Related papers: Tightening the Lieb-Robinson Bound in Locally-Inte…
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 provide a simple proof of the Lieb-Robinson bound and use it to prove the existence of the dynamics for interactions with polynomial decay. We then use our results to demonstrate that there is an upper bound on the rate at which…
We consider the quantum dynamics of a many-fermion system in $\mathbb R^d$ with an ultraviolet regularized pair interaction as previously studied in [M. Gebert, B. Nachtergaele, J. Reschke, and R. Sims, Ann. Henri Poincar\'e 21.11 (2020)].…
The speed of information propagation in long-range interacting quantum systems is limited by Lieb-Robinson-type bounds, whose tightness can be established by finding specific quantum state-transfer protocols. Previous works have given…
We study correlations in fermionic lattice systems with long-range interactions in thermal equilibrium. We prove a bound on the correlation decay between anti-commuting operators and generalize a long-range Lieb-Robinson type bound. Our…
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 present a statistical mechanical framework based on the Kullback-Leibler divergence (KLD) to analyze the relativistic limits of decoding time-encoded information from a moving source. By modeling the symbol durations as…
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.
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 generalize to multi-commutators the usual Lieb-Robinson bounds for commutators. In the spirit of constructive QFT, this is done so as to allow the use of combinatorics of minimally connected graphs (tree expansions) in order to estimate…
Long-range interacting many-body systems exhibit a number of peculiar and intriguing properties. One of those is the scaling of relaxation times with the number $N$ of particles in a system. In this paper I give a survey of results on…
We theoretically study the response of a many-body localized system to a local quench from a quantum information perspective. We find that the local quench triggers entanglement growth throughout the whole system, giving rise to a…
We present a perturbation method to compute the out-of-time-ordered correlator in the strongly disordered Heisenberg XXZ model in the deep many-body localized regime. We characterize the discrete structure of the information propagation…
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 rigorous bounds on the growth of $\alpha$-Renyi entropies $S_{\alpha}(t)$ (the Von Neumann entropy being the special case $\alpha = 1$) associated with any subsystem $A$ of a general lattice quantum many-body system with finite…
During time evolution of many-body systems entanglement grows rapidly, limiting exact simulations to small-scale systems or small timescales. Quantum information tends however to flow towards larger scales without returning to local scales,…
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 investigate the out-of-equilibrium dynamics after a local quench that connects two spin-1/2 XXZ chains prepared in the ground state of the Hamiltonian in different phases, one in the ferromagnetic phase and the other in the critical…
Discoveries of fundamental limits for the rates of physical processes, from the speed of light to the Lieb-Robinson bound for information propagation, often lead to breakthroughs in the our understanding of the underlying physics. Here we…
Enhanced experimental capabilities to control nonlocal and power-law decaying interactions are currently fuelling intense research in the domain of quantum many-body physics. Compared to their counterparts with short-ranged interactions,…