Verification of a new quantum simulation approach through its application to two-dimensional Ising lattices
Abstract
A new quantum simulation approach has been applied in the present work to the two-dimensional (2D) ferromagnetic and antiferromagnetic Ising lattices to calculate their magnetic structures, magnetizations, free energies and specific heats in the absence of an external magnetic field. Surprisingly, no size effects could be observed in our simulations performed for the Ising lattices of different sizes.
Most importantly, our calculated spontaneous thermally averaged spins for the two kinds of systems are exactly same as those evaluated with quantum mean field theory, and the magnetic structures simulated at all chosen temperatures are perfectly ferromagnetic or antiferromagnetic, verifying the correctness and applicability of our quantum model and computational algorithm. On the other hand, if the classical Monte Carlo (CMC) method is applied to the ferromagnetic 2D Ising lattice with S = 1, it is able to generate correct magnetization well consistent with Onsager's theory; but in the case of S = 1/2, the computational results of CMC are incomparable to those redicted with the quantum mean field theory, giving rise to very much reduced magnetization and considerably underestimated Curie temperature.
The difficulty met by the CMC method is mainly caused by its improperly calculated exchange energy of the randomly selected spin in every simulation step, especially immediately below the transition temperature, where the thermal averages of spins are much less than 1/2, however they are assigned to +/- 1 /2 by CMC to evaluate the exchange energies of the spins, such improper manipulation is obviously impossible to lead the code to converge to the right equilibrium states of the spin systems.