Crystalline phases by an improved gradient expansion technique

Abstract

We develop an innovative technique for studying inhomogeneous phases with a spontaneous broken symmetry. The method relies on the knowledge of the exact form of the free energy in the homogeneous phase and on a specific gradient expansion of the order parameter. We apply this method to quark matter at vanishing temperature and large chemical potential, which is expected to be relevant for astrophysical considerations. The method is remarkably reliable and fast as compared to performing the full numerical diagonalization of the quark Hamiltonian in momentum space, and is designed to improve the standard Ginzburg-Landau expansion close to the phase transition points. For definiteness we focus on inhomogeneous chiral symmetry breaking, accurately reproducing known results for 1D and 2D modulations and examining novel crystalline structures, as well. Consistently with previous results, we find that the energetically favored modulation is the so-called 1D real kink crystal. We propose a qualitative description of the pairing mechanism to motivate this result.

11 pages, 8 figures. v2 with minor changes. Accepted for publication on Physical Review D

References in corpus (6)

• Inhomogeneous chiral condensates
• Inhomogeneous phases in the Nambu-Jona-Lasino and quark-meson model
• The Crystallography of Three-Flavor Quark Matter
• Inhomogeneous phases in the quark-meson model with vacuum fluctuations
• Testing the Ginzburg-Landau approximation for three-flavor crystalline color superconductivity
• Self-bound quark matter in the NJL model revisited: from schematic droplets to domain-wall solitons

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• Multicomponent meson superfluids in chiral perturbation theory
• Phase transitions and resilience of the MDCDW phase at finite temperature and density
• Influence of vector interactions on the favored shape of inhomogeneous chiral condensates
• Finite Density Two Color Chiral Perturbation Theory Revisited
• A novel Dual Chiral Density Wave in nuclear matter based on a parity doublet structure
• Chiral crystallization in an external magnetic background - Chiral spiral versus Real kink crystal -
• Dual chiral density waves in nuclear matter
• Analytic non-homogeneous condensates in the $(2+1)$-dimensional Yang-Mills-Higgs-Chern-Simons theory at finite density
• Time-dependent Ginzburg-Landau approach to the dynamics of inhomogeneous chiral condensates in a nonlocal Nambu--Jona-Lasinio model
• Gradient expansion technique for inhomogeneous, magnetized quark matter