Ginzburg–Landau Free Energy of Crystalline Color Superconductors: A Matrix Formalism from Solid-State Physics**Supported by the National Natural Science Foundation of China under Grant No. 11335005 and the Ministry of Science and Technology under Grant Nos. 2013CB922000 and 2014CB845400, and by the US Department of Energy Topical Collaboration “Neutrinos and Nucleosynthesis in Hot and Dense Matter”

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.