Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2106.09726 · Physical Review X

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

Chao Yin, Andrew Lucas

Published May 17, 2022• 28 citations
arXivHTMLPDF

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 the density matrix ρ ∝ exp½-μN (with N the total boson number), ensemble-averaged correlators of the form h½A 0 ; B r ðtÞi, along with outof-time-ordered correlators, must vanish as the distance r between two local operators grows, unless t ≥ 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 ½A 0 ; B r ðtÞ 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 highdensity 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.

DOI
10.1103/physrevx.12.021039

Related papers

A compellingly simple proof of the speed of sound for interacting bosons

J. Eisert

On physical grounds, one expects locally interacting quantum many-body systems to feature a finite group velocity. This intuition is rigorously underpinned by Lieb-Robinson bounds that state that locally interacting Hamiltonians with finite-dimensional constituents on suitably regular lattices always exhibit such a finite group velocity. This also implies that causality is always respected by the dynamics of quantum lattice models. It had been a long-standing open question whether interacting bosonic systems also feature finite speeds of sound in information and particle propagation, which was only recently resolved. This work proves a strikingly simple such bound for particle propagation - shown in literally a few elementary, yet not straightforward, lines - for generalized Bose-Hubbard models defined on general lattices, proving that appropriately locally perturbed stationary states feature a finite speed of sound in particle numbers.

quant-pharXiv:2601.00111•Jan 2, 2026•0 citations

Lieb-Robinson Bound and Almost-Linear Light Cone in Interacting Boson Systems

Tomotaka Kuwahara, Keiji Saito

In this work, we investigate how quickly local perturbations propagate in interacting boson systems with Bose-Hubbard-type Hamiltonians. In general, these systems have unbounded local energies, and arbitrarily fast information propagation may occur. We focus on a specific but experimentally natural situation in which the number of bosons at any one site in the unperturbed initial state is approximately limited. We rigorously prove the existence of an almost-linear information-propagation light cone, thus establishing a Lieb-Robinson bound: the wave front grows at most as t log^{2}(t). We prove the clustering theorem for gapped ground states and study the time complexity of classically simulating one-dimensional quench dynamics, a topic of great practical interest.

arXiv:2103.11592•Physical Review Letters•Aug 13, 2021•38 citations

Tightening the Lieb-Robinson Bound in Locally Interacting Systems

Zhiyuan Wang, Kaden R.A. Hazzard

The Lieb-Robinson (LR) bound rigorously shows that in quantum systems with short-range interactions, the maximum amount of information that travels beyond an effective "light cone" decays exponentially with distance from the light-cone front, which expands at finite velocity.Despite being a fundamental result, existing bounds are often extremely loose, limiting their applications.We introduce a method that dramatically and qualitatively improves LR bounds in models with finite-range interactions.Most prominently, in systems with a large local Hilbert space dimension D, our method gives a LR velocity that grows much slower than previous bounds with D as D → ∞.For example, in the Heisenberg model with spin S, we find v ≤ const.compared to the previous v ∝ S, which diverges at large S, and in multiorbital Hubbard models with N orbitals, we find v ∝ √ N instead of previous v ∝ N , and similarly in the Nstate truncated Bose-Hubbard model and Wen's quantum rotor model.Our bounds also scale qualitatively better in some systems when the spatial dimension or certain model parameters become large, for example in the d-dimensional quantum Ising model and perturbed toric code models.Even in spin-1/2 Ising and Fermi-Hubbard models, our method improves the LR velocity by an order of magnitude with typical model parameters, and significantly improves the LR bound at large distance and early time.

arXiv:1908.03997•PRX Quantum•Sep 3, 2020•62 citations

Symmetry-Enhanced Lieb–Robinson Bounds for a Class of Bose–Hubbard Type Hamiltonians

