Toda chain flow in Krylov space

TL;DR

This paper reveals that the imaginary-time correlation functions in quantum many-body systems are tau-functions of the Toda hierarchy, linking singularities to Krylov space delocalization and providing a new integrable systems perspective.

Contribution

It establishes a general analytical connection between imaginary-time correlation functions and Toda hierarchy tau-functions, highlighting the role of Krylov space delocalization in quantum chaos.

Findings

Imaginary-time correlation functions are tau-functions of the Toda hierarchy.

Singularities along the imaginary axis are due to Krylov space delocalization.

Provides a new integrable systems framework for quantum many-body dynamics.

Abstract

We show in full generality that time-correlation function of a physical observable analytically continued to imaginary time is a tau-function of integrable Toda hierarchy. Using this relation we show that the singularity along the imaginary axis, which is a generic behavior for quantum non-integrable many-body system, is due to delocalization in Krylov space.