Emergent Fermi surface in a many-body non-Hermitian fermionic chain

Quantum degeneracy pressure (QDP) underscores the stability of matter and is arguably the most ubiquitous many-body effect. The associated Fermi surface (FS) has broad implications for physical phenomena, ranging from electromagnetic responses to entanglement entropy (EE) area law violations. Given recent fruitful studies in condensed-matter physics under effectively non-Hermitian descriptions, it becomes urgent to study how QDP and many-body interactions interplay with non-Hermitian effects. Through a prototypical critical one-dimensional fermionic lattice with asymmetric gain/loss, a real space FS is shown to naturally emerge, in addition to any existing momentum space FS. We carefully characterize such real space FS with the EE, by a renormalized temperature that encapsulates the interplay of thermal excitations and non-Hermiticity. Nearest-neighbor repulsion is also found to induce a competing charge density wave (CDW) that may erode the real space FS. The underlying physics surrounding criticality and localization is further analyzed with complex flux spectral flows. Our findings can be experimentally demonstrated with ultracold fermions in a suitably designed optical lattice.