Floquet prethermalization in dipolar spin chains

Peng, Pai; Yin, Chao; Huang, Xiaoyang; Ramanathan, Chandrasekhar; Cappellaro, Paola

doi:10.1038/s41567-020-01120-z

Cited by 98 publications

(69 citation statements)

References 42 publications

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“…Both facts suggest that D pre is more robust than H pre , in agreement with the experimental results presented in Ref. [51]. This provides evidence that it is possible to realize novel Floquet phases beyond the effective Hamiltonian picture.…”

Section: B Emergent Dipolar Ordersupporting

confidence: 90%

“…Although it is generally believed that Floquet many-body systems should heat up to infinite temperature, some numerical works [53][54][55][56] have found signs of nonthermal behavior in various models. Here we provide evidence of thermalization in the long-time and thermodynamic limit, using numerics and experiments in a NMR quantum simulator [51,70,72], respectively. In simulations, we can access the infinite-time limit using exact diagonalization, but only for small system sizes.…”

Section: Toward Infinite Temperature: Experimental and Numerical Signaturesmentioning

confidence: 99%

“…In the presence of a transverse field, the system is known to show a quantum phase transition [85]. We use 16 rf pulses [51,70,72,86] to engineer the natural Hamiltonian into H (A) 1 = JD y and H (A) 2 = JD x with tunable J. This enables varying the Floquet steps by tuning J, while keeping τ fixed.…”

Section: Toward Infinite Temperature: Experimental and Numerical Signaturesmentioning

confidence: 99%

“…The heating is detrimental to any quantum application, as no local quantum information is retained and all interesting phenomena mentioned above disappear [43][44][45]. It has been shown theoretically [46][47][48][49][50] and experimentally [51,52] that even when the system heats up, the thermalization time can be exponentially long in the drive parameters (typically the frequency of a rapid drive). Then, a long-lived prethermal quasiequilibrium is established, which allows exploitation of the engineered Floquet Hamiltonian for quantum simulation [53][54][55].…”

Section: Introductionmentioning

confidence: 99%

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Prethermal quasiconserved observables in Floquet quantum systems

et al. 2021

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Prethermalization, by introducing emergent quasiconserved observables, plays a crucial role in protecting periodically driven (Floquet) many-body phases over an exponentially long time, while the ultimate fate of such quasiconserved operators can signal thermalization to infinite temperature. To elucidate the properties of prethermal quasiconservation in many-body Floquet systems, here we systematically analyze infinite-temperature correlations between observables. We numerically show that the late-time behavior of the autocorrelations unambiguously distinguishes quasiconserved observables from nonconserved ones, allowing one to single out a set of linearly independent quasiconserved observables. By investigating two Floquet spin models, we identify two different mechanisms underlying the quasiconservation law. First, we numerically verify energy quasiconservation when the driving frequency is large, so that the system dynamics is approximately described by a static prethermal Hamiltonian. More interestingly, under moderate driving frequency, another quasiconserved observable can still persist if the Floquet driving contains a large global rotation. We show theoretically how to calculate this conserved observable and provide numerical verification. Having systematically identified all quasiconserved observables, we can finally investigate their behavior in the infinite-time limit and thermodynamic limit, using autocorrelations obtained from both numerical simulation and experiments in solid-state nuclear magnetic resonance systems.

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Section: B Emergent Dipolar Ordersupporting

confidence: 90%

Section: Toward Infinite Temperature: Experimental and Numerical Signaturesmentioning

confidence: 99%

Section: Toward Infinite Temperature: Experimental and Numerical Signaturesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Prethermal quasiconserved observables in Floquet quantum systems

et al. 2021

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“…where ħ h is the Plank's constant, A and B are unitless constant. This exponential suppression was observed in several numerical studies [8][9][10][11] and in an experiment with dipolar spin chains [12]. The rigorous bound of Eq.…”

Section: Introductionsupporting

confidence: 53%

Statistical Floquet prethermalization of the Bose-Hubbard model

Torre

Dentelski

2021

SciPost Phys.

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The manipulation of many-body systems often involves time-dependent forces that cause unwanted heating. One strategy to suppress heating is to use time-periodic (Floquet) forces at large driving frequencies. For quantum spin systems with bounded spectra, it was shown rigorously that the heating rate is exponentially small in the driving frequency. Recently, such exponential suppression of heating has been observed in an experiment with ultracold atoms, realizing a periodically driven Bose-Hubbard model. This model has an unbounded spectrum and, hence, is beyond the reach of previous theoretical approaches. Here, we study this model with two semiclassical approaches valid, respectively, at large and weak interaction strengths. In both limits, we compute the heating rates by studying the statistical probability to encounter a many-body resonance, and obtain a quantitative agreement with the exact diagonalization of the quantum model. Our approach demonstrates the relevance of statistical arguments to Floquet perthermalization of interacting many-body quantum systems.

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