Finite speed of quantum information in models of interacting bosons at finite density

Abstract

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 density matrix $\rho \propto \exp [-\mu N]$ (with $N$ the total boson number), ensemble averaged correlators of the form $⟨[A_0,B_r(t)]⟩$, along with out-of-time-ordered correlators, must vanish as the distance $r$ between two local operators grows, unless $t\ge r/v$ for some finite speed $v$. In one dimensional models, we give a useful extension of this result that demonstrates the smallness of all matrix elements of the commutator $[A_0,B_r(t)]$ between finite density states if $t/r$ is sufficiently small. Our bounds are relevant for physically realistic initial conditions in experimentally realized models of interacting bosons. In particular, we prove that $v$ can 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.

35 pages, 1 figure. v2: substantially extended and published version

References in corpus (18)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Theory of universal incoherent metallic transport
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
• Nearly-linear light cones in long-range interacting quantum systems
• Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
• Hierarchy of linear light cones with long-range interactions
• The Lieb-Robinson light cone for power-law interactions
• Absence of fast scrambling in thermodynamically stable long-range interacting systems
• Lieb-Robinson bound and almost-linear light-cone in interacting boson systems
• Quantum operator growth bounds for kicked tops and semiclassical spin chains
• Bound on quantum scrambling with all-to-all interactions
• Many-body quantum dynamics slows down at low density
• Optimal Frobenius light cone in spin chains with power-law interactions
• Phase and group velocities for correlation spreading in the Mott phase of the Bose-Hubbard model in dimensions greater than one
• Operator growth bounds in a cartoon matrix model
• Concentration of OTOC and Lieb-Robinson velocity in random Hamiltonians

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• On Lieb-Robinson bounds for the Bose-Hubbard model
• Tensor-network study of correlation-spreading dynamics in the two-dimensional Bose-Hubbard model
• Optimal Frobenius light cone in spin chains with power-law interactions
• Exponential clustering of bipartite quantum entanglement at arbitrary temperatures
• Theory of metastable states in many-body quantum systems
• Disordered Lieb-Robinson bounds in one dimension
• Maximal Speed of Propagation in Open Quantum Systems
• Experimental tests of Lieb-Robinson bounds
• Optimal light cone for macroscopic particle transport in long-range systems: A quantum speed limit approach
• Thermal Area Law for Lattice Bosons
• Locality of gapped ground states in systems with power-law decaying interactions
• From Light-Cone to Supersonic Propagation of Correlations by Competing Short- and Long-Range Couplings
• Fractonic Quantum Quench in Dipole-constrained Bosons
• Efficient tensor network simulation of multi-emitter non-Markovian systems
• Out-of-time-ordered correlators of mean-field bosons via Bogoliubov theory
• Frobenius light cone and the shift unitary
• Lieb-Robinson bounds with exponential-in-volume tails
• Locality bounds for quantum dynamics at low energy
• Information scrambling of the dilute Bose gas at low temperature