Crystalline chiral condensates off the tricritical point in a generalized Ginzburg-Landau approach

TL;DR

This paper investigates inhomogeneous chiral condensates in QCD at finite density using a generalized Ginzburg-Landau approach, revealing complex phase structures including multidimensional modulations and a unique Lifshitz point with multiple critical lines.

Contribution

It extends the Ginzburg-Landau framework to analyze multidimensional modulations and complex phase structures in QCD, including new critical points and phase trajectories.

Findings

Solitonic chiral condensate is most favorable in 1D modulations.

Multiple critical lines converge at a Lifshitz point.

Discovery of a triple point in the phase diagram.

Abstract

We present an extensive study on inhomogeneous chiral condensates in QCD at finite density in the chiral limit using a generalized Ginzburg-Landau (GL) approach. Performing analyses on higher harmonics of one-dimensionally (1D) modulated condensates, we numerically confirm the previous claim that the solitonic chiral condensate characterized by Jacobi's elliptic function is the most favorable structure in 1D modulations. We then investigate the possibility of realization of several multidimensional modulations within the same framework. We also study the phase structure far away from the tricritical point by extending the GL functional expanded up to the eighth order in the order parameter and its spatial derivative. On the same basis, we explore a new regime in the extended GL parameter space and find that the Lifshitz point is the point where five critical lines meet at once. In particular, the existence of an intriguing triple point is demonstrated, and its trajectory consists of one of those critical lines.