Hilbert space connectivity in non-Hermitian many-body systems: emergent scale-dependent amplification and constraint-induced skin localization

RESUMO

Various exotic many-body phenomena such as quantum scars and fractons have been linked to Hilbert space fragmentation. In this work, we find that in non-Hermitian settings, Hilbert space connectivity has an even more universal and fundamental influence, tightly controlling the nature of spectral amplification and state localization. Far more complicated than real-space lattices, non-Hermitian many-body Hilbert space graphs not only possess intricate competing amplification channels, but also global feedback loops connecting remote Fock states related by particle symmetry. These features lead to amplification behavior with unconventional scaling and localization properties. Particle occupation constraints can furthermore remove selected Hilbert space pathways, leading to robust unipolar and asymmetric bipolar skin localization in otherwise reciprocal processes. These results extend beyond simple interacting bosonic models and establish Hilbert space connectivity as a versatile control knob for many-body non-Hermitian critical transitions.