We study an Ising model in one dimension with short-range ferromagnetic and long-range (power law) antiferromagnetic interactions. We show that the zero temperature phase diagram in a (longitudinal) field $H$ involves a sequence of up and down domains whose size varies continuously with $H$ , between $\ensuremath{-}{H}_{c}$ and ${H}_{c}$ , which represent the edges of the ferromagnetic up and down phases. The implications of long-range interaction in many body systems are discussed.We study an Ising model in one dimension with short-range ferromagnetic and long-range (power law) antiferromagnetic interactions. We show that the zero temperature phase diagram in a (longitudinal) field $H$ involves a sequence of up and down domains whose size varies continuously with $H$, between $\ensuremath{-}{H}_{c}$ and ${H}_{c}$, which represent the edges of the ferromagnetic up and down phases. The implications of long-range interaction in many body systems are discussed.

arXiv:0710.1341Physical Review BFeb 25, 20087 citations

Relaxation timescales and decay of correlations in a long-range interacting quantum simulator

Mauritz van den Worm, Brian C. Sawyer, J. J. Bollinger +1 more

We study the time evolution of correlation functions in long-range interacting quantum Ising models. For a large class of initial conditions, exact analytic results are obtained in arbitrary lattice dimension, both for ferromagnetic and antiferromagnetic coupling, and hence also in the presence of geometric frustration. In contrast to the nearest-neighbour case, we find that correlations decay like stretched or compressed exponentials in time. Provided the long-range character of the interactions is sufficiently strong, pronounced prethermalization plateaus are observed and relaxation timescales are widely separated. Specializing to a triangular lattice in two spatial dimensions, we propose to utilize these results for benchmarking a recently developed ion-trap-based quantum simulator.We study the time evolution of correlation functions in long-range interacting quantum Ising models. For a large class of initial conditions, exact analytic results are obtained in arbitrary lattice dimension, both for ferromagnetic and antiferromagnetic coupling, and hence also in the presence of geometric frustration. In contrast to the nearest-neighbour case, we find that correlations decay like stretched or compressed exponentials in time. Provided the long-range character of the interactions is sufficiently strong, pronounced prethermalization plateaus are observed and relaxation timescales are widely separated. Specializing to a triangular lattice in two spatial dimensions, we propose to utilize these results for benchmarking a recently developed ion-trap-based quantum simulator.

arXiv:1209.3697New Journal of PhysicsAug 2, 201379 citations

H

involves a sequence of up and down domains whose size varies continuously with

H

, between $\ensuremath{-}{H}_{c}$ and

{H}_{c}

, which represent the edges of the ferromagnetic up and down phases. The implications of long-range interaction in many body systems are discussed.