# Blockspin cluster algorithms for quantum spin systems

@article{Wiese1992BlockspinCA,
title={Blockspin cluster algorithms for quantum spin systems},
author={U. Wiese and Heping Ying},
journal={Physics Letters A},
year={1992},
volume={168},
pages={143-150}
}
• Published 28 April 1992
• Physics
• Physics Letters A
Abstract Cluster algorithms are developed for simulating quantum spin systems like the one- and two-dimensional Heisenberg ferro- and anti-ferromagnets. The corresponding two- and three-dimensional classical spin models with four-spin couplings are mapped to blockspin models with two-blockspin interactions. Clusters of blockspins are updated collectively. The efficiency of the method is investigated in detail for one-dimensional spin chains. Then in most cases the new algorithms solve the…
21 Citations

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## References

SHOWING 1-10 OF 14 REFERENCES
Monte Carlo Simulation of Quantum Spin Systems. I
• Physics
• 1977
A general explicit formulation of Monte Carlo simulation for quantum systems is given in this paper on the basis of the previous fundamental proposal by Suzuki. This paper also demonstrates
Relationship between d-Dimensional Quantal Spin Systems and (d+1)-Dimensional Ising Systems: Equivalence, Critical Exponents and Systematic Approximants of the Partition Function and Spin Correlations
The partition function of a quantal spin system is expressed by that of the Ising model, on the basis of the generalized Trotter formula. Thereby the ground state of the d-dimensional Ising model
Two-dimensional spin-1/2 Heisenberg antiferromagnet: A quantum Monte Carlo study.
• Physics, Medicine
Physical review. B, Condensed matter
• 1991
A fast and efficient multispin coding algorithm on a parallel supercomputer, based on the Suzuki-Trotter transformation, is developed, which shows that the correlation length and staggered susceptibility are quantitatively well described by the renormalized classical picture at the two-loop level of approximation.
Collective Monte Carlo updating for spin systems.
• Wolff
• Physics, Medicine
Physical review letters
• 1989
A Monte Carlo algorithm is presented that updates large clusters of spins simultaneously in systems at and near criticality. We demonstrate its efficiency in the two-dimensional $\mathrm{O}(n)$
THE 2D HEISENBERG ANTIFERROMAGNET IN HIGH-Tc SUPERCONDUCTIVITY: A Review of Numerical Techniques and Results
In this article we review numerical studies of the quantum Heisenberg antiferromagnet on a square lattice, which is a model of the magnetic properties of the undoped “precursor insulators” of the
Monte Carlo studies of one-dimensional quantum Heisenberg and XY models
• Physics
• 1983
The Suzuki-Trotter transformation has been used to transform $N$-spin $S=\frac{1}{2}$ Heisenberg and $\mathrm{XY}$ chains into two-dimensional ($N\ifmmode\times\else\texttimes\fi{}2m$) classical
Nonuniversal critical dynamics in Monte Carlo simulations.
• Physics, Medicine
Physical review letters
• 1987
A new approach to Monte Carlo simulations is presented, giving a highly efficient method of simulation for large systems near criticality. The algorithm violates dynamic universality at second-order
Phys. Rev
• Phys. Rev
• 1991
Phys. Rev. Lett
• Phys. Rev. Lett
• 1989
Phys. Rev. Lett
• Phys. Rev. Lett
• 1987