Floquet Superheating

TL;DR

The paper reveals a Floquet heating pathway termed Floquet superheating, where heating is globally slow but locally triggered by rare hot spots, leading to a long-lived prethermal plateau and non-ergodic bimodal macroscopic behavior. Central to this mechanism is the state-selective spin echo (SSSE), which suppresses heating for low-energy states and allows rare nucleation events to dominate the dynamics, yielding a phase diagram with an intermediate-frequency Floquet superheating window. A droplet-rate theory establishes a critical droplet size $R_c$ that governs whether a hot spot can trigger fast heating, with spontaneous nucleation explained by minimizing a fluctuation functional $F(E_D)$ and a doubly-exponentially small nucleation probability at high frequencies. The work extends the understanding of heating pathways in driven systems, suggests routes to stabilize non-equilibrium phases, and highlights the potential for boundary engineering and interaction-driven echoes to control heating in quantum simulators.

Abstract

Periodically driven many-body systems generally heat towards a featureless 'infinite-temperature' state. As an alternative to uniform heating in a clean system, here we establish a Floquet superheating regime, where fast heating nucleates at ''hot spots" generated by rare fluctuations in the local energy with respect to an appropriate effective Hamiltonian. Striking macroscopic consequences include exceptionally long-lived prethermalization and non-ergodic bimodal distributions of macroscopic observables. Superheating is predicated on a heating rate depending strongly on the local fluctuation; in our example, this is supplied by a sharp state-selective spin-echo, where the energy absorption is strongly suppressed for low-energy states, while thermal fluctuations open up excessive heating channels. A simple phenomenological theory is developed to show the existence of a critical droplet size, which incorporates heating by the driving field as well as the heat current out of the droplet. Our results shine light on a new heating mechanism and suggest new routes towards stabilizing non-equilibrium phases of matter in driven systems.

Figures (14)

• Figure 1: (a) Dynamics of conventional heating (yellow traces) and superheating (red traces) as reflected in the total $z-$magnetization. Each ensemble depicts 32 individual realizations, which stay close to each other conventionally, but not for superheating. We use $L=100$, $J=0.5$, $g=0.17$ for numerical simulations. (b) Snapshots of the $z$-component spin configurations for conventional heating(up) and superheating (down). Floquet superheating occurs via the nucleation process of a 'hot spot', which quickly expands and destabilizes the system. The markers correspond to those in (a). The color denotes the value of the $z-$magnetization, such that blue and red colors correspond to spins pointing along the positive and negative $z$-directions, respectively. (c) (d) Probability distribution of the total magnetization. A bimodal distribution appears during the superheating for low-energy initial states, while a Gaussian unimodal distribution appears for conventional heating with higher energy initial states. 512 independent realizations are used here. (e) Schematic for the state-selective spin echo. Ising interaction effectively echoes out the transverse field, hence suppressing heating of the low-energy background.
• Figure 2: (a) Mean value $\langle\tau\rangle$ of the prethermal lifetime. For large $\omega$, an exponential scaling appears. For intermediate frequencies, instead, $\langle\tau\rangle$ peaks around $\omega{\approx}1$ where superheating occurs. Seeding a droplet of linear size $R$ generally speeds up heating. (b) The relative standard deviation of $\tau$ exhibits a notable peak for $R{=}0,3$, indicating that superheating occurs due to rare events. For $R{=}10$, the initially seeded droplet induces fast heating deterministically. We use $\delta\theta{=}0.12\pi$ with $J{=}0.5$, $g{=}0.17$, and $L{=}100$ for numerical simulations. (c) $\langle\tau\rangle$ on a log scale for $L{=}50$. The dark region around $\omega{\approx}1$ features Floquet superheating. The gray squares correspond to the critical frequencies, obtained by averaging over three values of $\omega$ where $r$ exceeds the threshold values $0.3,0.35,0.4$, with error bars denoting their standard deviation.
• Figure 3: (a) Heating rate $\gamma$ versus initial energy (measured w.r.t the ground state energy) for parameters corresponding to SSSE. For sufficiently low-energy initial states, $\gamma$ is greatly reduced due to SSSE and a sharp drop is observed. For the ground state, heating is strictly forbidden. (b) Phenomenological result for $F(\mathcal{E}_D)$ in Eq. \ref{['eq.probRc']} for a low background energy $\mathcal{E}_B$. A global minimum $\mathcal{E}_D^*$ different from $\mathcal{E}_B$ exists, suggesting that nucleation events can occur spontaneously. (c) Spontaneous nucleation only occurs when the difference between $\mathcal{E}_D^*$ and $\mathcal{E}_B$ is finite. For large $\mathcal{E}_B$, this is not allowed.
• Figure 4: Energy input and output for a droplet. $\gamma_{B}$ and $\gamma_{D}$ correspond to the energy absorption rate from the drive at the corresponding energy density, $\mathcal{E}_B$ and $\mathcal{E}_D$, respectively. $\kappa(\mathcal{E}_D-\mathcal{E}_B)$ quantifies the energy diffusion through the droplet surface to the background.
• Figure 5: Heating rate $\gamma$ versus initial energy. We fit the curve using the logistic function (black dashed line), which works well for finite energies but fails to describe the sharp drop in the low-energy regime.