A Twisted Kink Crystal in the Chiral Gross-Neveu model

Abstract

We present the detailed properties of a self-consistent crystalline chiral condensate in the massless chiral Gross-Neveu model. We show that a suitable ansatz for the Gorkov resolvent reduces the functional gap equation, for the inhomogeneous condensate, to a nonlinear Schrödinger equation, which is exactly soluble. The general crystalline solution includes as special cases all previously known real and complex condensate solutions to the gap equation. Furthermore, the associated Bogoliubov-de Gennes equation is also soluble with this inhomogeneous chiral condensate, and the exact spectral properties are derived. We find an all-orders expansion of the Ginzburg-Landau effective Lagrangian and show how the gap equation is solved order-by-order.

arXiv comment28 pages, 13 figs; v2: new appendix on Eilenberger eq and refs; version in PRD

References in corpus (26)

• Theory of ultracold Fermi gases
• Inhomogeneous Superconductivity in Condensed Matter and QCD
• The Condensed Matter Physics of QCD
• Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems
• Generalized Ginzburg-Landau theory for non-uniform FFLO superconductors
• From relativistic quantum fields to condensed matter and back again: Updating the Gross-Neveu phase diagram
• Emergence of Skyrme crystal in Gross-Neveu and 't Hooft models at finite density
• Free Energy of an Inhomogeneous Superconductor: a Wave Function Approach
• All about the Static Fermion Bags in the Gross-Neveu Model
• Quantum diffusion of magnetic fields in a numerical worldline approach
• The Four-Fermi Model in Three Dimensions at Non-Zero Density and Temperature
• Loops and loop clouds - a numerical approach to the worldline formalism in QED -
• Analytical solution of the Gross-Neveu model at finite density
• Cluster simulation of relativistic fermions in two space-time dimensions
• Skyrme Crystal from a Twisted Instanton on a Four-Torus
• Chiral crystals in strong-coupling lattice QCD at nonzero chemical potential
• Tricritical behavior of the massive chiral Gross-Neveu model
• Dynamical Generation of Extended Objects in a $1+1$ Dimensional Chiral Field Theory: Non-Perturbative Dirac Operator Resolvent Analysis
• Crystalline ground state in chiral Gross-Neveu and Cooper pair models at finite densities
• Baryons in the large N limit of the massive two-dimensional Nambu-Jona-Lasinio model
• The Gradient Expansion for the Free-Energy of a Clean Superconductor
• New baryon matter in the lattice Gross-Neveu model
• Divergence of the axial current and fermion density in Gross-Neveu models
• Nontopological Finite Temperature Induced Fermion Number
• Is Schwinger Model at Finite Density a Crystal?
• Fermion Bag Solitons in the Massive Gross-Neveu and Massive Nambu-Jona-Lasinio Models in 1+1 Dimensions: Inverse Scattering Analysis

Cited by in corpus (100)

