large-$N_{\mathrm{f}}$ inhomogeneities in the 2-flavor chiral Gross-Neveu model
• Applications of the potential algebras of the two-dimensional Dirac-like operators
• Beyond integrability: Baryon-baryon backward scattering in the massive Gross-Neveu model
• Analytic Baby Skyrmions at Finite Density
• Competing mechanisms of chiral symmetry breaking in a generalized Gross-Neveu model
• Functional renormalization of QCD in $1+1$ dimensions: four-fermion interactions from quark-gluon dynamics
• Exciton-driven quantum phase transitions in holography
• Cascade of phase transitions in a planar Dirac material
• Condensates, crystals, and renormalons in the Gross-Neveu model at finite density
• Inhomogeneous Chiral Phase in Quark Matter
• Temperature effects on the magnetization of quasi-one-dimensional Peierls distorted materials
• On S-duality for holographic p-wave superconductors
• Detecting inhomogeneous chiral condensation from the bosonic two-point function in the $(1+1)$-dimensional Gross-Neveu model in the mean-field approximation
• Supersymmetric construction of self-consistent condensates in large N GN model: solitons on finite-gap potentials
• Axial anomaly and nesting in the inhomogeneous chiral phase
• Exploring new states of matter with a photonic emulator