Dynamical Freezing in Exactly Solvable Models of Driven Chaotic Quantum Dots

TL;DR

This paper investigates a solvable model of driven chaotic quantum dots, revealing universal dynamical freezing and emergent conservation laws that preserve coherence and slow relaxation under periodic Floquet driving.

Contribution

It introduces an exactly solvable model demonstrating dynamical freezing and emergent conservation laws in driven chaotic quantum systems, supported by analytical and numerical analysis.

Findings

Universal freezing behavior observed regardless of disorder averaging.

Long-lived coherence and suppressed chaos at frozen points.

Explicit characterization of relaxation timescales in high-frequency limit.

Abstract

The late-time equilibrium behavior of generic interacting models is determined by the coupled hydrodynamic equations associated with the globally conserved quantities. In the presence of an external time-dependent drive, non-integrable systems typically thermalize to an effectively infinite-temperature state, losing all memory of their initial states. However, in the presence of a large time-periodic Floquet drive, there exist special points in phase-space where the strongly interacting system develops approximate {\it emergent} conservation laws. Here we present results for an exactly solvable model of two coupled chaotic quantum dots with multiple orbitals interacting via random two and four-fermion interactions in the presence of a Floquet drive. We analyze the phenomenology of dynamically generated freezing using a combination of exact diagonalization, and field-theoretic analysis in the limit of a large number of electronic orbitals. The model displays universal freezing behavior irrespective of whether the theory is averaged over the disorder configurations or not. We present explicit computations for the growth of many-body chaos and entanglement entropy, which demonstrates the long-lived coherence associated with the interacting degrees of freedom even at late-times at the dynamically frozen points. We also compute the slow timescale that controls relaxation away from exact freezing in a high-frequency expansion.