Related papers: Enhanced Lieb-Robinson bounds for commuting long-r…
Models of interacting dark radiation have been shown to alleviate the Hubble tension. Extensions incorporating a coupling between dark matter and dark radiation (DM-DR) have been proposed as combined solutions to both the Hubble and $S_8$…
We provide a rigorous justification of the linearized Boltzmann- and Landau equations from interacting particle systems with long-range interaction. The result shows that the fluctuations of Hamiltonian $N$- particle systems governed by…
We analyze the effects of disorder on the correlation functions of one-dimensional quantum models of fermions and spins with long-range interactions that decay with distance $\ell$ as a power-law $1/\ell^\alpha$. Using a combination of…
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…
The spurious interaction of quantum systems with their environment known as decoherence leads, as a function of time, to a decay of coherence of superposition states. Since the interactions between system and environment are local, they can…
We announce and sketch the rigorous proof of a new kind of anomalous (or sub-ballistic) Lieb-Robinson bound for an isotropic XY chain in a quasi-periodic transversal magnetic field. By "anomalous", we mean that the usual effective light…
Thermodynamic and dynamical properties of systems with long range pairwise interactions (LRI) which decay as 1/r^{d+\sigma} at large distances r in $d$ dimensions are reviewed in these Notes. Two broad classes of such systems are…
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 evaluate the coordinate space dependence of the matrix elements of the commutator of the electromagnetic and gluon currents in the vicinity of the light-cone but at large distances within the parton model, DGLAP, the resummation…
We consider many-body quantum systems on a finite lattice, where the Hilbert space is the tensor product of finite-dimensional Hilbert spaces associated with each site, and where the Hamiltonian of the system is a sum of local terms. We are…
A unified approach has been developed to study nonlinear dynamics of a 1D lattice of particles with long-range power-law interaction. A classical case is treated in the framework of the generalization of the well-known Frenkel-Kontorova…
Experiments on quasi-one-dimensional systems such as quantum wires and metallic chains on surfaces suggest the existence of electron-electron interactions of substantial range and hence physics beyond the Hubbard model. We therefore…
In recent experiments with ion traps, long-range interactions were associated with the exceptionally fast propagation of perturbation, while in some theoretical works they have also been related with the suppression of propagation. Here, we…
We consider a generic one dimensional spin system of length $ L $, arbitrarily large, with strictly local interactions, for example nearest neighbor, and prove that the dynamical $ \alpha $-R\'enyi entropies, $ 0 < \alpha \le 1 $, of an…
The area law for entanglement provides one of the most important connections between information theory and quantum many-body physics. It is not only related to the universality of quantum phases, but also to efficient numerical simulations…
Exchange interaction strongly influences the long-range behaviour of localised electron orbitals. It violates the oscillation theorem (creates extra nodes) and produces a power-law decay instead of the usual exponential decrease at large…
We review the mathematical speed limits on quantum information processing in many-body systems. After the proof of the Lieb-Robinson Theorem in 1972, the past two decades have seen substantial developments in its application to other…
We study the momentum space entanglement between different energy modes of interacting scalar fields propagating in general (D + 1)-dimensional flat space-time. As opposed to some of the recent works [1], we use Lorentz invariant normalized…
The non-equilibrium dynamics of disordered many-body quantum systems after a global quantum quench unveils important insights about the competition between interactions and disorder, yielding in particular an insightful perspective on many…
The Hubbard model underlies our understanding of strongly correlated materials. While its standard form only comprises interaction between particles at the same lattice site, its extension to encompass long-range interaction, which…