Quantum correlations curvature, memory functions, and fundamental bounds

TL;DR

This paper explores the fundamental limits of quantum correlation curvature in imaginary time, revealing how quantum geometry influences correlation decay and proposing curvature as a universal probe of quantum timescales.

Contribution

It introduces a universal bound on correlation curvature in interacting quantum systems and links it to the memory-function formalism, advancing understanding of quantum correlations in thermal equilibrium.

Findings

Quantum geometry modifies imaginary-time correlation decay.

A universal bound on correlation curvature is established.

Imaginary-time curvature serves as a probe of quantum timescales.

Abstract

We investigate fundamental bounds on the curvature of quantum correlation functions in imaginary time. Focusing first on topological phases, we show that quantum geometry can qualitatively modify the imaginary-time decay of correlations, leading to nontrivial curvature behavior beyond simple exponential scaling. More generally, we show a universal bound on correlation curvature that holds for interacting systems in thermal equilibrium, and establish connection to leading invariants of the memory-function formalism. Our results identify imaginary-time curvature as a robust probe of intrinsic quantum timescales.