Operator dynamics in chaotic long-range interaction sytems

G. Piccitto, Bojan Žunkovič, Alessandro Silva

We investigate the effect of short-range correlations on the dynamical phase diagram of quantum many-body systems with long-range interactions. Focusing on Ising spin chains with power-law decaying interactions and accounting for short-range correlations by a cluster mean field theory we show that short-range correlations are responsible for the emergence of a chaotic dynamical region. Analyzing the fine details of the phase diagram, we show that the resulting chaotic dynamics bears close analogies with that of a tossed coin.

Wahb Ettoumi, Marie-Christine Firpo

G. Piccitto, Alessandro Silva

Abstract 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 and whose critical dynamics depend crucially on the power : for systems with the transition is sharp while for 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 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.

Alexey Vyacheslavovich Gorshkov

Michael Foss‐Feig, Zhexuan Gong, Charles W. Clark +1 more

Paolo Molignini, Barnali Chakrabarti

Abstract We study the non-equilibrium dynamics of a one-dimensional Bose gas with long-range interactions that decay as ( 1 r α ) ( 0.5 < α < 4.0 ). We investigate exotic dynamics when the interactions are suddenly switched from strongly repulsive to strongly attractive, a procedure known to generate super-Tonks-Girardeau gases in systems with contact interactions. We find that relaxation is achieved through a complex intermediate dynamics demonstrated by violent fragmentation and chaotic delocalization. We establish that the relaxed state exhibits classical gaseous characteristics and an asymptotic state associated with unbounded entropy production. The phase diagram shows an exponential boundary between the coherent (quantum) gas and the chaotic (classical) gas. We show the universality of the dynamics by also presenting analogous results for spinless fermions. Weaker quench protocols give a certain degree of control over the relaxation process and induce a slower initial entropy growth. Our study showcases the complex relaxation behavior of tunable long-range interacting systems that could be engineered in state-of-the-art experiments, e.g. in trapped ions or Rydberg atoms.