Spatially oscillating correlation functions in $\left(2+1\right)$-dimensional four-fermion models: The mixing of scalar and vector modes at finite density

Abstract

In this work, we demonstrate that the mixing of scalar and vector condensates produces spatially oscillating, but exponentially damped correlation functions in fermionic theories at finite density and temperature. We find a regime exhibiting this oscillatory behavior in a Gross-Neveu-type model that also features vector interactions within the mean-field approximation. The existence of this regime aligns with expectations based on symmetry arguments, that are also applicable to QCD at finite baryon density. We compute the phase diagram including both homogeneous phases and regions with spatially oscillating, exponentially damped correlation functions at finite temperature and chemical potential for different strengths of the vector coupling. Furthermore, we find that inhomogeneous condensates are disfavored compared to homogeneous ones akin to previous findings without vector interactions. We show that our results are valid for a broad class of $\left(2+1\right)$-dimensional models with local four-fermion interactions.

arXiv comment20 pages, 10 figures, 29 pages including appendices & references; v2: Corrected typos, added some explanations on methodology in section III, version as accepted for publication in Physical Review D

References in corpus (92)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Array Programming with NumPy
• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Non-Hermitian Physics
• NJL-model analysis of dense quark matter
• Is there still any Tc mystery in lattice QCD? Results with physical masses in the continuum limit III
• "Strongly interacting matter in magnetic fields": an overview
• The QCD phase structure at finite temperature and density
• High density QCD on a Lefschetz thimble?
• Is graphene in vacuum an insulator?
• Chiral Phase Transition within Effective Models with Constituent Quarks
• QCD at finite temperature and chemical potential from Dyson-Schwinger equations
• Inhomogeneous chiral condensates
• The Phase Diagram of the Quark-Meson Model
• Inhomogeneous phases in the Nambu-Jona-Lasino and quark-meson model
• Chiral symmetry and density wave in quark matter
• From Quarks and Gluons to Hadrons: Chiral Symmetry Breaking in Dynamical QCD
• 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
• Quark Number Fluctuations in a Chiral Model at Finite Baryon Chemical Potential
• Revised Phase Diagram of the Gross-Neveu Model
• The Vacuum Structure of Vector Mesons in QCD
• Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
• Phase Structure of Four-Fermion Theories at Finite Temperature and Chemical Potential in Arbitrary Dimensions
• Inhomogeneous phases in the quark-meson model with vacuum fluctuations
• Phonons, pions and quasi-long-range order in spatially modulated chiral condensates
• Inhomogeneous phases in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Landau-Peierls instability in a Fulde-Ferrell type inhomogeneous chiral condensed phase
• The Four-Fermi Model in Three Dimensions at Non-Zero Density and Temperature
• The low-temperature behavior of the quark-meson model
• Large $N$ critical exponents for the chiral Heisenberg Gross-Neveu universality class
• Monte Carlo calculations of the finite density Thirring model
• Signatures of Moat Regimes in Heavy-Ion Collisions
• Dyson-Schwinger study of chiral density waves in QCD
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• Thermodynamics of quark matter with a chiral imbalance
• Updating the Phase Diagram of the Gross-Neveu Model in 2+1 Dimensions
• How transverse thermal fluctuations disorder a condensate of chiral spirals into a quantum spin liquid
• Inhomogeneous chiral phases away from the chiral limit
• Renormalization Group Study of Magnetic Catalysis in the 3d Gross-Neveu Model
• Complex Saddle Points and Disorder Lines in QCD at finite temperature and density
• Inhomogeneous charged pion condensation in chiral asymmetric dense quark matter in the framework of NJL${}_2$ model
• Fluctuations in cool quark matter and the phase diagram of Quantum Chromodynamics
