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.

–

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