Quantum chaos, thermalization and entanglement generation in real-time simulations of the BFSS matrix model

TL;DR

This paper numerically investigates chaos, thermalization, and entanglement in the BFSS matrix model, revealing how quantum effects influence classical chaos indicators and entanglement dynamics across temperature regimes.

Contribution

It introduces a Gaussian density matrix approach for real-time quantum simulations of the BFSS model, extending classical methods and analyzing quantum corrections to chaos and entanglement.

Findings

Quantum corrections decrease Lyapunov exponents at low temperatures.

Entanglement entropy exhibits rapid growth and saturation consistent with scrambling.

Fermionic BFSS model remains chaotic with finite Lyapunov exponent at low temperatures.

Abstract

We study numerically the onset of chaos and thermalization in the Banks-Fischler-Shenker-Susskind (BFSS) matrix model with and without fermions, considering Lyapunov exponents, entanglement generation, and quasinormal ringing. We approximate the real-time dynamics in terms of the most general Gaussian density matrices with parameters which obey self-consistent equations of motion, thus extending the applicability of real-time simulations beyond the classical limit. Initial values of these Gaussian density matrices are optimized to be as close as possible to the thermal equilibrium state of the system. Thus attempting to bridge between the low-energy regime with a calculable holographic description and the classical regime at high energies, we find that quantum corrections to classical dynamics tend to decrease the Lyapunov exponents, which is essential for consistency with the Maldacena-Shenker-Stanford (MSS) bound at low temperatures. The entanglement entropy is found to exhibit an expected "scrambling" behavior - rapid initial growth followed by saturation. At least at high temperatures the entanglement saturation time appears to be governed by classical Lyapunov exponents. Decay of quasinormal modes is found to be characterized by the shortest time scale of all. We also find that while the bosonic matrix model becomes non-chaotic in the low-temperature regime, for the full BFSS model with fermions the leading Lyapunov exponent, entanglement saturation time, and decay rate of quasinormal modes all remain finite and non-zero down to the lowest temperatures.