Scaling of free cumulants in closed system-bath setups

TL;DR

This paper investigates how free cumulants scale in system-bath quantum setups, revealing universal behavior linked to thermalization, extending previous closed-system analyses to more realistic models.

Contribution

It extends the analysis of free cumulants to system-bath setups, demonstrating universal scaling and connecting it to thermalization dynamics in both idealized and realistic baths.

Findings

Universal scaling of microcanonical free cumulants with interaction strength.

Connection between cumulant scaling and thermalization dynamics.

Analysis includes both random-matrix and defect Ising chain baths.

Abstract

The Eigenstate Thermalization Hypothesis (ETH) has been established as a cornerstone for understanding thermalization in quantum many-body systems. Recently, there has been growing interest in the full ETH, which extends the framework of the conventional ETH and postulates a smooth function to describe the multi-point correlations among matrix elements. Within this framework, free cumulants play a central role, and most previous studies have primarily focused on closed systems. In this paper, we extend the analysis to a system-bath setup, considering both an idealized case with a random-matrix bath and a more realistic scenario where the bath is modeled as a defect Ising chain. In both cases, we uncover a universal scaling of the microcanonical free cumulants of observables associated with the central system Hamiltonian with respect to the interaction strength. Furthermore we establish a connection between this scaling behavior and the thermalization dynamics of the thermal free cumulants of corresponding observables.