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We study equilibration of an isolated quantum system by mapping it onto a network of classical oscillators in Hilbert space. By choosing a suitable basis for this mapping, the degree of locality of the quantum system reflects in the…
The Lieb-Robinson bound shows the existence of a maximum speed of signal propagation in discrete quantum mechanical systems with local interactions. This generalizes the concept of relativistic causality beyond field theory, and provides a…
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 if an efficient classical representation of the dynamics exists, optimal control problems on many-body quantum systems can be solved efficiently with finite precision. We show that the size of the space of parameters necessary…
Perturbative gadgets are general techniques for reducing many-body spin interactions to two-body ones using perturbation theory. This allows for potential realization of effective many-body interactions using more physically viable two-body…
Many-body localisation is studied in a disordered quantum spin-1/2 chain with long-ranged power-law interactions, and distinct power-law exponents for interactions between longitudinal and transverse spin components. Using a self-consistent…
We present a phenomenological constraint on a pseudovector light boson beyond the Standard Model, which can induce a long-range spin-dependent interaction $\alpha^{\prime\prime}({\bf s}_1\cdot{\bf s}_2)\,{\rm e}^{-\lambda r}/r$. In the…
Here we consider an integral equation describing a fixed number of scalar particles which interact not through boson exchange but directly along light cones, similarly as in bound state equations such as the Bethe-Salpeter equation. The…
We consider a system of $N\gg 1$ interacting fermionic particles in three dimensions, confined in a periodic box of volume $1$, in the mean-field scaling. We assume that the interaction potential is bounded and small enough. We prove upper…
Quantum many-body systems realise many different phases of matter characterised by their exotic emergent phenomena. While some simple versions of these properties can occur in systems of free fermions, their occurrence generally implies…
Weakly interacting Fermi gases simulate spin-lattices in energy-space, offering a rich platform for investigating information spreading and spin coherence in a large many-body quantum system. We show that the collective spin vector can be…
A two-body interaction or force between quantum particles is ubiquitous in nature, and the microscopic description in terms of the bare two-body interaction is the basis for quantitatively describing interacting few- and many-body systems.…
The standard circuit model for quantum computation presumes the ability to directly perform gates between arbitrary pairs of qubits, which is unlikely to be practical for large-scale experiments. Power-law interactions with strength…
We numerically construct slowly relaxing local operators in a nonintegrable spin-1/2 chain. Restricting the support of the operator to $M$ consecutive spins along the chain, we exhaustively search for the operator that minimizes the…
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 discuss the generic slowing down of quantum dynamics in low energy density states of spatially local Hamiltonians. Beginning with quantum walks of a single particle, we prove that for certain classes of Hamiltonians (deformations of…
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…
Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the…
In this article we discuss the accuracy of effective one-dimensional theories used to describe the behavior of ultracold atomic ensembles confined in quantum wires by a harmonic trap. We derive within a fully many-body approach the…
Interacting bosons or fermions give rise to some of the most fascinating phases of matter, including high-temperature superconductivity, the fractional quantum Hall effect, quantum spin liquids and Mott insulators. While these systems are…