A statistical mechanism for operator growth
- URL: http://arxiv.org/abs/2012.06544v2
- Date: Thu, 10 Jun 2021 09:26:57 GMT
- Title: A statistical mechanism for operator growth
- Abstract summary: 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.
The disordered chaotic Ising chain that exhibits many-body localization can have the same high-frequency spectral density decay as thermalizing models.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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