Liquid-Gas Phase Transitions and $\mathcal{CK}$ Symmetry in Quantum Field Theories

TL;DR

This paper develops a field-theoretic framework to analyze liquid-gas phase transitions in quantum field theories with $\\mathcal{CK}$ symmetry, revealing the nature of phase transitions, disorder lines, and the role of complex eigenvalues in correlation functions.

Contribution

It introduces a new effective three-dimensional field theory approach incorporating $\\mathcal{CK}$ symmetry to study phase transitions at finite density.

Findings

Relativistic and static fermions exhibit first-order liquid-gas transitions with critical points.

Nonrelativistic fermions and classical particles show no first-order transitions at tree level.

The mass matrix eigenvalues can be complex, leading to disorder lines and a connection to the critical line.

Abstract

A general field-theoretic framework for the treatment of liquid-gas phase transitions is developed. Starting from a fundamental four-dimensional field theory at nonzero temperature and density, an effective three-dimensional field theory with a sign problem is derived. Although charge conjugation $\mathcal{C}$ is broken at finite density, there remains a symmetry under $\mathcal{CK}$, where $\mathcal{K}$ is complex conjugation. We consider four models: relativistic fermions, nonrelativistic fermions, static fermions and classical particles. The thermodynamic behavior is extracted from $\mathcal{CK}$-symmetric complex saddle points of the effective field theory at tree level. The relativistic and static fermions show a liquid-gas transition, manifesting as a first-order line at low temperature and high density, terminated by a critical end point. In the cases of nonrelativistic fermions and classical particles, we find no first-order liquid-gas transitions at tree level. The mass matrix controlling the behavior of correlation functions is obtained from fluctuations around the saddle points. Due to the $\mathcal{CK}$ symmetry of the models, the eigenvalues of the mass matrix can be complex. This leads to the existence of disorder lines, which mark the boundaries where the eigenvalues go from purely real to complex. The regions where the mass matrix eigenvalues are complex are associated with the critical line. In the case of static fermions, a powerful duality between particles and holes allows for the analytic determination of both the critical line and the disorder lines. Depending on the values of the parameters, either zero, one or two disorder lines are found. Numerical results for relativistic fermions give a very similar picture.