Q-deformed fermion in many-particle systems and its application to BCS theory

Abstract

In recent decades, there have been increasing interests in quantum statistics beyond the standard Fermi–Dirac and Bose–Einstein statistics, such as the fractional statistics, quon statistics, anyon statistics and quantum groups, since they can provide new insights into the cosmology, nuclear physics and condensed matter. In this paper, we study the many-particle system formed by the q-deformed fermions (q-fermion), which is realized by deforming the quantum algebra of the anticommutation relations. From the standard perspective of the finite temperature field theory, we first construct the finite temperature Green’s function formalism for the free many-q-fermion system, then generalize it to the well known interacting fermionic system, the superconductor, and finally obtain a consistent q-deformed BCS (qBCS) theory. Interesting features can be implied from this model. For example, it predicts a Sarma-like ordered phase, which we call the q-deformed Sarma phase, at low temperature. It also presents a symmetric phase diagram in the parameter space and modified thermodynamic relations.