Theoretical Basis of the Decoupled Cell Monte Carlo Simulation for Quantum System | Zendy

H. Matsuda | Zendy; K. Ishii | Zendy; Shigeo Homma | Zendy; N. Ogita | Zendy

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Theoretical Basis of the Decoupled Cell Monte Carlo Simulation for Quantum System

Author(s) -

H. Matsuda,

K. Ishii,

Shigeo Homma,

N. Ogita

Publication year - 1988

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.80.583

Subject(s) - physics , monte carlo method , statistical physics , basis (linear algebra) , decoupling (probability) , quantum monte carlo , quantum , monte carlo molecular modeling , radius , quantum mechanics , markov chain monte carlo , statistics , mathematics , computer science , geometry , computer security , control engineering , engineering

(j / is the a-component of the Pauli spin operator of the ith site, fa is the a-coupling constant (a=x, y, z; i=l, 2, "', N), and the summation in (1) is ovdr all possible nearest neighbor pairs . However, no a priori justification has been given as to the accuracy of DCM. In this paper we give a theortical basis of DCM by proving some theorem and lemmas. In the Metropolis method, a required probability distribution is generated as the limit distribution of a Markov chain. This Markov chain can be anyone so long as (i) the transition probability W(S --> S') from state S to state S' satisfies the condition of detailed balance:

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