ETH-monotonicity in two-dimensional systems

TL;DR

This paper investigates ETH-monotonicity in two-dimensional quantum chaotic systems, demonstrating that the flattening rate of the $f$-function scales with system size and particle number, supporting the property in higher dimensions.

Contribution

It provides new evidence that ETH-monotonicity holds in 2D systems and quantifies how the flattening rate depends on system size and particle number.

Findings

Flattening rate scales with the square of the linear size, $L^2$, in 2D systems.

Flattening rate is proportional to particle or hole number.

Supports ETH-monotonicity in higher-dimensional quantum chaotic systems.

Abstract

We study a recently discovered property of many-body quantum chaotic systems called ETH-monotonicity in two-dimensional systems. Our new results further support ETH-monotonicity in these higher dimensional systems. We show that the flattening rate of the $f$-function is directly proportional to the number of degrees of freedom in the system, so as $L^2$ where $L$ is the linear size of the system, and in general, expected to be $L^d$ where $d$ is the spatial dimension of the system. We also show that the flattening rate is directly proportional to the particle (or hole) number for systems of same spatial size.