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

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 $i{B}_{\nu }\bar{\psi }{\gamma }_5{\gamma }^{\nu }\psi$, 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.

arXiv comment25 pages, 15 figures

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Cited by in corpus (1)

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