Related papers: Lieb-Robinson Bound at Finite Temperature
We develop a diagrammatic approach for calculating the high temperature expansion of dynamic correlation functions, such as the electron Green's function and the time-dependent density-density and spin-spin correlation functions, for the…
We prove that the time required for sustained information scrambling in any Hamiltonian quantum system is universally at least logarithmic in the entanglement entropy of scrambled states. This addresses two foundational problems in…
Given a quantum many-body system with few-body interactions, how rapidly can quantum information be hidden during time evolution? The fast scrambling conjecture is that the time to thoroughly mix information among N degrees of freedom grows…
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…
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…
The ability to measure single quanta has allowed complete characterization of small quantum systems such as quantum dots in terms of statistics of detected signals known as full-counting statistics. Quantum gas microscopy enables one to…
The non-equilibrium response of a quantum many-body system defines its fundamental transport properties and how initially localized quantum information spreads. However, for long-range-interacting quantum systems little is known. We address…
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…
Macroscopic quantum effects play central roles in the appearance of inexplicable phenomena in low-temperature quantum many-body physics. Such macroscopic quantumness is often evaluated using long-range entanglement, i.e., entanglement in…
We introduce "local uncertainty relations" in thermal many body systems. Using these relations, we derive basic bounds. These results include the demonstration of universal non-relativistic speed limits (regardless of interaction range),…
We implement numerical linked cluster expansions (NLCEs) to study dynamics of lattice systems following quantum quenches, and focus on a hard-core boson model in one-dimensional lattices. We find that, in the nonintegrable regime and within…
In many-body localized systems, propagation of information forms a light cone that grows logarithmically with time. However, local changes in energy or other conserved quantities typically spread only within a finite distance. Is it…
We prove bounds on operator growth and infinite temperature out-of-time-ordered correlators in many-body systems with $N$ spin-$\frac{1}{2}$ degrees of freedom which interact via two-body all-to-all interactions. Our results parametrically…
A quantum quench is the simplest protocol to investigate nonequilibrium many-body quantum dynamics. Previous studies on the entanglement properties of quenched quantum many-body systems mainly focus on the growth of entanglement entropy.…
We prove a general theorem which provides a strict lower bound on high-temperature Green-Kubo diffusion constants in locally interacting quantum lattice systems, under the assumption of existence of a quadratically extensive almost…
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 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…
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…
The locality of thermal quantum states has emerged as a key input for applications to thermalization, response theory, and efficient simulability. Locality is either captured by the decay of correlations or by local indistinguishability,…
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…