Cluster algorithms with empahsis on quantum spin systems

Conference · Fri Oct 06 04:00:00 EDT 1995

OSTI ID:212436

Gubernatis, J E ^[1]; Kawashima, Naoki ^[2]

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1. Los Alamos National Lab., NM (United States)
2. Tokyo Univ. (Japan). Dept. of Physics

The purpose of this lecture is to discuss in detail the generalized approach of Kawashima and Gubernatis for the construction of cluster algorithms. We first present a brief refresher on the Monte Carlo method, describe the Swendsen-Wang algorithm, show how this algorithm follows from the Fortuin-Kastelyn transformation, and re=interpret this transformation in a form which is the basis of the generalized approach. We then derive the essential equations of the generalized approach. This derivation is remarkably simple if done from the viewpoint of probability theory, and the essential assumptions will be clearly stated. These assumptions are implicit in all useful cluster algorithms of which we are aware. They lead to a quite different perspective on cluster algorithms than found in the seminal works and in Ising model applications. Next, we illustrate how the generalized approach leads to a cluster algorithm for world-line quantum Monte Carlo simulations of Heisenberg models with S = 1/2. More succinctly, we also discuss the generalization of the Fortuin- Kasetelyn transformation to higher spin models and illustrate the essential steps for a S = 1 Heisenberg model. Finally, we summarize how to go beyond S = 1 to a general spin, XYZ model.

• Research Organization: Los Alamos National Lab., NM (United States)
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 212436
• Report Number(s): LA-UR--95-3999; CONF-9507154--2; ON: DE96005505
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
ALGORITHMS
HEISENBERG MODEL
MONTE CARLO METHOD
NONLINEAR PROBLEMS
SPIN
STATISTICAL MECHANICS
TRANSFORMATIONS