Related papers: Lieb-Robinson Bound and Locality for General Marko…
Laplace operators on metric graphs give rise to Klein-Gordon and wave operators. Solutions of the Klein-Gordon equation and the wave equation are studied and finite propagation speed is established. Massive, free quantum fields are then…
I review the role of Lieb-Robinson bounds in characterizing and utilizing the locality properties of the Heisenberg dynamics of quantum lattice systems. In particular, I discuss two definitions of gapped ground state phases and show that…
We study many-body properties of quantum harmonic oscillator lattices with disorder. A sufficient condition for dynamical localization, expressed as a zero-velocity Lieb-Robinson bound, is formulated in terms of the decay of the…
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 discuss the properties of two open quantum systems with a general class of irreversible quantum dynamics. First we study Lieb-Robinson bounds in a quantum lattice systems. The time-dependent generator of the dynamics of the system is of…
We derive a Margolus-Levitin type bound on the minimal evolution time of an arbitrarily driven open quantum system. We express this quantum speed limit time in terms of the operator norm of the nonunitary generator of the dynamics. We apply…
We study the out-of-equilibrium dynamics induced by a local perturbation in fracton field theory. For the ${\mathbb Z}_4$ and ${\mathbb Z}_8$-symmetric free fractonic theories, we compute the time dynamics of several observables such as the…
We apply algorithms based on Lieb-Robinson bounds to simulate time-dependent and thermal quantities in quantum systems. For time-dependent systems, we modify a previous mapping to quantum circuits to significantly reduce the computer…
We consider a quantum spin chain with nearest neighbor interactions and sparsely distributed on-site impurities. We prove commutator bounds for its Heisenberg dynamics which incorporate the coupling strengths of the impurities. The…
Relaxation rates provide important characteristics both for classical and quantum processes. Essentially they control how fast the system thermalizes, equilibrates, {decoheres, and/or dissipates}. Moreover, very often they are directly…
The pace of evolution of physical systems is fundamentally constrained by quantum speed limits (QSL), which have found broad applications in quantum science and technology. We consider the speed of evolution for quantum systems undergoing…
The generic bound of quantum speed limit time (the minimal evolution time) for a qubit system interacting with structural environment is investigated. We define a new bound for the quantum speed limit. It is shown that the non-Markovianity…
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…
We show that whenever the Gibbs state of a quantum spin system satisfies decay of correlations, then it is stable, in the sense that local perturbations affect the Gibbs state only locally, and it satisfies local indistinguishability, i.e.…
We supply the mathematical arguments required to complete the proofs of two previously published results: Lieb-Robinson bounds for the dynamics of quantum lattice systems with unbounded on-site terms in the Hamiltonian and the existence of…
We say that a quantum spin system is dynamically localized if the time-evolution of local observables satisfies a zero-velocity Lieb-Robinson bound. In terms of this definition we have the following main results: First, for general systems…
The transverse-field Ising model is useful for studying interacting qubit arrays. The Lieb--Robinson correlation function can be used to characterize the propagation of quantum information in Ising chains. Considerable work has been done to…
The propagation of an external transverse magnetic signal acting locally on a 1d chain of spins generates a disturbance which runs through the system. This quantum effect can be interpreted as a classical traveling wave which contains a…
We study quantum oscillator lattice systems with disorder, in arbitrary dimension, requiring only partial localization of the associated effective one-particle Hamiltonian. This leads to a many-body localized regime of excited states with…
We derive a sharp bound as the quantum speed limit (QSL) for the minimal evolution time of quantum open systems in the non-Markovian strong-coupling regime with initial mixed states by considering the effects of both renormalized…