Emergent non-Hermitian conservation laws at exceptional points

TL;DR

This paper uncovers a new class of non-Hermitian conservation laws emerging at exceptional points in non-Hermitian systems, demonstrated through theoretical formulation and quantum circuit simulations.

Contribution

It introduces a general theory linking conservation laws at EPs to emergent symmetries in auxiliary Hermitian systems, with practical verification in quantum circuits.

Findings

Identification of non-Hermitian conservation laws at EPs

Establishment of a correspondence with auxiliary Hermitian systems

Simulation of conserved dynamics in quantum circuits

Abstract

Non-Hermitian systems can manifest rich static and dynamical properties at their exceptional points (EPs). Here, we identify yet another class of distinct phenomena that is hinged on EPs, namely, the emergence of a series of non-Hermitian conservation laws. We demonstrate these distinct phenomena concretely in the non-Hermitian Heisenberg chain and formulate a general theory for identifying these emergent non-Hermitian conservation laws at EPs. By establishing a one-to-one correspondence between the constant of motions at EPs and those in corresponding auxiliary Hermitian systems, we trace their physical origin back to the presence of emergent symmetries in the auxiliary systems. Concrete simulations on quantum circuits show that these emergent conserved dynamics can be readily observed in current digital quantum computing systems.