Strongly Interacting Fermions and Phases of the Casimir Effect

TL;DR

This paper investigates how boundary effects and chiral symmetry breaking influence the thermodynamics of strongly interacting fermions between parallel layers, revealing phase transitions and unique temperature-dependent behaviors in the Casimir effect.

Contribution

It introduces a four-fermion effective field theory analysis of the Casimir effect with finite separation, showing boundary-induced phase transitions and temperature-geometry interplay.

Findings

Finite size effects change phase transition order from second to first.

Chiral symmetry breaking leads to distinct massless and massive phases.

Temperature and separation variations can compensate each other in thermodynamic behavior.

Abstract

With the intent of exploring how the interplay between boundary effects and chiral symmetry breaking may alter the thermodynamical behavior of a system of strongly interacting fermions, we study the Casimir effect for the setup of two parallel layers using a four-fermion effective field theory at zero density. This system reveals a number of interesting features. While for infinitely large separation (no boundaries), chiral symmetry is broken or restored via a second order phase transition, in the opposite case of small (and, in general, finite) separation the transition becomes first order, rendering effects of finite size, for the present setup, similar to those of a chemical potential. Appropriately moving on the separation-temperature plane, it is possible to generate a peculiar behavior in the temperature dependence of the thermodynamic potential and of the condensate, compensating thermal with geometrical variations. A behavior similar to what we find here has been predicted to occur in bilayer graphene. Chiral symmetry breaking induces different phases (massless and massive) in the Casimir force separated by critical lines.