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.

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

References in corpus (8)

• Theory of ultracold Fermi gases
• Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems
• Cluster simulation of relativistic fermions in two space-time dimensions
• Tricritical behavior of the massive chiral Gross-Neveu model
• Baryons in the large N limit of the massive two-dimensional Nambu-Jona-Lasinio model
• New baryon matter in the lattice Gross-Neveu model
• Divergence of the axial current and fermion density in Gross-Neveu models
• Is Schwinger Model at Finite Density a Crystal?

Cited by in corpus (43)

• Inhomogeneous phases in the Nambu-Jona-Lasino and quark-meson model
• Asymptotic safety: a simple example
• Chiral Magnetic Spiral
• Aharonov-Bohm effect on AdS_2 and nonlinear supersymmetry of reflectionless Poschl-Teller system
• 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
• 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
• Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems
• Crystals of superconducting Baryonic tubes in the low energy limit of QCD at finite density
• Spectrally isomorphic Dirac systems: graphene in electromagnetic field
• Pion crystals hosting topologically stable baryons
• Fermionic solutions of chiral Gross-Neveu and Bogoliubov-de Gennes systems in nonlinear Schrödinger hierarchy
• Twisted kinks, Dirac transparent systems and Darboux transformations
• Analytic SU(N) Skyrmions at finite Baryon density
• Spin imbalance effect on Larkin-Ovchinnikov-Fulde-Ferrel state
• Quark beta decay in the inhomogeneous chiral phase and cooling of compact stars
• Regularization effects in the Nambu-Jona-Lasinio model: Strong scheme dependence of inhomogeneous phases and persistence of the moat regime
• Structure formation during phase transitions in strongly interacting matter
• Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems
• Crystals of gauged solitons, force free plasma and resurgence
• Solitonic ground state in supersymmetric theory in background
• Dilepton production from moaton quasiparticles
• Analytic non-homogeneous condensates in the $(2+1)$-dimensional Yang-Mills-Higgs-Chern-Simons theory at finite density
• Exact BPS double-kinks in generalized ${\varphi }^4$, ${\varphi }^6$ and sine-Gordon models
• Kink Crystal
• 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
• SQCD, Superconducting Gaps and Cyclic RG Flows
• Cascade of phase transitions in a planar Dirac material
• Inhomogeneous Polyakov loop induced by inhomogeneous chiral condensates
• Tsunami Solitons Emerging from Superconducting Gap
• Collective modes in Fulde-Ferrell-Larkin-Ovchinnikov superconductors: The role of long-range Coulomb interaction and signatures in density response
• Sine-Gordon kink lattice
• Detecting Topological Phase Transition in Superconductor-Semiconductor Hybrids by Electronic Raman Spectroscopy
• Low energy physics of interacting bosons with a moat spectrum, and the implications for condensed matter and cold nuclear matter
• 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
• Solitons in lattice field theories via tight-binding supersymmetry