Entanglement growth in quench dynamics with variable range interactions

TL;DR

This paper investigates how entanglement grows after a quantum quench in systems with variable-range interactions, revealing different growth behaviors depending on interaction range and providing insights for quantum simulation complexity.

Contribution

It characterizes entanglement dynamics across different interaction ranges in long-range transverse Ising models, highlighting the impact on simulation difficulty and experimental realization.

Findings

Linear entanglement growth for short-range interactions

Logarithmic entanglement growth for long-range interactions

Robustness of phenomena in finite-size and noisy systems

Abstract

Studying entanglement growth in quantum dynamics provides both insight into the underlying microscopic processes and information about the complexity of the quantum states, which is related to the efficiency of simulations on classical computers. Recently, experiments with trapped ions, polar molecules, and Rydberg excitations have provided new opportunities to observe dynamics with long-range interactions. We explore nonequilibrium coherent dynamics after a quantum quench in such systems, identifying qualitatively different behavior as the exponent of algebraically decaying spin-spin interactions in a transverse Ising chain is varied. Computing the build-up of bipartite entanglement as well as mutual information between distant spins, we identify linear growth of entanglement entropy corresponding to propagation of quasiparticles for shorter range interactions, with the maximum rate of growth occurring when the Hamiltonian parameters match those for the quantum phase transition. Counter-intuitively, the growth of bipartite entanglement for long-range interactions is only logarithmic for most regimes, i.e., substantially slower than for shorter range interactions. Experiments with trapped ions allow for the realization of this system with a tunable interaction range, and we show that the different phenomena are robust for finite system sizes and in the presence of noise. These results can act as a direct guide for the generation of large-scale entanglement in such experiments, towards a regime where the entanglement growth can render existing classical simulations inefficient.