Quantum Geometric Bounds in Non-Hermitian Systems

TL;DR

This paper establishes quantum geometric bounds for observables in non-Hermitian systems, linking geometric constraints to response functions and demonstrating their relevance in open quantum systems with potential experimental implications.

Contribution

It introduces novel quantum geometric bounds specific to non-Hermitian systems and connects these bounds to physical response functions in open quantum systems.

Findings

Derived bounds on non-Hermitian quantum geometric tensors

Identified geometric constraints on response correlators and conductivities

Applied results to topological systems with non-Hermitian Chern numbers

Abstract

We identify quantum geometric bounds for observables in non-Hermitian systems. We find unique bounds on non-Hermitian quantum geometric tensors, generalized two-point response correlators, conductivity tensors, and optical weights. We showcase these findings in topological systems with non-Hermitian Chern numbers. We demonstrate that the non-Hermitian geometric constraints on response functions naturally arise in open quantum systems governed by out-of-equilibrium Lindbladian dynamics. Our findings are relevant to experimental observables and responses under the realistic setups that fall beyond the idealized closed-system descriptions.