Two-dimensional chiral crystals in the NJL model

Abstract

We investigate the phase structure of the Nambu--Jona-Lasinio model at zero temperature, allowing for a two-dimensional spatial dependence of the chiral condensate. Applying the mean-field approximation, we consider various periodic structures with rectangular and hexagonal geometries, and minimize the corresponding free energy. We find that these two-dimensional chiral crystals are favored over homogeneous phases in a certain window in the region where the phase transition would take place when the analysis was restricted to homogeneous condensates. It turns out, however, that in this regime they are disfavored against a phase with a one-dimensional modulation of the chiral condensate. On the other hand, we find that square and hexagonal lattices eventually get favored at higher chemical potentials. Although stretching the limits of the model to some extent, this would support predictions from quarkyonic-matter studies.

12 pages, 6 figures. v2: added figure, small modifications, matches published version

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• Landau-Peierls instability in a Fulde-Ferrell type inhomogeneous chiral condensed phase
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• Inhomogeneous condensation in effective models for QCD using the finite-mode approach
• Fluctuations in cool quark matter and the phase diagram of Quantum Chromodynamics
• Inhomogeneous chiral condensates in three-flavor quark matter
• Hybrid chiral condensate in the external magnetic field
• Discussions on the crossover property within the Nambu--Jona-Lasinio model
• Inhomogeneous phases in the quark-meson model with explicit chiral-symmetry breaking
• Many-flavor Phase Diagram of the (2+1)d Gross-Neveu Model at Finite Temperature
• Crystalline phases by an improved gradient expansion technique
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• Influence of vector interactions on the favored shape of inhomogeneous chiral condensates
• Fate of chiral critical point under the strong isospin asymmetry
• Chiral pair fluctuations for the inhomogeneous chiral transition
• Regularization effects in the Nambu-Jona-Lasinio model: Strong scheme dependence of inhomogeneous phases and persistence of the moat regime
• 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 $1\le d<3$
• Self-bound quark matter in the NJL model revisited: from schematic droplets to domain-wall solitons
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• Gradient expansion technique for inhomogeneous, magnetized quark matter
• Inhomogeneous Polyakov loop induced by inhomogeneous chiral condensates
• Inhomogeneous Chiral Phase in Quark Matter
• Spatially modulated chiral condensates
• Detecting inhomogeneous chiral condensation from the bosonic two-point function in the $(1+1)$-dimensional Gross-Neveu model in the mean-field approximation
• Color-superconductivity and inhomogeneous chiral symmetry breaking in isospin-asymmetric quark matter