Lesser Green's Function and Chirality Entanglement Entropy via the In-Medium NJL Model

We study chiral symmetry restoration in hot and dense quark matter using the von Neumann chirality entropy within the in-medium Nambu-Jona-Lasinio (NJL) model. Starting from the lesser Green’s function G<(k), we construct the chirality-reduced correlator C_L = P_L G<(k) P_L and define the associated entropy S_chi = -Tr[C_L ln C_L + (1 - C_L) ln(1 - C_L)] to quantify quantum entanglement between left- and right-handed quark sectors. The dynamical quark mass M_q(T, mu_q) reproduces the expected QCD-like phase structure, showing a second-order transition in the chiral limit and a smooth crossover for finite current quark mass. The chirality entropy S_chi increases monotonically with temperature and chemical potential and approaches a maximal value as M_q -> 0. Analyzing its critical behavior, we find a scaling exponent beta_Schi ~ 1, distinct from that of the chiral order parameter. This indicates that S_chi is not an order parameter but a thermodynamic measure of chiral quantum decoherence. Our results demonstrate that chiral symmetry restoration and chiral decoherence are not identical phenomena, and that the chirality entropy reveals information inaccessible to conventional symmetry-breaking observables.

💡 Research Summary

In this work the authors investigate chiral symmetry restoration in hot and dense quark matter from a quantum‑information perspective, using the in‑medium Nambu–Jona‑Lasinio (NJL) model as a concrete framework. The novelty lies in starting from the real‑time (Schwinger‑Keldysh) lesser Green’s function (G^{<}(k)), which encodes the occupied part of the fermionic spectral density, and projecting it onto the left‑handed subspace with the chiral projector (P_{L}= (1-\gamma^{5})/2). The resulting reduced correlator, \