Related papers: Speed limits and locality in many-body quantum dyn…
The speed of light $c$ sets a strict upper bound on the speed of information transfer in both classical and quantum systems. In nonrelativistic quantum systems, the Lieb-Robinson Theorem imposes an emergent speed limit $v \hspace{-0.2mm}…
The Lieb-Robinson bound shows the existence of a maximum speed of signal propagation in discrete quantum mechanical systems with local interactions. This generalizes the concept of relativistic causality beyond field theory, and provides a…
We review various bounds concerning out-of-equilibrium dynamics in few-level and many-body quantum systems. We primarily focus on closed quantum systems but will also mention some related results for open quantum systems and classical…
We review a recently proven Lieb-Robinson bound for general, many-body quantum systems with bounded interactions. Several basic examples are discussed as well as the connection between commutator estimates and quasi-locality.
This is an introductory text reviewing Lieb-Robinson bounds for open and closed quantum many-body systems. We introduce the Heisenberg picture for time-dependent local Liouvillians and state a Lieb-Robinson bound that gives rise to a…
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…
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.
These lecture notes focus on the application of ideas of locality, in particular Lieb-Robinson bounds, to quantum many-body systems. We consider applications including correlation decay, topological order, a higher dimensional…
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…
We propose new Lieb-Robinson bounds (bounds on the speed of propagation of information in quantum systems) with an explicit dependence on the interaction strengths of the Hamiltonian. For systems with more than two interactions it is found…
The Lieb-Robinson bound (LRB) states that the range and strength of interactions between the constituents of a complex many-body system impose upper limits to how fast the signal can propagate. It manifests in a light cone-like growth of…
We review some recent results that express or rely on the locality properties of the dynamics of quantum spin systems. In particular, we present a slightly sharper version of the recently obtained Lieb-Robinson bound on the group velocity…
We revisit key notions related to the evolution of quantum information in few-body quantum mechanics (fbQM) and, for a wide class of dispersion relations, prove uniform bounds on the maximal speed of propagation of quantum information for…
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,…
We consider the time-dependent Schr\"odinger equation that is generated on the bosonic Fock space by a long-range quantum many-body Hamiltonian. We derive the first bound on the maximal speed of particle transport in these systems that is…
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…
The Lieb-Robinson bound shows that the speed of propagating information in a nonrelativistic quantum lattice system is bounded by a finite velocity, which entails the clustering of correlations. In this paper, we extend the Lieb-Robinson…
Quantum speed limit is a fundamental speed limit for the evolution of quantum states. It is the single-most important interpretation of the time energy uncertainty relation. Recently the speed limit of quantum correlations have been…
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…
Study how quantum information propagates through spacetime manifold provides a means of identifying, distinguishing, and classifying novel phases of matter fertilized by many-body effects in strongly interacting systems in and out of…