• Regulator dependence of inhomogeneous phases in the 2+1-dimensional Gross-Neveu model
• Inhomogeneous chiral condensates in three-flavor quark matter
• Inhomogeneous phases in one-dimensional mass- and spin-imbalanced Fermi gases
• QCD phase transitions in the light quark chiral limit
• Monte Carlo Simulation of the Three Dimensional Thirring Model
• Phase diagram of the large $N$ Gross-Neveu model in a finite periodic box
• Phase structure of the 1+1 dimensional Nambu--Jona-Lasinio model with isospin
• Emergent Hadrons and Diquarks
• Phase transitions in hexagonal, graphene-like lattice sheets and nanotubes under the influence of external conditions
• Particle Interferometry in a Moat Regime
• Inhomogeneous phases in the quark-meson model with explicit chiral-symmetry breaking
• Evidence for BCS Diquark Condensation in the 3+1d Lattice NJL Model
• Absence of Landau-Peierls Instability in the Magnetic Dual Chiral Density Wave Phase of Dense QCD
• Hot QCD at finite isospin density: confronting SU(3) Nambu-Jona-Lasinio model with recent lattice data
• Universality of Pattern Formation
• Inhomogeneities in the $2$-Flavor Chiral Gross-Neveu Model
• Coexistence of pion condensation and color superconductivity in two flavor quark matter
• Competition of inhomogeneous chiral phases and two-flavor color superconductivity in the NJL model
• Catalysis of Dynamical Chiral Symmetry Breaking by Chiral Chemical Potential in Dirac semimetals
• PT Symmetry in Classical and Quantum Statistical Mechanics
• QCD equation of state at finite isospin density from the linear sigma model with quarks: The cold case
• Numerical Portrait of a Relativistic BCS Gapped Superfluid
• Phase transitions and resilience of the MDCDW phase at finite temperature and density
• Inhomogeneous phases in the chirally imbalanced $2+1$-dimensional Gross-Neveu model and their absence in the continuum limit
• Critical Behaviour in the Dense Planar NJL Model
• Absence of inhomogeneous chiral phases in 2+1-dimensional four-fermion and Yukawa models
• Non-Hermitian extension of the Nambu--Jona-Lasinio model in 3+1 and 1+1 dimensions
• Fermi Surface Phenomena in the (2+1)d Four-Fermi Model
• Influence of vector interactions on the favored shape of inhomogeneous chiral condensates
• The 2+1 Dimensional NJL Model at Finite Temperature
• Lefschetz thimbles in fermionic effective models with repulsive vector-field
• $\mathcal{P}T$ symmetry, pattern formation, and finite-density QCD
• 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
• Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model
• Stability of homogeneous chiral phases against inhomogeneous perturbations in 2+1 dimensions
• Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions $1\le d<3$
• Finite-volume effects in baryon number fluctuations around the QCD critical endpoint
• Superconductivity phenomenon induced by external in-plane magnetic field in (2+1)-dimensional Gross--Neveu type model
• Oscillating propagators in heavy-dense QCD
• Chiral spiral in the presence of chiral imbalance
• First-order phase boundaries of the massive 1+1 dimensional Nambu--Jona-Lasinio model with isospin
• Effects of Quark Interactions on Dynamical Chiral Symmetry Breaking by a Magnetic Field
• Gross-Neveu model with O(2)${}_L\times$O(2)${}_R$ chiral symmetry: Duality with Zakharov-Mikhailov model and large $N$ solution
• Interaction of static charges in graphene within Monte-Carlo simulation
• Remnants of large-$N_{\mathrm{f}}$ inhomogeneities in the 2-flavor chiral Gross-Neveu model
• Thermal phonon fluctuations and stability of the magnetic dual chiral density wave phase in dense QCD
• QCD phase diagram and charge fluctuations
• Mesons at finite baryon density in (2+1)d

Cited by in corpus (5)

• The QCD moat regime and its real-time properties
• Regularization effects in the Nambu-Jona-Lasinio model: Strong scheme dependence of inhomogeneous phases and persistence of the moat regime
• Dilepton production from moaton quasiparticles
• 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
• Dissecting the moat regime at low energies I: Renormalization and the phase structure