An improved Lieb-Robinson bound for many-body Hamiltonians with power-law interactions

ORAL

Abstract

The Lieb-Robinson bound limits the velocity of the spread of information in non-relativistic short-range interacting quantum systems, inducing a notion of speed of light. More specifically, it proves that, under time evolution, any local operator remains confined (up to exponentially decaying tails) to a region whose radius grows linearly with time. Motivated by experimental platforms such as ion traps, Rydberg atoms and spin defects in solids, recent work has investigated such bounds in long-range interacting systems, where the interaction strength decays as a power-law of the distance. In these results, the extent of the time evolved local operator is characterized by power-law tails and one obtains a power-law light-cone. In this talk, we introduce a new notion of light-cone for power-law interacting systems that induces a more stringent definition of locality. We prove new Lieb-Robinson bounds for multi-body interacting systems which improve the spatial decay profile of the time evolved local operator and thus lead to a better light-cone. These improvements enable the proof of the existence of a long-lived prethermal regime in long-range interacting systems.

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Presenters

  • Francisco Machado

    • University of California, Berkeley
    • Physics, University of California, Berkeley
    • Department of Physics, University of California, Berkeley

Authors

  • Francisco Machado

    • University of California, Berkeley
    • Physics, University of California, Berkeley
    • Department of Physics, University of California, Berkeley

  • Dominic Else

    • Massachusetts Institute of Technology
    • Massachusetts Institute of Technology and University of California, Santa Barbara

  • Chetan Nayak

    • University of California, Santa Barbara and Microsoft Research, Station Q

  • Norman Yao

    • University of California, Berkeley
    • Department of Physics, University of California, Berkeley, California 94720, USA
    • Physics, University of California, Berkeley
    • Department of Physics, University of California, Berkeley
    • University of California, Berkeley and Lawrence Berkeley National Laboratory, Materials Sciences Division