Journal Article

Finite Speed of Quantum Information in Models of Interacting Bosons at Finite Density

Lucas, Andrew, Yin, Chao

2022

Overview

We prove that quantum information propagates with a finite velocity in any model of interacting bosons whose (possibly time-dependent) Hamiltonian contains spatially local single-boson hopping terms along with arbitrary local density-dependent interactions. More precisely, with the density matrixρ∝exp[−μN](withNthe total boson number), ensemble-averaged correlators of the form⟨[A0,Br(t)]⟩, along with out-of-time-ordered correlators, must vanish as the distancerbetween two local operators grows, unlesst≥r/vfor some finite speedv. In one-dimensional models, we give a useful extension of this result that demonstrates the smallness of all matrix elements of the commutator[A0,Br(t)]between finite-density states ift/ris sufficiently small. Our bounds are relevant for physically realistic initial conditions in experimentally realized models of interacting bosons. In particular, we prove thatvcan scale no faster than linear in number density in the Bose-Hubbard model: This scaling matches previous results in the high-density limit. The quantum-walk formalism underlying our proof provides an alternative method for bounding quantum dynamics in models with unbounded operators and infinite-dimensional Hilbert spaces, where Lieb-Robinson bounds have been notoriously challenging to prove.

• Publisher: American Physical Society
• Subject: Atomic physics / Bosons / Commutators / Correlators / Data processing / Density / Fermions / Hilbert space / Initial conditions / One dimensional models / Operators (mathematics) / Quantum phenomena / Relativity / Speed limits / Thermalization (energy absorption) / Time dependence