Related papers: Locality Estimates for Quantum Spin Systems
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…
We give a Lieb-Robinson bound for the group velocity of a large class of discrete quantum systems which can be used to prove that a non-vanishing spectral gap implies exponential clustering in the ground state of such systems.
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.
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…
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…
The Lieb-Robinson theorem states that locality is approximately preserved in the dynamics of quantum lattice systems. Whenever one has finite-dimensional constituents, observables evolving in time under a local Hamiltonian will essentially…
We consider models of open quantum spin systems with irreversible dynamics and show that general quasi-locality results for long-range models, e.g. as proven for the Heisenberg dynamics associated to quantum systems in [27], naturally…
We give an introduction into some aspects of the emerging mathematical theory of many-body localization (MBL) for disordered quantum spin chains. In particular, we discuss manifestations of MBL such as zero-velocity Lieb-Robinson bounds,…
This work provides an overview of gapped quantum spin systems, including concepts, techniques, properties, and results. The basic framework and objects of interest for quantum spin systems are introduced, and the main ideas behind methods…
We define various notions of locality for *-automorphisms of the algebra of observables for an infinitely extended quantum spin system and study their relationship. In particular, we show that the ubiquitous characterization which arises…
We characterise and study dynamical localisation of a finite interacting quantum many-body system. We present explicit bounds on the disorder strength required for the onset of localisation of the dynamics of arbitrary ensemble of sites of…
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…
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}…
We study the out-of-equilibrium dynamics of quantum systems with long-range interactions. Two different models describing, respectively, interacting lattice bosons and spins are considered. Our study relies on a combined approach based on…
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 consider open many-body systems governed by a time-dependent quantum master equation with short-range interactions. With a generalized Lieb-Robinson bound, we show that the evolution in this very generic framework is quasi-local, i.e.,…
We rigorously show that a local spin system giving rise to a slow Hamiltonian dynamics is stable against generic, even time-dependent, local perturbations. The sum of these perturbations can cover a significant amount of the system's size.…
For quantum lattice systems with local interactions, the Lieb-Robinson bound acts as an alternative for the strict causality of relativistic systems and allows to prove many interesting results, in particular when the energy spectrum…
We consider translation invariant gapped quantum spin systems satisfying the Lieb-Robinson bound and containing single-particle states in a ground state representation. Following the Haag-Ruelle approach from relativistic quantum field…
We introduce the notion of transmission time to study the dynamics of disordered quantum spin chains and prove results relating its behavior to many-body localization properties. We also study two versions of the so-called Local Integrals…