Entanglement and correlations in long-range interacting spin chains in and out of equilibrium

Long-range interacting quantum systems have attracted considerable attention in recent years both from an experimental and theoretical perspective. Latest experimental and technological progress made it possible to realise long-ranged systems on several quantum simulation platforms. In the theoretical framework of quantum many-body systems, long-range interactions break various fundamental concepts and theorems with far-reaching consequences.

Among those are Lieb–Robinson bounds which guarantee the emergence of causality in short- ranged non-relativistic lattice systems, as well as the Mermin–Wagner–Hohenberg theorem stating that continuous symmetries in short-ranged one dimensional quantum systems cannot be spontaneously broken by the ground state. In this seminar, I will present two works on long-range interacting spin chains, focusing on the equilibrium ground state phase diagram and on out-of-equilibrium dynamics.

First, in the long-range transverse-field Ising model, we show the emergence of a weak form of causality characterised by non-universal dynamical exponents. 
Second, we determine the equilibrium quantum phase diagram of the long-range XXZ model in terms of the anisotropic coupling and the long-range interaction exponent through studying a representation of the spectrum of the reduced density matrix following a half-chain bipartition, the so-called entanglement spectrum.