Alessandro Silva

Quantum many body systems with long range interactions are known to display many fascinating phenomena experimentally observable in trapped ions, Rydberg atoms and polar molecules. Among these are dynamical phase transitions which occur after an abrupt quench in spin chains with interactions decaying as $r^{-α}$ and whose critical dynamics depend crucially on the power $α$: for systems with $α<1$ the transition is sharp while for $α>1$ it fans out in a chaotic crossover region. In this paper we explore the fate of critical dynamics in Ising chains with long-range interactions when the transverse field is ramped up with a finite speed. While for abrupt quenches we observe a chaotic region that widens as $α$ is increased, the width of the crossover region diminishes as the time of the ramp increases, suggesting that chaos will disappear altogether and be replaced by a sharp transition in the adiabatic limit.

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.

As realized by Kapitza long ago, a rigid pendulum can be stabilized upside down by periodically driving its suspension point with tuned amplitude and frequency. While this dynamical stabilization is feasible in a variety of instances in systems with few degrees of freedom, it is natural to search for generalizations to multi-particle systems. In particular, a fundamental question is whether, by periodically driving a single parameter in a many-body system, one can stabilize an otherwise unstable phase of matter against all possible fluctuations of its microscopic degrees of freedom. In this work we show that such stabilization occurs in experimentally realizable quantum many-body systems: a periodic modulation of a transverse magnetic field can make ferromagnetic spin systems with long-range interactions stably trapped around unstable paramagnetic configurations as well as in other unconventional dynamical phases with no equilibrium counterparts. We demonstrate that these quantum Kapitza phases have a long lifetime and can be observed 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.