Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor

TL;DR

This paper analyzes eigenstate correlations in chaotic dual-unitary quantum circuits using the partial spectral form factor, revealing deviations from random matrix theory at short times and agreement at longer times.

Contribution

It provides exact analytical results for the partial spectral form factor in dual-unitary circuits, demonstrating time-dependent deviations and convergence to RMT predictions.

Findings

Partial spectral form factor is constant at short times due to locality and unitarity.

At longer times, it matches the random matrix theory prediction with exponentially small corrections.

Numerical and semi-analytical methods support the analytical results.

Abstract

While the notion of quantum chaos is tied to random matrix spectral correlations, also eigenstate properties in chaotic systems are often assumed to be described by random matrix theory. Analytic insights into eigenstate correlations can be obtained by the recently introduced partial spectral form factor. Here, we study the partial spectral form factor in chaotic dual-unitary quantum circuits in the thermodynamic limit. We compute the latter for a finite subsystem in a brickwork circuit coupled to an infinite complement. For initial times, shorter than the subsystem's size, spatial locality and (dual) unitarity implies a constant partial spectral form factor, clearly deviating from the linear ramp of the random matrix prediction. In contrast, for larger times we prove, that the partial spectral form factor follows the random matrix result up to exponentially suppressed corrections. We supplement our exact analytical results by semi-analytic computations performed in the thermodynamic limit as well as with numerics for finite-size systems.