• Quarkyonic Chiral Spirals
• Inhomogeneous phases in the Nambu-Jona-Lasino and quark-meson model
• Inhomogeneous Condensates in the Thermodynamics of the Chiral NJL_2 model
• How many phases meet at the chiral critical point?
• Asymptotic safety: a simple example
• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Vortices and Other Topological Solitons in Dense Quark Matter
• Interweaving Chiral Spirals
• Chiral Magnetic Spiral
• Aharonov-Bohm effect on AdS_2 and nonlinear supersymmetry of reflectionless Poschl-Teller system
• Phonons, pions and quasi-long-range order in spatially modulated chiral condensates
• Crystalline chiral condensates off the tricritical point in a generalized Ginzburg-Landau approach
• Phase structure of the massive chiral Gross-Neveu model from Hartree-Fock
• Covering the Fermi Surface with Patches of Quarkyonic Chiral Spirals
• Spectral singularities in PT-symmetric periodic finite-gap systems
• Solitonic ground states in (color-) superconductivity
• The Bogoliubov/de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry
• Signatures of Moat Regimes in Heavy-Ion Collisions
• Phase structure of mass- and spin-imbalanced unitary Fermi gases
• How transverse thermal fluctuations disorder a condensate of chiral spirals into a quantum spin liquid
• Self-consistent multiple complex-kink solutions in Bogoliubov-de Gennes and chiral Gross-Neveu systems
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Recent progresses on QCD phases in a strong magnetic field -- views from Nambu--Jona-Lasinio model
• Sign Flip in the Casimir Force for Interacting Fermion Systems
• Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems
• Exotic supersymmetry of the kink-antikink crystal, and the infinite period limit
• Fluctuations in cool quark matter and the phase diagram of Quantum Chromodynamics
• Grey solitons in a strongly interacting superfluid Fermi Gas
• Crystals of superconducting Baryonic tubes in the low energy limit of QCD at finite density
• Pion condensation in the Gross-Neveu model with nonzero baryon and isospin chemical potentials
• Properties of the massive Gross-Neveu model with nonzero baryon and isospin chemical potentials
• Spectrally isomorphic Dirac systems: graphene in electromagnetic field
• Hybrid chiral condensate in the external magnetic field
• Supersymmetric twisting of carbon nanotubes
• Pion crystals hosting topologically stable baryons
• Chiral asymmetry in propagation of soliton defects in crystalline backgrounds
• Fermionic solutions of chiral Gross-Neveu and Bogoliubov-de Gennes systems in nonlinear Schrödinger hierarchy
• Integrable model for density-modulated quantum condensates: solitons passing through a soliton lattice
• Crystalline Ground States in Polyakov-loop extended Nambu--Jona-Lasinio Models
• Many-flavor Phase Diagram of the (2+1)d Gross-Neveu Model at Finite Temperature
• The Chiral Magnetic Effect and Axial Anomalies
• Twisted kinks, Dirac transparent systems and Darboux transformations
• Multifaceted properties of Andreev bound states: Interplay of symmetry and topology
• Analytic SU(N) Skyrmions at finite Baryon density
• Worldline Monte Carlo for fermion models at large N_f
• Spontaneous magnetization of quark matter in the inhomogeneous chiral phase
• Spatially Modulated Vacua in a Lorentz-invariant Scalar Field Theory
• Spin imbalance effect on Larkin-Ovchinnikov-Fulde-Ferrel state
• Full time-dependent Hartree-Fock solution of large N Gross-Neveu models
• The nonlinear Dirac equation in Bose-Einstein condensates: I. Relativistic solitons in armchair nanoribbon optical lattices
• Extended supersymmetry of the self-isospectral crystalline and soliton chains
• Quark beta decay in the inhomogeneous chiral phase and cooling of compact stars
• Kink dynamics, sinh-Gordon solitons and strings in AdS(3) from the Gross-Neveu model
• Fulde-Ferrell-Larkin-Ovchinnikov states in a superconducting ring with magnetic fields: Phase diagram and the first-order phase transitions
• Regularization effects in the Nambu-Jona-Lasinio model: Strong scheme dependence of inhomogeneous phases and persistence of the moat regime
• Temporally, Spatially or Light-like Modulated Vacua in Lorentz Invariant Theories
• Structure formation during phase transitions in strongly interacting matter
• Bogoliubov-de Gennes Soliton Dynamics in Unconventional Fermi Superfluids
• Large N solution of generalized Gross-Neveu model with two coupling constants
• Symmetry breaking effect on the inhomogeneous chiral transition in the magnetic field
• Chiral density wave versus pion condensation in the 1+1 dimensional NJL model
• The Sign Problem, PT Symmetry and Abelian Lattice Duality
• Consistent regularization and renormalization in models with inhomogeneous phases
• Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems
• Spinning flavour branes and fermion pairing instabilities
• Crystals of gauged solitons, force free plasma and resurgence
• QED at a finite chemical potential
• Finite-gap twists of carbon nanotubes and an emergent hidden supersymmetry
• Confining solitons in the Higgs phase of $\mathbb{C}{P}^{N-1}$ model: Self-consistent exact solutions in large-$N$ limit
• Dilepton production from moaton quasiparticles
• Solitonic ground state in supersymmetric theory in background
• Analytic non-homogeneous condensates in the $(2+1)$-dimensional Yang-Mills-Higgs-Chern-Simons theory at finite density
• Kink Crystalline Condensate and Multi-kink Solution in Holographic Superconductor
• 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
• Twisted kink crystal in holographic superconductor
• Analytic Baby Skyrmions at Finite Density
• Applications of the potential algebras of the two-dimensional Dirac-like operators
• Exact BPS double-kinks in generalized ${\varphi }^4$, ${\varphi }^6$ and sine-Gordon models
• Kink Crystal
• SQCD, Superconducting Gaps and Cyclic RG Flows
• On instability of ground states in 2D CP(N-1) and O(N) models at large N
• Competing mechanisms of chiral symmetry breaking in a generalized Gross-Neveu model
• Time-dependent Ginzburg-Landau approach to the dynamics of inhomogeneous chiral condensates in a nonlocal Nambu--Jona-Lasinio model
• Ginzburg-Landau Type Approach to the 1+1 Gross Neveu Model - Beyond Lowest Non-Trivial Order
• Cascade of phase transitions in a planar Dirac material
• Inhomogeneous Polyakov loop induced by inhomogeneous chiral condensates
• Detecting Topological Phase Transition in Superconductor-Semiconductor Hybrids by Electronic Raman Spectroscopy
• Tsunami Solitons Emerging from Superconducting Gap
• Inhomogeneous Chiral Phase in Quark Matter
• Collective modes in Fulde-Ferrell-Larkin-Ovchinnikov superconductors: The role of long-range Coulomb interaction and signatures in density response
• Inhomogeneous chiral phase in the magnetic field
• Sine-Gordon kink lattice
• A domain wall and chiral edge currents in holographic chiral phase transitions
• Possibility of quantum Hall effect in dense quark matter environments: A chiral model approach
• The sign problem and Abelian lattice duality
• Low energy physics of interacting bosons with a moat spectrum, and the implications for condensed matter and cold nuclear matter
• Solitons in lattice field theories via tight-binding supersymmetry
• 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
• Spontaneous Magnetization of Quark Matter in Inhomogeneous Chiral Phase