Ginzburg-Landau free energy of crystalline color superconductors: A matrix formalism from solid-state physics

TL;DR

This paper introduces a matrix formalism using the discrete Bloch representation to compute the Ginzburg-Landau free energy of crystalline color superconductors to arbitrary order, enhancing predictive accuracy for phase transition analysis.

Contribution

It presents a novel matrix formalism based on solid-state physics techniques to evaluate higher-order terms in the Ginzburg-Landau free energy for crystalline color superconductors.

Findings

New matrix formalism enables calculation of free energy to arbitrary order.

Simplifies the evaluation process without momentum constraints.

Facilitates more accurate predictions of phase transitions.

Abstract

The Ginzburg-Landau (GL) free energy of crystalline color superconductors is important for understanding the nature of the phase transition to the normal quark matter and predicting the preferred crystal structure. So far the GL free energy at zero temperature has only been evaluated up to the sixth order in the condensate. To give quantitative reliable predictions we need to evaluate the higher-order terms. In this work, we present a new derivation of the GL free energy by using the discrete Bloch representation of the fermion field. This derivation introduces a simple matrix formalism without any momentum constraint, which may enable us to calculate the GL free energy to arbitrary order by using a computer.