Non-Hermitian Linear Response Theory

TL;DR

This paper develops a non-Hermitian linear response theory connecting dynamical responses to equilibrium properties, with applications to quantum many-body systems and experimental validation.

Contribution

It introduces a novel non-Hermitian linear response framework applicable to quantum systems, linking response dynamics to spectral functions and critical exponents.

Findings

Universal function governing momentum distribution dynamics

Slower dynamics in critical states without quasi-particles

Good agreement with experimental data on Bose-Hubbard model

Abstract

Linear response theory lies at the heart of quantum many-body physics because it builds up connections between the dynamical response to an external probe and correlation functions at equilibrium. Here we consider the dynamical response of a Hermitian system to a non-Hermitian probe, and we develop a non-Hermitian linear response theory that can also relate this dynamical response to equilibrium properties. As an application of our theory, we consider the real-time dynamics of momentum distribution induced by one-body and two-body dissipations. We find that, for many cases, the dynamics of momentum occupation and the width of momentum distribution obey the same universal function, governed by the single-particle spectral function. We also find that, for critical state with no well-defined quasi-particles, the dynamics are slower than normal state and our theory provides a model independent way to extract the critical exponent. We apply our results to analyze recent experiment on the Bose-Hubbard model and find surprising good agreement between theory and experiment. We also propose to further verify our theory by carrying out a similar experiment on a one-dimensional Luttinger liquid.