Bojan Zunkovic

We show that long-range ferromagnetic interactions in quantum spin chains can induce spatial quasi-localization of topological magnetic defects, i.e., domain-walls, even in the absence of quenched disorder. By means of matrix-product-states numerical techniques, we study the non-equilibrium evolution of initial states with one or more domain-walls under the effect of a transverse field in variable-range quantum Ising chains. Upon increasing the range of these interactions, we demonstrate the occurrence of a sharp transition characterized by the suppression of spatial diffusion of the magnetic defects during the accessible time scale: the excess energy density remains localized around the initial domain-wall positions, hindering thermalization. This quasi-localization is accurately reproduced by an effective semiclassical model, which elucidates the crucial role that long-range interactions play in this phenomenon. These predictions can be tested in current experiments with trapped ions.

We theoretically study the dynamics of a transverse-field Ising chain with power-law decaying interactions characterized by an exponent $α$, which can be experimentally realized in ion traps. We focus on two classes of emergent dynamical critical phenomena following a quantum quench from a ferromagnetic initial state: The first one manifests in the time averaged order parameter, which vanishes at a critical transverse field. We argue that such a transition occurs only for long-range interactions $α\leq 2$ . The second class corresponds to the emergence of time-periodic singularities in the return probability to the ground state manifold (a.k.a. Loschmidt echo) which is obtained for all values of $α$ and agrees with the order parameter transition for $α\leq 2$. We characterize how the two classes of nonequilibrium criticality correspond to each other and give a physical interpretation based on the symmetry of the time-evolved quantum states.