Quantum correlations curvature, memory functions, and fundamental bounds

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.

Figures (1)

• Figure 1: Curvature of quantum correlators at imaginary time $\tau = \beta/2$ contains critical information on the internal timescales (see main text). Solid line: Imaginary-time correlator in a model of dispersionless weakly- interacting two-band Chern insulator ( Kruchkov2024Kruchkov2023). We here consider two flat bands of Chern number $C=|1|$ separated by a topological gap $\Delta$, at temperature $T=0.2,\Delta$.