Aufbau Principle for Non-Hermitian Systems

TL;DR

This paper introduces a generalized Aufbau principle for non-Hermitian systems, demonstrating its similarity to Hermitian systems and revealing unique many-body phenomena like skin effects and anomalous Bose-Einstein condensation.

Contribution

It develops a comprehensive framework for many-body physics in non-Hermitian systems, including the derivation of spectra and analysis of boundary effects.

Findings

Many-body non-Hermitian skin effects persist in all eigenstates.

Ground state bosons exhibit anomalous Bose-Einstein condensation.

Hard-core bosons cannot be mapped to fermions under periodic boundary conditions.

Abstract

We develop a generalized Aufbau principle for non-Hermitian systems that allows for building up the configurations of indistinguishable particles. The Aufbau rule of non-Hermitian systems is unexpectedly shown to be identical to that developed in Hermitian systems when the real parts of the complex energy levels are considered. We derive full many-body energy spectra of the fermionic and bosonic Hatano-Nelson models as examples by filling single-particle energy levels in the momentum space. For open boundary conditions, we show that many-body non-Hermitian skin effects persist in all many-body eigenstates for both fermions and bosons. Furthermore, we find surprisingly that the ground state of bosons is an anomalous Bose-Einstein condensation with all of the particles simultaneously localizing in both the real and momentum space beyond the Heisenberg uncertainty principle. For periodic boundary conditions, we show that hard-core bosons cannot be mapped to fermions. This work establishes a general framework for understanding the many-body physics of non-Hermitian systems, revealing rich unique non-Hermitian many-body physics.