Phase Diagram of the Gross-Neveu Model: Exact Results and Condensed Matter Precursors

Abstract

Recently the revised phase diagram of the (large N) Gross-Neveu model in 1+1 dimensions with discrete chiral symmetry has been determined numerically. It features three phases, a massless and a massive Fermi gas and a kink-antikink crystal. Here we investigate the phase diagram by analytical means, mapping the Dirac-Hartree-Fock equation onto the non-relativistic Schroedinger equation with the (single gap) Lame potential. It is pointed out that mathematically identical phase diagrams appeared in the condensed matter literature some time ago in the context of the Peierls-Froehlich model and ferromagnetic superconductors.

28 pages, 8 figures, v2: streamlined derivations using complex functions; 3 figures and 2 references added, v3: 6 references added, to appear in Ann. of Phys., v4: minor typos corrected

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• Revised Phase Diagram of the Gross-Neveu Model
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• Analytical solution of the Gross-Neveu model at finite density
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Cited by in corpus (80)

• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Inhomogeneous chiral condensates
• Inhomogeneous phases in the Nambu-Jona-Lasino and quark-meson model
• How many phases meet at the chiral critical point?
• Influence of vector interaction and Polyakov loop dynamics on inhomogeneous chiral symmetry breaking phases
• From relativistic quantum fields to condensed matter and back again: Updating the Gross-Neveu phase diagram
• Interweaving Chiral Spirals
• Full Phase Diagram of the Massive Gross-Neveu Model
• Crystalline chiral condensates off the tricritical point in a generalized Ginzburg-Landau approach
• Inhomogeneous phases in the quark-meson model with vacuum fluctuations
• Emergence of Tricritical Point and Liquid-Gas Phase in the Massless 2+1 Dimensional Gross-Neveu Model
• Inhomogeneous phases in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Chiral density wave in nuclear matter
• 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
• Inhomogeneous chiral phases away from the chiral limit
• Recent progresses on QCD phases in a strong magnetic field -- views from Nambu--Jona-Lasinio model
• Chiral density waves in the NJL${}_2$ model with quark number and isospin chemical potentials
• Two-dimensional chiral crystals in the NJL model
• Inhomogeneous chiral symmetry breaking in dense neutron-star matter
• Inhomogeneous condensation in effective models for QCD using the finite-mode approach
• Meson supercurrents and the Meissner effect in the Sakai-Sugimoto model
• Regulator dependence of inhomogeneous phases in the 2+1-dimensional Gross-Neveu model
• Critical and Tricritical Points for the Massless 2d Gross-Neveu Model Beyond Large N
• Fluctuations in cool quark matter and the phase diagram of Quantum Chromodynamics
• Critical Dopant Concentration in Polyacetylene and Phase Diagram from a Continuous Four-Fermi Model
• Baryons in Massive Gross-Neveu Models
• Tricritical behavior of the massive chiral Gross-Neveu model
• Dualities and inhomogeneous phases in dense quark matter with chiral and isospin imbalances in framework of effective model
• Anatomy of the sign-problem in heavy-dense QCD
• From non-degenerate conducting polymers to dense matter in the massive Gross-Neveu model
• Phase structure of the 1+1 dimensional Nambu--Jona-Lasinio model with isospin
• Baryons in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Integrable model for density-modulated quantum condensates: solitons passing through a soliton lattice
• Crystalline Ground States in Polyakov-loop extended Nambu--Jona-Lasinio Models
• Fermions in the pseudoparticle approach
• Worldline Monte Carlo for fermion models at large N_f
• Chiral Modulations in Curved Space I: Formalism
• Competition and duality correspondence between inhomogeneous fermion-antifermion and fermion-fermion condensations in the NJL${}_2$ model
• Inhomogeneous phases in the chirally imbalanced $2+1$-dimensional Gross-Neveu model and their absence in the continuum limit
• Interplay between superconductivity and chiral symmetry breaking in a (2+1)-dimensional model with compactified spatial coordinate
• Exact solution of N baryon problem in the Gross-Neveu model
• Kink dynamics, sinh-Gordon solitons and strings in AdS(3) from the Gross-Neveu model
• Solitonic modulation and Lifshitz point in an external magnetic field within Nambu--Jona-Lasinio model
• Lattice investigation of an inhomogeneous phase of the 2+1-dimensional Gross-Neveu model in the limit of infinitely many flavors
• Integrable Gross-Neveu models with fermion-fermion and fermion-antifermion pairing
• Bogoliubov-de Gennes Soliton Dynamics in Unconventional Fermi Superfluids
• Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions $1\le d<3$. II. Nonzero temperature and chemical potential
• Duality study of chiral Heisenberg Gross-Neveu model in 1+1 dimensions
• Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions $1\le d<3$
• Chiral Modulations in Curved Space II: Conifold Geometries
• Baryon-baryon scattering in the Gross-Neveu model: the large N solution
• Self-bound quark matter in the NJL model revisited: from schematic droplets to domain-wall solitons
• Fermi-Einstein condensation in dense QCD-like theories
• Covariant boost and structure functions of baryons in Gross-Neveu models
• Dimensional reduction in quantum field theories at finite temperature and density
• Speeding up Pontus-Mpemba effects via dynamical phase transitions
• Crystals of gauged solitons, force free plasma and resurgence
• First-order phase boundaries of the massive 1+1 dimensional Nambu--Jona-Lasinio model with isospin
• An Effective Field Theory Model for One-Dimensional $\mathrm{CH}$ Chains: Effects at Finite Chemical Potential, Temperature and External Zeeman Magnetic Field
• Breathers and their interaction in the massless Gross-Neveu model
• Non-Abelian twisted kinks in chiral Gross-Neveu model with isospin
• Phase diagram of the 2+1-dimensional Gross-Neveu model with chiral imbalance
• Generative learning for the problem of critical slowing down in lattice Gross Neveu model
• Suppression of superconductivity by inhomogeneous chiral condensation in the NJL${}_2$ model
• Gross-Neveu model with O(2)${}_L\times$O(2)${}_R$ chiral symmetry: Duality with Zakharov-Mikhailov model and large $N$ solution
• Revisiting the spatially inhomogeneous condensates in the $(1+1)$-dimensional chiral Gross-Neveu model via the bosonic two-point function in the infinite-$N$ limit
• Tricritical curve of massive chiral Gross-Neveu model with isospin
• Functional renormalization of QCD in $1+1$ dimensions: four-fermion interactions from quark-gluon dynamics
• Confinement and the quark Fermi-surface in SU(2N) QCD-like theories
• Phases of a fermionic model with chiral condensates and Cooper pairs in 1+1 dimensions
• Universality, Lee-Yang singularities and series expansions
• Temperature effects on the magnetization of quasi-one-dimensional Peierls distorted materials
• Condensates, crystals, and renormalons in the Gross-Neveu model at finite density
• Fate of surface gaps in magnetic topological insulators
• Low energy physics of interacting bosons with a moat spectrum, and the implications for condensed matter and cold nuclear matter
• Spatially modulated chiral condensates
• On the Inhomogeneous Phase of the Chiral Gross-Neveu Model
• Detecting inhomogeneous chiral condensation from the bosonic two-point function in the $(1+1)$-dimensional Gross-Neveu model in the mean-field approximation
• Exploring new states of matter with a photonic emulator