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Quantum Simulation

A statistical mechanism for operator growth

arXiv
Authors: Xiangyu Cao

Year

2020

Paper ID

18495

Status

Preprint

Abstract Read

~2 min

Abstract Words

115

Citations

N/A

Abstract

It was recently conjectured that in generic quantum many-body systems, the spectral density of local operators has the slowest high-frequency decay as permitted by locality. We show that the infinite-temperature version of this "universal operator growth hypothesis" holds for the quantum Ising spin model in d ge 2 dimensions, and for the chaotic Ising chain (with longitudinal and transverse fields) in one dimension. Moreover, the disordered chaotic Ising chain that exhibits many-body localization can have the same high-frequency spectral density decay as thermalizing models. Our argument is statistical in nature, and is based on the observation that the moments of the spectral density can be written as a sign-problem-free sum over paths of Pauli string operators.

Why This Paper Matters

  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2020 reference point for readers tracking recent quantum research.
  • It was recently conjectured that in generic quantum many-body systems, the spectral density of local operators has the slowest high-frequency decay as permitted by locality.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2012.06544 [2] arXiv https://arxiv.org/abs/2012.06544 [3] Publisher https://arxiv.org/abs/2012.06544

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