From spin chains to real-time thermal field theory using tensor networks

TL;DR

This paper demonstrates how tensor networks, combined with signal analysis, can be used to compute retarded correlators in (1+1)-dimensional quantum field theories, revealing insights into their thermal response and singularity structure.

Contribution

It introduces a tensor network approach for ab initio calculation of retarded correlators in quantum field theories derived from quantum Ising chains, including nonintegrable models.

Findings

Tensor networks effectively compute correlators at intermediate times.

Prony analysis reveals singularity structures in the complex frequency plane.

Method predicts thermal responses in nonintegrable quantum field theories.

Abstract

One of the most interesting directions in theoretical high-energy and condensed-matter physics is understanding dynamical properties of collective states of quantum field theories. The most elementary tool in this quest is retarded equilibrium correlators governing the linear response theory. In this article we examine tensor networks as a way of determining them in a fully ab initio way in a class of (1+1)-dimensional quantum field theories arising as infrared descriptions of quantum Ising chains.We show that, complemented with signal analysis using the Prony method, tensor network calculations for intermediate times provide a powerful way to explore the structure of singularities of the correlator in the complex frequency plane and to make predictions about the thermal response to perturbations in a class of nonintegrable interacting quantum field theories.