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The dynamics of quantum systems strongly depends on the local structure of the Hamiltonian. For short-range interacting systems, the well-known Lieb-Robinson bound defines the effective light cone with an exponentially small error with…

Quantum Physics · Physics 2016-05-31 Tomotaka Kuwahara

How fast can correlations spread in a quantum many-body system? Based on the seminal work by Lieb and Robinson, it has recently been shown that several interacting many-body systems exhibit an effective light cone that bounds the…

We give an overview of recent results on Lieb-Robinson bounds and some of their applications in the study of quantum many-body models in condensed matter physics.

Mathematical Physics · Physics 2011-01-06 Bruno Nachtergaele , Robert Sims

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently…

The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light-cone with exponentially decaying tails. We discuss several consequences of this…

Quantum Physics · Physics 2007-05-23 S. Bravyi , M. B. Hastings , F. Verstraete

We consider many-body quantum systems on a finite lattice, where the Hilbert space is the tensor product of finite-dimensional Hilbert spaces associated with each site, and where the Hamiltonian of the system is a sum of local terms. We are…

Mathematical Physics · Physics 2021-11-04 Matthew B. Hastings

In non-relativistic quantum theories the Lieb-Robinson bound defines an effective light cone with exponentially small tails outside of it. In this work we use it to derive a bound for the time evolution of the correlation function of two…

Quantum Gases · Physics 2018-11-28 Nils O. Abeling , Lorenzo Cevolani , Stefan Kehrein

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…

Quantum Physics · Physics 2020-09-08 Zhiyuan Wang , Kaden R. A. Hazzard

We derive a dynamical bound on the propagation of correlations in local random quantum circuits - lattice spin systems where piecewise quantum operations - in space and time - occur with classical probabilities. Correlations are quantified…

Quantum Physics · Physics 2017-05-15 Siddhartha Santra , Radhakrishnan Balu

We review the mathematical speed limits on quantum information processing in many-body systems. After the proof of the Lieb-Robinson Theorem in 1972, the past two decades have seen substantial developments in its application to other…

Quantum Physics · Physics 2023-10-02 Chi-Fang Chen , Andrew Lucas , Chao Yin

We prove bounds on the minimal time for quantum messaging, propagation/creation of correlations, and control of states for general lattice quantum many-body systems. The proofs are based on a maximal velocity bound, which states that the…

Mathematical Physics · Physics 2025-02-18 Israel Michael Sigal , Jingxuan Zhang

We study the non-equilibrium dynamics of correlations in quantum lattice models in the presence of long-range interactions decaying asymptotically as a power law. For exponents larger than the lattice dimensionality, a Lieb-Robinson-type…

Quantum Physics · Physics 2016-09-19 J. Eisert , M. van den Worm , S. R. Manmana , M. Kastner

The propagation of information in non-relativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance $r$ as a power law,…

The speed limit of information propagation is one of the most fundamental features in non-equilibrium physics. The region of information propagation by finite-time dynamics is approximately restricted inside the effective light cone that is…

Quantum Physics · Physics 2024-03-25 Tomotaka Kuwahara , Tan Van Vu , Keiji Saito

In this work, we prove a new family of Lieb-Robinson bounds for lattice spin systems with long-range interactions. Our results apply for arbitrary $k$-body interactions, so long as they decay with a power-law greater than $kd$, where $d$ is…

Quantum Physics · Physics 2020-03-04 Dominic V. Else , Francisco Machado , Chetan Nayak , Norman Y. Yao

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…

Quantum Physics · Physics 2026-01-05 J. Eisert

Lieb-Robinson bounds show that the speed of propagation of information under the Heisenberg dynamics in a wide class of non-relativistic quantum lattice systems is essentially bounded. We review work of the past dozen years that has turned…

Mathematical Physics · Physics 2019-06-25 Bruno Nachtergaele , Robert Sims , Amanda Young

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…

Quantum Physics · Physics 2021-08-17 Tomotaka Kuwahara , Keiji Saito

Lieb-Robinson bounds demonstrate the emergence of locality in many-body quantum systems. Intuitively, Lieb-Robinson bounds state that with local or exponentially decaying interactions, the correlation that can be built up between two sites…

Quantum Physics · Physics 2026-01-27 Ben T. McDonough , Chao Yin , Andrew Lucas , Carolyn Zhang

The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law…