Phonons, pions and quasi-long-range order in spatially modulated chiral condensates

TL;DR

This paper analyzes low-energy excitations in a spatially modulated chiral condensate phase of dense quark matter, revealing how thermal fluctuations affect its long-range order and discussing implications for neutron stars.

Contribution

It derives elastic free energies for phonons and pions in the modulated phase using Ginzburg-Landau theory and assesses the stability of the phase under thermal fluctuations.

Findings

Thermal fluctuations destroy one-dimensional modulation at nonzero temperature.

Quasicondensate correlations decay algebraically with distance.

Finite-volume effects influence the stability of the real kink crystal.

Abstract

We investigate low-energy fluctuations in the real kink crystal phase of dense quark matter within the Nambu--Jona-Lasinio model. The modulated chiral condensate breaks both the translational symmetry and chiral symmetry spontaneously, which leads to the appearance of phonons and pions that are dominant degrees of freedom in the infrared. Using the Ginzburg-Landau expansion near the Lifshitz point, we derive elastic free energies for phonons and pions in dependence on the temperature and chemical potential. We show that the one-dimensional modulation is destroyed by thermal fluctuations of phonons at nonzero temperature, and compute the exponent that characterizes the anisotropic algebraic decay of quasicondensate correlations at long distance. We also estimate finite-volume effects on the stability of the real kink crystal and briefly discuss the possibility of its existence in neutron stars.