Locality and heating in periodically driven, power-law-interacting systems.

@article{Tran2019LocalityAH,
  title={Locality and heating in periodically driven, power-law-interacting systems.},
  author={Minh C. Tran and Adam Ehrenberg and Andrew Y Guo and Paraj Titum and Dmitry A. Abanin and Alexey V. Gorshkov},
  journal={Physical review. A},
  year={2019},
  volume={100 5}
}
We study the heating time in periodically driven D-dimensional systems with interactions that decay with the distance r as a power law 1 / r α . Using linear-response theory, we show that the heating time is exponentially long as a function of the drive frequency for α > D . For systems that may not obey linear-response theory, we use a more general Magnus-like expansion to show the existence of quasiconserved observables, which imply exponentially long heating time, for α > 2 D . We also… 

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References

SHOWING 1-10 OF 44 REFERENCES

Persistence of locality in systems with power-law interactions.

A new bound on the propagation of information in D-dimensional lattice models exhibiting 1/r^{α} interactions with α>D is derived, which qualitatively reproduce the short- and long-distance dynamical behavior following a local quench in an XY chain and a transverse-field Ising chain.

Bounds on Energy Absorption and Prethermalization in Quantum Systems with Long-Range Interactions.

It is shown that the disorder averaged energy absorption rate at high temperatures decays exponentially with the driving frequency, which strongly suggests the presence of a prethermal plateau in which dynamics is governed by an effective, static Hamiltonian for long times.

Nearly linear light cones in long-range interacting quantum systems.

This work rules out the possibility that light cones of power-law interacting systems are bounded by a polynomial for α>2D and become linear as α→∞, suggesting that the velocity, as calculated from the slope of the light cone, may grow exponentially in time.

Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering

We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is

Exponentially Slow Heating in Periodically Driven Many-Body Systems.

It is shown that, for systems with local interactions, the energy absorption rate decays exponentially as a function of driving frequency in any number of spatial dimensions, implying that topological many-body states in periodically driven systems, although generally metastable, can have very long lifetimes.

Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems

We establish some general dynamical properties of quantum many-body systems that are subject to a high-frequency periodic driving. We prove that such systems have a quasiconserved extensive quantity

Fast Quantum State Transfer and Entanglement Renormalization Using Long-Range Interactions.

This protocol realizes an exponential speedup in cases of α=d, which could be useful in creating large entangled states for dipole-dipole (1/r^{3}) interactions in three dimensions.

Spectral Gap and Exponential Decay of Correlations

We study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with short-range interactions on a wide