Asymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics

Abstract

We study the non-equilibrium dynamics of Abelian anyons in a one-dimensional system. We find that the interplay of anyonic statistics and interactions gives rise to spatially asymmetric particle transport together with a novel dynamical symmetry that depends on the anyonic statistical angle and the sign of interactions. Moreover, we show that anyonic statistics induces asymmetric spreading of quantum information, characterized by asymmetric light cones of out-of-time-ordered correlators. Such asymmetric dynamics is in sharp contrast with the dynamics of conventional fermions or bosons, where both the transport and information dynamics are spatially symmetric. We further discuss experiments with cold atoms where the predicted phenomena can be observed using state-of-the-art technologies. Our results pave the way toward experimentally probing anyonic statistics through non-equilibrium dynamics.

Asymmetric butterfly velocities in 2-local Hamiltonians

“…We show how the butterfly speed can be made asymmetric in such models, before generalizing to non-integrable Hamiltonians by adding interactions. The model and mechanism we present for obtaining asymmetric butterfly velocities is orthogonal to prior works on this topic, and provides a counterexample to the claim that one needs exotic anyonic particle statistics for asymmetric transport [69] -instead showing how this feature can be simply and generically obtained in solvable free fermionic models. Indeed, providing 'minimal models' for physical phenomena are often helpful in distilling necessary ingredients, and our work serves this purpose by furnishing much simpler classes of models with asymmetric information spreading than prior examples in the literature.…”

“…A set of recent papers illustrated that the butterfly velocity can depend on the direction of information spreading [69,70]. In one dimension, the asymmetry between the different directions can be quantified by the butterfly speeds v r B and v l B , where the superscript r (l) represent propagation directions to the right (left).…”

“…Thus, the existence of asymmetric information spreading in Hamiltonian models was an open question, recently addressed by Refs. [69,70]. Ref.…”

“…On the other hand, Ref. [69] showed how this asymmetry could be induced by anyonic particle statistics.…”

Anyon optics with time-of-flight two-particle interference of double-well-trapped interacting ultracold atoms

“…In particular, an anyonic Hubbard model (related to spinless bosons) was formulated and, in analogy with condensed-matter themes, the influence of 1D anyonic statistics on ground-state phase transitions in extended optical lattices was explicitly studied in these [27][28][29] and subsequent publications [30][31][32]. Current interest in 1D anyonic Hubbard models remains expansive [33][34][35][36].…”