Tomotaka Kuwahara, Marius Lemm

Abstract Several recent works have derived Lieb–Robinson bounds (LRBs) for Bose–Hubbard-type Hamiltonians. For certain structured initial states, e.g., vacuum perturbations or near-stationary states, information propagates with velocity $$v \le C$$ v ≤ C . However, for general bounded-density initial states, it was shown by the first author, Vu, and Saito that the velocity can grow in time as $$v \sim t^{D-1}$$ v ∼ t D - 1 , where D is the spatial dimension—demonstrating the possibility of accelerated information spreading in bosonic systems. In this work, we introduce a new perspective on this phenomenon: we show that translation invariance combined with local p -body repulsion ( $$n^p$$ n p with $$p > D+1$$ p > D + 1 ) qualitatively alters the propagation behavior, leading to a bound of the form $$v \sim t^{\frac{D}{p - D - 1}}$$ v ∼ t D p - D - 1 for general bounded-energy-density initial states. In particular, this establishes an almost-linear light cone at large p , in stark contrast to the previously found accelerated regimes. Our result identifies symmetry-driven constraints as a new mechanism for suppressing propagation speed in bosonic systems and thereby reframes the scope of what types of LRBs can hold. We further provide matching examples showing that, under the given assumptions, this bound is sharp—no further improvement in the power of t is possible without invoking additional dynamical constraints.

arXiv:2405.04672•Annales Henri Poincaré•Jul 28, 2026•0 citations

Maximal Speed for Macroscopic Particle Transport in the Bose-Hubbard Model

Jérémy Faupin, Marius Lemm, Israel Michael Sigal

The Lieb-Robinson bound asserts the existence of a maximal propagation speed for the quantum dynamics of lattice spin systems. Such general bounds are not available for most bosonic lattice gases due to their unbounded local interactions. Here we establish for the first time a general ballistic upper bound on macroscopic particle transport in the paradigmatic Bose-Hubbard model. The bound is the first to cover a broad class of initial states with positive density including Mott states, which resolves a longstanding open problem. It applies to Bose-Hubbard-type models on any lattice with not too long-ranged hopping. The proof is rigorous and rests on controlling the time evolution of a new kind of adiabatic spacetime localization observable via iterative differential inequalities.

arXiv:2110.04313•Physical Review Letters•Apr 12, 2022•31 citations

Dynamical Behaviour of Density Correlations Across the Chaotic Phase for Interacting Bosons

Óscar Dueñas, Alberto Rodríguez

We investigate the propagation of two-point density correlations in the one-dimensional Bose-Hubbard Hamiltonian in the thermodynamic limit in terms of the correlation transport distance (CTD), an experimentally measurable magnitude that characterizes the spatial spreading of correlations in time. We confirm that the integrable limits of the model exhibit CTD ballistic growth, while the onset of the chaotic phase leads to the emergence of a pronounced sub-ballistic regime, in agreement with previous results for finite systems. By a meticulous analysis of the spatio-temporal correlation profiles, we show that the correlation front nonetheless propagates ballistically for all interaction strengths, and that the chaos-induced slowdown of the CTD originates from the emergence of long-time distance-dependent correlation tails, together with an enhanced decay of the correlation front amplitude. Our results thus provide a detailed characterization of correlation transport that goes beyond a simple light-cone picture.

