Random Multipolar Driving: Tunably Slow Heating through Spectral Engineering

Driven quantum systems may realize novel phenomena absent in static systems, but driving-induced heating can limit the timescale on which these persist. We study heating in interacting quantum many-body systems driven by random sequences with $n$-multipolar correlations, corresponding to a polynomially suppressed low-frequency spectrum. For $n\ge 1$, we find a prethermal regime, the lifetime of which grows algebraically with the driving rate, with exponent $2n+1$. A simple theory based on Fermi’s golden rule accounts for this behavior. The quasiperiodic Thue-Morse sequence corresponds to the $n\to \infty$ limit and, accordingly, exhibits an exponentially long-lived prethermal regime. Despite the absence of periodicity in the drive, and in spite of its eventual heat death, the prethermal regime can host versatile nonequilibrium phases, which we illustrate with a random multipolar discrete time crystal.

Figure 1

Left: schematic diagram for different driving protocols. Unitaries $U_{\pm }=\exp (-iT{H}_{\pm })$ can form two types of dipoles, $U_{+}{U}_{-}$ or $U_{-}{U}_{+}$. A Floquet drive is given by a perfect sequence of a single type of dipole, whereas a random succession of both dipole types corresponds to a random dipolar drive. Right: sketch of entanglement entropy dynamics. For a random drive ($n=0$), the system heats rapidly to infinite temperature (inverse temperature $\beta =0$), but for $n$-multipolar ($n\ge 1$) driving a prethermal plateau emerges. Quasiperiodic ($n\to \infty$) drives have an exponentially long (in driving rate) prethermal regime.

Figure 2

Evolution of (a) mean energy and (b) entanglement entropy with Thue-Morse driving as a function of characteristic time $T$, using parameters $\{J_z,J_x,B_x,B_z,B_0\}=\{1,0.243,0.809,0.357,0.21\}$, $L=18$. Prethermalization appears with an entanglement plateau and a lack of energy absorption. (c) Exponential scaling of the thermalization time versus $1/T$.

Figure 3

Evolution of (a) mean energy and (b) entanglement entropy with quadrupolar random driving, with parameters $\{J_z,J_x,B_x,B_z,B_0\}=\{1,0.71,3.2,0.25,0.21\}$, $L=16$. Prethermal plateau of entanglement entropy appears for $1/T\ge 20$. Thermalization time dependence on $1/T$ in (c) log-log and (d) log scale for $n$-multipolar drivings, which confirms the algebraic dependence $(1/T{)}^{\alpha }$ with $\alpha \approx 2n+1$ for $n\ge 1$.

Figure 4

Dynamics of the magnetization of the central spin induced by a random dipolar drive with additional spin flips, using parameters $\{J_z,J_x,B_z,B_0,B_x\}=\{1,0.315,0.21,-0.05,0.75\},L=18$. A long-lived prethermal DTC exists with (a) $n=1$ RMD driving, while heating is inevitably fast for (b) the $n=0$ random case.