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arXiv:2105.09959 · Physical review. B./Physical review. B

Suppression of heating by long-range interactions in periodically driven spin chains

Devendra Singh Bhakuni, Léa Ferreira dos Santos, Yevgeny Bar Lev

Published Oct 8, 2021• 20 citations
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Abstract

We propose a mechanism to suppress heating in periodically driven many-body quantum systems by employing sufficiently long-range interactions and experimentally relevant initial conditions. The mechanism is robust to local perturbations and does not rely on disorder or high driving frequencies. Instead, it makes use of an approximate fragmentation of the many-body spectrum of the nondriven system into bands, with band gaps that grow with the system size. We show that when these systems are driven, there is a regime where decreasing the driving frequency decreases heating and entanglement buildup. This is demonstrated numerically for a prototypical system of spins in one dimension, but the results can be readily generalized to higher dimensions.

DOI
10.1103/physrevb.104.l140301

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We propose a mechanism to suppress heating in periodically driven many-body quantum systems by employing sufficiently long-range interactions and experimentally relevant initial conditions. The mechanism is robust to local perturbations and does not rely on disorder or high driving frequencies. Instead, it makes use of an approximate fragmentation of the many-body spectrum of the nondriven system into bands, with band gaps that grow with the system size. We show that when these systems are driven, there is a regime where decreasing the driving frequency decreases heating and entanglement buildup. This is demonstrated numerically for a prototypical system of spins in one dimension, but the results can be readily generalized to higher dimensions.
We propose a mechanism to suppress heating in periodically driven many-body quantum systems by employing sufficiently long-range interactions and experimentally relevant initial conditions. The mechanism is robust to local perturbations and does \emph{not} rely on disorder or high driving frequencies. Instead, it makes use of an approximate fragmentation of the many-body spectrum of the non-driven system into bands, with band gaps that grow with the system size. We show that when these systems are driven, there is a regime where \emph{decreasing} the driving frequency \emph{decreases} heating and entanglement build-up. This is demonstrated numerically for a prototypical system of spins in one dimension, but the results can be readily generalized to higher dimensions.
We study the non-equilibrium dynamics of a disordered periodically driven quantum spin chain, with the competition between the interaction, disorder, and Floquet driving being of particular interest. We study dynamics of entanglement entropy, energy absorption to characterize dynamical regimes of the system whether it stays in the Floquet-MBL(many-body localization) region or thermalized region. Starting with a product state in the computational basis, followed by reduced density matrix which in turn gives rise to the entanglement entropy density. With the strength of the interaction, the transverse field, the parallel field, the disorder strength W and the driving frequency, we discover the distinct behaviors of fast delocalization and logarithmic entanglement growth and long-lasting memory of the initial state, indicative of localized or prethermal Floquet regimes. We observe that strong disorder arrests transport and enables slow entanglement dynamics, whereas strong driving frequency arrests energy absorption and creates a long-lived non-equilibrium state. Conversely, weak disorder or low driving frequency leads to delocalization. The outcomes show strong support for non-equilibrium phases in driven many-body systems.
Long-range interacting systems such as nitrogen vacancy centers in diamond and trapped ions serve as useful experimental setups to probe a range of nonequilibrium many-body phenomena. In particular, via driving, various effective Hamiltonians with physics potentially quite distinct from short-range systems can be realized. In this Letter, we derive general bounds on the linear response energy absorption rates of periodically driven systems of spins or fermions with long-range interactions that are sign changing and fall off as 1/rα1/r^\alpha1/rα with α>d/2\alpha > d/2α>d/2. We show that the disordered averaged energy absorption rate at high temperature decays exponentially with the driving frequency. This strongly suggests the presence of a prethermal plateau in which dynamics is governed by an effective, static Hamiltonian for long times, and we provide numerical evidence to support such a statement. Our results are relevant for understanding timescales of both heating and hence new dynamical regimes described by effective Hamiltonians in such long-range systems.
Long-range interacting systems such as nitrogen vacancy centers in diamond and trapped ions serve as experimental setups to probe a range of nonequilibrium many-body phenomena. In particular, via driving, various effective Hamiltonians with physics potentially quite distinct from short-range systems can be realized. In this Letter, we derive general rigorous bounds on the linear response energy absorption rates of periodically driven systems of spins or fermions with long-range interactions that are sign changing and fall off as 1/r^{α} with α>d/2. We show that the disorder averaged energy absorption rate at high temperatures decays exponentially with the driving frequency. This strongly suggests the presence of a prethermal plateau in which dynamics is governed by an effective, static Hamiltonian for long times, and we provide numerical evidence to support such a statement. Our results are relevant for understanding timescales of heating and new dynamical regimes described by effective Hamiltonians in such long-range systems.
We study the dynamics of periodically kicked many-body systems away from the high-frequency regime, and discuss a family of Floquet systems where the notion of prethermalization can be naturally extended to intermediate and low driving frequencies. We investigate numerically the dynamics of both integrable and nonintegrable systems, and report on the formation of a long-lived prethermal plateau, akin to the high-frequency limit, where the system thermalizes with respect to an effective Hamiltonian captured by the inverse-frequency expansion (IFE). Unlike the high-frequency regime, we find that the relevant heating times are model dependent: we analyze the stability of the prethermal plateau to small perturbations in the drive period and show that, in a spin chain whose IFE is intractable, the plateau duration is insensitive to the perturbation strength, in contrast to a chain where the IFE admits the resummation of an entire subseries. Infinitesimal perturbations are enough to restore the ergodic properties of the system, and decrease residual finite-size effects. Although the regime where the Floquet system leaves the prethermal plateau and starts heating up to infinite temperature is not captured by the IFE, we provide evidence that the evolved subsystem is described well by a thermal state with respect to the IFE Hamiltonian, with a gradually changing temperature, in accord with the eigenstate thermalization hypothesis.
We derive general bounds on the linear response energy absorption rates of periodically driven many-body systems of spins or fermions on a lattice. We show that, for systems with local interactions, the energy absorption rate decays exponentially as a function of driving frequency in any number of spatial dimensions. These results imply that topological many-body states in periodically driven systems, although generally metastable, can have very long lifetimes. We discuss applications to other problems, including the decay of highly energetic excitations in cold atomic and solid-state systems.