Dynamical correlation functions from complex time evolution

TL;DR

This paper introduces a tensor network method combining complex time evolution and perturbative reconstruction to efficiently compute spectral functions and self-energies in quantum impurity models, reducing computational complexity.

Contribution

It presents a novel approach that mitigates entanglement growth during time evolution by integrating complex time techniques with correlation function reconstruction.

Findings

Reduces bond dimension compared to real-time evolution

Achieves high-precision low-frequency self-energy results

Successfully captures the Kondo energy scale

Abstract

We present an approach to tame the growth of entanglement during time evolution by tensor network methods. It combines time evolution in the complex plane with a perturbative and controlled reconstruction of correlation functions on the real-time axis. We benchmark our approach on the single impurity Anderson model. Compared to purely real-time evolution, the complex time evolution significantly reduces the required bond dimension to obtain the spectral function. Notably, our approach yields self-energy results with high precision at low frequencies, comparable to numerical renormalization group (NRG) results, and it successfully captures the exponentially small Kondo energy scale.