Decoupled Cell Monte Carlo: Theory and Convergence Studies of a New Method for Quantum Simulations.

Shigeo Homma, Kazuhiro Sano, H. Matsuda +1 more

Cynthia J. Sisson

Shigeo Homma

H. Matsuda, Kazuyuki ISHII, Shigeo Homma +1 more

As a theoretical basis of the decoupled cell Monte Carlo simulation (DCM) for quantum systems, it is proved that the error caused in the transition probabilities of the simulation by decoupling the cell with radius ν is at most of the order of βν+1 in the limit of β=1/kT →0. Relative merits of DCM and the Trotter method are discussed.

Shigeo Homma, H. Matsuda, N. Ogita

The internal energy and perpendicular susceptibility of the one-dimentional XY-model are calculated by the decoupled cell method Monte Carlo simulation for quantum systems. Above a cenrain demarcation temperature depending on the cell size the agreement with the exact result is excellent, whereas below it the result of simulation becomes unreliable.

Sanzo Miyazawa, Seiji Miyashita, M. S. Makivić +1 more

A modified Decoupled Cell Method (mDCM) for quantum Monte Carlo simulation is proposed to remove the difficulty in the Decoupled Cell Method (DCM), which causes a negative specific heat and an unexpected sudden increase of a susceptibility in a low temperature region. In one-dimensional XY-model (s = 1/2), the results obtained by mDCM were shown not to have any negative specific heat and for the susceptibility along z-axis, gave fairly good agreement with the exact one.