Related papers: Improving the Lieb-Robinson bound for long-range i…
We review recent progress on state-dependent Lieb-Robinson bounds for Bose-Hubbard Hamiltonians. In particular, Kuwahara, Vu, and Saito established that, for general bounded-density initial states, the Lieb-Robinson velocity is bounded by…
We derive quantitative estimates proving the conditional propagation of chaos for large stochastic systems of interacting particles subject to both idiosyncratic and common noise. We obtain explicit bounds on the relative entropy between…
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…
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 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…
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…
We show that some gapped quantum many-body systems have a ground state degeneracy that is stable to long-range (e.g., power-law) perturbations, in the sense that any ground state energy splitting induced by such perturbations is…
We study the spreading of information in a wide class of quantum systems, with variable-range interactions. We show that, after a quench, it generally features a double structure, whose scaling laws are related to a set of universal…
A common feature of collapse models and an expected signature of the quantization of gravity at energies well below the Planck scale is the deviation from ordinary quantum-mechanical behavior. Here, we analyze the general consequences of…
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…
When locally exciting a quantum lattice model, the excitation will propagate through the lattice. The effect is responsible for a wealth of non-equilibrium phenomena, and has been exploited to transmit quantum information through spin…
The speed limit of quantum state transfer (QST) in a system of interacting particles is not only important for quantum information processing, but also directly linked to Lieb-Robinson-type bounds that are crucial for understanding various…
We investigate how much information about a quantum system can be simultaneously communicated to independent observers, by establishing quantitative limits to bipartite quantum correlations in many-body systems. As recently reported in…
As disorder strength increases in quantum many-body systems a new phase of matter, the so-called anybody localization, emerges across the whole spectrum. This transition is energy dependent, a phenomenon known as mobility edge, such that…
We consider interacting particle systems with unbounded interaction range on general countably infinite graphs $S$ and prove explicit non-asymptotic error bounds for approximations of the infinite-volume dynamics by systems of finitely many…
Interacting quantum many-body systems are usually expected to thermalise, in the sense that the evolution of local expectation values approach a stationary value resembling a thermal ensemble. This intuition is notably contradicted in…
The presence of non-local and long-range interactions in quantum systems induces several peculiar features in their equilibrium and out-of-equilibrium behavior. In current experimental platforms control parameters such as interaction range,…
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…
The principles of behavior of the system with discrete interactions are applied to description of motion of the relativistic particle. Applying the concept of non-local behavior both to position in space and to time, the apparently…
We argue that chaotic power-law interacting systems have emergent limits on information propagation, analogous to relativistic light cones, which depend on the spatial dimension $d$ and the exponent $\alpha$ governing the decay of…