Extracting Nonlinear Dynamical Response Functions from Time Evolution

TL;DR

This paper introduces a functional derivative-based framework to extract nonlinear dynamical response functions directly from time evolution data, avoiding complex correlation calculations, and demonstrates its effectiveness on models including the Rice-Mele and many-body systems.

Contribution

It presents a novel, broadly applicable method for obtaining nonlinear response functions from real-time dynamics without explicit multipoint correlation computations.

Findings

Successfully calculated second- and third-order optical responses in the Rice-Mele model.

Extended the method to a many-body interacting system using tensor network techniques.

Validated the framework's broad applicability to various dynamical systems.

Abstract

We develop a general framework based on the functional derivative to extract nonlinear dynamical response functions from the temporal evolution of physical quantities, without explicitly computing multipoint correlation functions. We validate our approach by calculating the second- and third-order optical responses in the Rice-Mele model and further apply it to a many-body interacting system using a tensor network method. This framework is broadly applicable to any method that can compute real-time dynamics, offering a powerful and versatile tool for investigating nonlinear responses in dynamical systems.