Thermodynamic properties of non-Hermitian Nambu--Jona-Lasinio models

TL;DR

This paper explores how non-Hermitian extensions to the NJL model affect thermodynamic properties, phase transitions, and potential fermion-antifermion asymmetries, with implications for strongly interacting fermion systems like neutron stars.

Contribution

It introduces non-Hermitian bilinear extensions to the NJL model and analyzes their impact on phase transitions and thermodynamic quantities, revealing tunable effects and potential fermion asymmetries.

Findings

Altered chiral phase transition points and critical end-points.

Signatures of fermion or antifermion excess due to non-Hermitian terms.

Regions with negative interaction measure indicating unusual thermodynamic behavior.

Abstract

We investigate the impact of non-Hermiticity on the thermodynamic properties of interacting fermions by examining bilinear extensions to the $3+1$ dimensional $SU(2)$-symmetric Nambu--Jona-Lasinio (NJL) model of quantum chromodynamics at finite temperature and chemical potential. The system is modified through the anti-$PT$-symmetric pseudoscalar bilinear $\bar{\psi}\gamma_5 \psi$ and the $PT$-symmetric pseudovector bilinear $iB_\nu \,\bar{\psi}\gamma_5\gamma^\nu \psi$, introduced with a coupling $g$. Beyond the possibility of dynamical fermion mass generation at finite temperature and chemical potential, our findings establish model-dependent changes in the position of the chiral phase transition and the critical end-point. These are tunable with respect to $g$ in the former case, and both $g$ and $|B|/B_0$ in the latter case, for both lightlike and spacelike fields. Moreover, the behavior of the quark number, entropy, pressure, and energy densities signal a potential fermion or antifermion excess compared to the standard NJL model, due to the pseudoscalar and pseudovector extension respectively. In both cases regions with negative interaction measure $I = \epsilon-3p$ are found. Future indications of such behaviors in strongly interacting fermion systems, for example in the context of neutron star physics, may point toward the presence of non-Hermitian contributions. These trends provide a first indication of curious potential mechanisms for producing non-Hermitian baryon asymmetry. In addition, the formalism described in this study is expected to apply more generally to other Hamiltonians with four-fermion interactions and thus the effects of the non-Hermitian bilinears are likely to be generic.