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

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 arbitrary density-dependent interactions. More precisely, the density matrix ρ∝exp[−μN] (with N total boson number), ensemble-averaged correlators form ⟨[A0,Br(t)]⟩, out-of-time-ordered correlators, must vanish as distance r between two operators grows, unless t≥r/v for some speed v. In one-dimensional models, we give useful extension this result demonstrates smallness all elements commutator [A0,Br(t)] finite-density states if t/r is sufficiently small. Our bounds are relevant physically realistic initial conditions experimentally realized models bosons. particular, v can scale no faster than linear number Bose-Hubbard model: This scaling matches previous results high-density limit. The quantum-walk formalism underlying our proof provides an alternative method bounding dynamics unbounded and infinite-dimensional Hilbert spaces, where Lieb-Robinson have been notoriously challenging to prove.Received 25 June 2021Accepted 22 March 2022DOI:https://doi.org/10.1103/PhysRevX.12.021039Published by American Physical Society under Creative Commons Attribution 4.0 International license. Further distribution work maintain attribution author(s) published article’s title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasMathematical physicsPhysical SystemsBose gasesTechniquesBose-Hubbard modelAtomic, Molecular & OpticalCondensed Matter, Materials Applied PhysicsQuantum InformationGeneral Physics