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Coarse-grained loop algorithms for Monte Carlo simulation of quantum spin systems.

Kenji Harada¹, Naoki Kawashima

¹Department of Applied Analysis and Complex Dynamical Systems, Kyoto University, Kyoto 606-8501, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|January 7, 2003

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Researchers developed an efficient quantum Monte Carlo simulation algorithm, extending the loop algorithm with split-spin representation. This provides a complete table for the general XXZ model under a magnetic field.

Area of Science:

Quantum physics
Computational methods

Background:

A new framework for quantum Monte Carlo (QMC) simulation algorithms was recently proposed.
Finding efficient algorithms within this framework for specific models remains challenging.

Purpose of the Study:

To propose an efficient QMC algorithm based on the new framework.
To extend the conventional loop algorithm using the split-spin representation.

Main Methods:

Development of a novel QMC algorithm.
Application of the split-spin representation.
Analysis of the general XXZ model with arbitrary spin (S) and a uniform magnetic field.

Main Results:

A complete table of vertex density and worm-scattering probability for the specified model.

Related Experiment Videos

Demonstration of an efficient algorithm as a natural extension of existing methods.

Conclusions:

The proposed algorithm offers an efficient approach for the general XXZ model within the new QMC framework.
The provided tables facilitate the application of QMC simulations for this model.