quant-pharXiv:2603.04373•New Journal of Physics•Mar 5, 2026•0 citations
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 matrix ρ ∝ exp½-μN (with N the total boson number), ensemble-averaged correlators of the form h½A 0 ; B r ðtÞi, along with outof-time-ordered correlators, must vanish as the distance r between two local operators grows, unless t ≥ 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 ½A 0 ; B r ðtÞ 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 highdensity 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.
On physical grounds, one expects locally interacting quantum many-body systems to feature a finite group velocity. This intuition is rigorously underpinned by Lieb-Robinson bounds that state that locally interacting Hamiltonians with finite-dimensional constituents on suitably regular lattices always exhibit such a finite group velocity. This also implies that causality is always respected by the dynamics of quantum lattice models. It had been a long-standing open question whether interacting bosonic systems also feature finite speeds of sound in information and particle propagation, which was only recently resolved. This work proves a strikingly simple such bound for particle propagation - shown in literally a few elementary, yet not straightforward, lines - for generalized Bose-Hubbard models defined on general lattices, proving that appropriately locally perturbed stationary states feature a finite speed of sound in particle numbers.
In this work, we investigate how quickly local perturbations propagate in interacting boson systems with Bose-Hubbard-type Hamiltonians. In general, these systems have unbounded local energies, and arbitrarily fast information propagation may occur. We focus on a specific but experimentally natural situation in which the number of bosons at any one site in the unperturbed initial state is approximately limited. We rigorously prove the existence of an almost-linear information-propagation light cone, thus establishing a Lieb-Robinson bound: the wave front grows at most as t log^{2}(t). We prove the clustering theorem for gapped ground states and study the time complexity of classically simulating one-dimensional quench dynamics, a topic of great practical interest.
The Lieb-Robinson (LR) bound rigorously shows that in quantum systems with short-range interactions, the maximum amount of information that travels beyond an effective "light cone" decays exponentially with distance from the light-cone front, which expands at finite velocity.Despite being a fundamental result, existing bounds are often extremely loose, limiting their applications.We introduce a method that dramatically and qualitatively improves LR bounds in models with finite-range interactions.Most prominently, in systems with a large local Hilbert space dimension D, our method gives a LR velocity that grows much slower than previous bounds with D as D → ∞.For example, in the Heisenberg model with spin S, we find v ≤ const.compared to the previous v ∝ S, which diverges at large S, and in multiorbital Hubbard models with N orbitals, we find v ∝ √ N instead of previous v ∝ N , and similarly in the Nstate truncated Bose-Hubbard model and Wen's quantum rotor model.Our bounds also scale qualitatively better in some systems when the spatial dimension or certain model parameters become large, for example in the d-dimensional quantum Ising model and perturbed toric code models.Even in spin-1/2 Ising and Fermi-Hubbard models, our method improves the LR velocity by an order of magnitude with typical model parameters, and significantly improves the LR bound at large distance and early time.
Abstract Several recent works have derived Lieb–Robinson bounds (LRBs) for Bose–Hubbard-type Hamiltonians. For certain structured initial states, e.g., vacuum perturbations or near-stationary states, information propagates with velocity v≤Cv \le Cv≤C v ≤ C . However, for general bounded-density initial states, it was shown by the first author, Vu, and Saito that the velocity can grow in time as v∼tD−1v \sim t^{D-1}v∼tD−1 v ∼ t D - 1 , where D is the spatial dimension—demonstrating the possibility of accelerated information spreading in bosonic systems. In this work, we introduce a new perspective on this phenomenon: we show that translation invariance combined with local p -body repulsion ( npn^pnp n p with p>D+1p > D+1p>D+1 p > D + 1 ) qualitatively alters the propagation behavior, leading to a bound of the form v∼tDp−D−1v \sim t^{\frac{D}{p - D - 1}}v∼tp−D−1D​ v ∼ t D p - D - 1 for general bounded-energy-density initial states. In particular, this establishes an almost-linear light cone at large p , in stark contrast to the previously found accelerated regimes. Our result identifies symmetry-driven constraints as a new mechanism for suppressing propagation speed in bosonic systems and thereby reframes the scope of what types of LRBs can hold. We further provide matching examples showing that, under the given assumptions, this bound is sharp—no further improvement in the power of t is possible without invoking additional dynamical constraints.
The Lieb-Robinson bound asserts the existence of a maximal propagation speed for the quantum dynamics of lattice spin systems. Such general bounds are not available for most bosonic lattice gases due to their unbounded local interactions. Here we establish for the first time a general ballistic upper bound on macroscopic particle transport in the paradigmatic Bose-Hubbard model. The bound is the first to cover a broad class of initial states with positive density including Mott states, which resolves a longstanding open problem. It applies to Bose-Hubbard-type models on any lattice with not too long-ranged hopping. The proof is rigorous and rests on controlling the time evolution of a new kind of adiabatic spacetime localization observable via iterative differential inequalities.
We investigate the propagation of two-point density correlations in the one-dimensional Bose-Hubbard Hamiltonian in the thermodynamic limit in terms of the correlation transport distance (CTD), an experimentally measurable magnitude that characterizes the spatial spreading of correlations in time. We confirm that the integrable limits of the model exhibit CTD ballistic growth, while the onset of the chaotic phase leads to the emergence of a pronounced sub-ballistic regime, in agreement with previous results for finite systems. By a meticulous analysis of the spatio-temporal correlation profiles, we show that the correlation front nonetheless propagates ballistically for all interaction strengths, and that the chaos-induced slowdown of the CTD originates from the emergence of long-time distance-dependent correlation tails, together with an enhanced decay of the correlation front amplitude. Our results thus provide a detailed characterization of correlation transport that goes beyond a simple light-cone picture.