Related papers: Lieb-Robinson Bound and Locality for General Marko…
The relational framework of canonical quantum gravity with non-ultralocal constraints is explored. After demonstrating the absence of anomalies, a spatially discretized version of the relational framework is introduced. This allows the…
Speed of state transitions in macroscopic systems is a crucial concept for foundations of nonequilibrium statistical mechanics as well as various applications in quantum technology represented by optimal quantum control. While extensive…
Recent advances in emergent geometry have identified a new class of models that represent spacetime as the graph obtained as the ground state of interacting Ising spins. These models have many desirable features, including stable…
We study the quantum dynamics generated by Bose-Hubbard Hamiltonians with long-ranged (power law) terms. We prove two ballistic propagation bounds for suitable initial states: (i) A bound on all moments of the local particle number for all…
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…
We demonstrate that the dynamics of an open quantum system can be calculated efficiently and with predefined error, provided a basis exists in which the system-environment interactions are local and hence obey the Lieb-Robinson bound. We…
We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that…
Instances of discrete quantum systems coupled to a continuum of oscillators are ubiquitous in physics. Often the continua are approximated by a discrete set of modes. We derive analytical error bounds on expectation values of system…
We state and prove four types of Lieb-Robinson bounds valid for many-body open quantum systems with power law decaying interactions undergoing out of equilibrium dynamics. We also provide an introductory and self-contained discussion of the…
We apply the Lieb-Robinson bounds technique to find the maximum speed of interaction in a spin model with topological order whose low-energy effective theory describes light [see X.-G. Wen, \prb {\bf 68}, 115413 (2003)]. The maximum speed…
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…
We extend the concept of locality to enclose a situation where a tensor-product structure for the Hilbert space is not \textit {a priori} assumed; rather, this locality is related to a given matrix representation of the Hamiltonian…
Recent works have revealed the intricate effect of long-range interactions on information transport in quantum many-body systems: In $D$ spatial dimensions, interactions decaying as a power-law $r^{-\alpha}$ with $\alpha > 2 D+1$ exhibit a…
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…
Lieb-Robinson-type bounds are reported for a large class of classical Hamiltonian lattice models. By a suitable rescaling of energy or time, such bounds can be constructed for interactions of arbitrarily long range. The bound quantifies the…
Quantum many-body interactions can induce quantum entanglement among particles, rendering them valuable resources for quantum-enhanced sensing. In this work, we derive a universal and fundamental bound for the growth of the quantum Fisher…
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…
We prove a Lieb-Robinson bound for lattice fermion models with polynomially decaying interactions, which can be used to show the locality of the quasi-local inverse Liouvillian. This allows us to prove automorphic equivalence and the local…
In locally interacting quantum many-body systems, the velocity of information propagation is finitely bounded and a linear light cone can be defined. Outside the light cone, the amount of information rapidly decays with distance. When…
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…