Improved Lieb-Robinson bound for many-body Hamiltonians with power-law interactions
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PhysRevA.101.022333.pdf
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Author(s)
Else, Dominic V.
Machado, Francisco
Nayak, Chetan
Yao, Norman Y.
Date Issued
February 26, 2020
Journal
Physical Review A
Publisher
American Physical Society
Citation
Else, Dominic V., et al. “Improved Lieb-Robinson Bound for Many-Body Hamiltonians with Power-Law Interactions.” Physical Review A 101, 2 (February 2020): 022333. © 2020 American Physical Society
Version
Final published version
Abstract
In this paper, we prove a family of Lieb-Robinson bounds for discrete spin systems with long-range interactions. Our results apply for arbitrary k-body interactions, so long as they decay with a power law greater than kd, where d is the dimension of the system. More precisely, we require that the sum of the norm of terms with diameter greater than or equal to R, acting on any one site, decays as a power law 1/R[superscript α], with α>d. These bounds allow us to prove that, at any fixed time, the spatial decay of a time evolved operator follows arbitrarily closely to 1/r[superscript α]. Moreover, we introduce an alternative light cone definition for power-law interacting quantum systems which captures the region of the system where changing the Hamiltonian can affect the evolution of a local operator. In short-range interacting systems, this light cone agrees with the conventional definition. However, in long-range interacting systems, our definition yields a stricter light cone, which is more relevant in most physical contexts.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevA.101.022333
