Dynamical Critical Scaling of LongRange Interacting Quantum Magnets
Abstract
Slow quenches of the magnetic field across the paramagneticferromagnetic phase transition of spin systems produce heat. In systems with shortrange interactions the heat exhibits universal powerlaw scaling as a function of the quench rate, known as KibbleZurek scaling. In this work we analyze slow quenches of the magnetic field in the LipkinMeshkovGlick (LMG) model, which describes fully connected quantum spins. We analytically determine the quantum contribution to the residual heat as a function of the quench rate δ by means of a HolsteinPrimakoff expansion about the meanfield value. Unlike in the case of shortrange interactions, scaling laws in the LMG model are only found for a ramp starting or ending at the critical point. If instead the ramp is symmetric, as in the typical KibbleZurek scenario, then the number of excitations exhibits a crossover behavior as a function of δ and tends to a constant in the thermodynamic limit. Previous, and seemingly contradictory, theoretical studies are identified as specific limits of this dynamics. Our results can be tested on several experimental platforms, including quantum gases and trapped ions.
 Publication:

Physical Review Letters
 Pub Date:
 December 2018
 DOI:
 10.1103/PhysRevLett.121.240403
 arXiv:
 arXiv:1805.00008
 Bibcode:
 2018PhRvL.121x0403D
 Keywords:

 Condensed Matter  Quantum Gases;
 Quantum Physics
 EPrint:
 10 pages, 5 figures, new version improves figure 1 quality and expands the discussion of the results