# 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} }

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

Blockspin scheme and cluster algorithm for quantum spin systems

- Physics
- 1992

Abstract We present a numerical study using a cluster algorithm for the 1-d S = 1 2 quantum Heisenberg models. The dynamical critical exponent for anti-ferromagnetic chains is z = 0.0(1) such that…

The Efficiency of a Cluster Algorithm for the Quantum Heisenberg Model on a Kagome Lattice

- 2010

Experiments with electronand hole-doped antiferromagnetic materials show interesting properties at low temperatures, such as high temperature superconductivity (high Tc) and quantum…

Loop-cluster algorithm: an application for the 2D quantum Heisenberg antiferromagnet

- Physics
- 1993

Abstract A new type of cluster algorithm that strongly reduces the critical slowing down and frustration effects is developed to stimulate the spin one half quantum Heisenberg antiferromagnet. The…

Cluster Monte Carlo Method for Quantum Systems

- Computer Science
- 1997

The general framework of the cluster Monte Carlo algorithms for quantum systems is reviewed and a new algorithm is applied to the one-dimensional t-J model and has proved to reduce the autocorrelation time by a few orders of magnitude.

Quantum Monte Carlo Methods

- Physics
- 2007

We present a review of quantum Monte Carlo algorithms for the simulation of quantum magnets. A general introduction to Monte Carlo sampling is followed by an overview of local updates, cluster…

Improvements in cluster algorithms for quantum spin systems

- Physics
- 1996

Loop cluster algorithms provide an efficient implementation of the Monte Carlo technique for evaluating path integrals. The work described here represents improvement in the state of the art in…

Meron-cluster solution of fermion and other sign problems

- Physics
- 2000

Abstract Numerical simulations of numerous quantum systems suffer from the notorious sign problem. Important examples include QCD and other field theories at non-zero chemical potential, at non-zero…

AN UPDATING SCHEME FOR THE LOOP-CLUSTER ALGORITHM FOR THE ANISOTROPIC HEISENBERG ANTIFERROMAGNET

- Physics
- 1995

Abstract A loop-cluster algorithm is proposed to overcome the critical slowing down in simulations of the anisotropic Heisenberg antiferromagnet, the XYZ model. The primary features of the algorithm…

Monte Carlo Simulations of the Quantum X-Y Model by a Loop-Cluster Algorithm

- Physics
- 1994

The quantum X-Y model of interacting spins on square lattices is simulated by a loop-cluster algorithm. It is shown that the method can be used to simulate the systems efficiently at low temperatures…

Generalization of the Fortuin-Kasteleyn transformation and its application to quantum spin simulations

- Mathematics, Physics
- 1995

We generalize the Fortuin-Kasteleyn (FK) cluster representation of the partition function of the Ising model to represent the partition function of quantum spin models with an arbitrary spin…

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