Spreading of correlations and entanglement in the long-range transverse Ising chain

J. T. Schneider,J. Despres,S. J. Thomson,L. Sanchez-Palencia,L. Tagliacozzo

doi:10.1103/physrevresearch.3.l012022

Abstract

Whether long-range interactions allow for a form of causality in non-relativistic quantum models remains an open question with far-reaching implications for the propagation of information and thermalization processes. Here, we study the out-of-equilibrium dynamics of the one-dimensional transverse Ising model with algebraic long-range exchange coupling. Using a state of the art tensor-network approach, complemented by analytic calculations and considering various observables, we show that a weak form of causality emerges, characterized by non-universal dynamical exponents. While the local spin and spin correlation causal edges are sub-ballistic, the causal region has a rich internal structure, which, depending on the observable, displays ballistic or super-ballistic features. In contrast, the causal region of entanglement entropy is featureless and its edge is always ballistic, irrespective of the interaction range. Our results shed light on the propagation of information in long-range interacting lattice models and pave the way to future experiments, which are discussed.

Highlights

Published by the American Physical SocietyIn the vicinity of the edge, the local maxima propagate differently, i.e., ballistically (βm = 1) for spin-spin correlations and super-ballistically (βm < 1) for local spins
Long-range interactions may dramatically impact the dynamics of correlated systems [1]
Whether long-range interactions allow for a form of causality in nonrelativistic quantum models remains an open question with far-reaching implications for the propagation of information and thermalization processes

Summary

Published by the American Physical Society

In the vicinity of the edge, the local maxima propagate differently, i.e., ballistically (βm = 1) for spin-spin correlations and super-ballistically (βm < 1) for local spins. The Rényi entanglement entropies always propagate ballistically, irrespective of the range of interactions, in both the local and quasilocal regime. The analytic quasiparticle picture, based on linear spin wave theory (LSWT), accurately reproduces the numerics and provides a clear interpretation of the numerical results. The different algebraic space-time patterns of correlation functions provide an unambiguous fingerprint of the dynamical regimes of the model, suggesting the emergence of a dynamical phase diagram. These correlation patterns can be directly measured in state-of-the-art experiments. The dynamics of the LRTI chain is governed by the Hamiltonian,

SRx SRx

Conclusion