  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 1D fermionic lattice with asymmetric gain/loss, a real space FS is
shown to naturally emerge, in addition to any existing momentum space FS. We
also carefully characterize such real space FS with the EE, via a renormalized
temperature that encapsulates the interplay of thermal excitations and
non-Hermiticity. Nearest neighbor repulsion is also found to induce 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.
