Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-lat/9211034

Blockspin Scheme and Cluster Algorithm for Quantum Spin Systems

He-Ping Ying, U.‐J. Wiese

Published Nov 12, 1992• 0 citations
arXivHTMLPDF

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 critical slowing down is eliminated.

DOI
10.48550/arxiv.hep-lat/9211034

Related papers

An Efficient Cluster Algorithm and Its Numerical Study for the Quantum Spin systems

He-Ping Ying, JI DA-REN

Using a blockspin scheme, a cluster algorithm is developed for the numerical study of the quantum spin systems. The method is tested in detail for the ferro- and antiferromagnetic Heisenberg chains, of which our calculations show that the new algorithm can be used to simulate the induced classical spin systems efficiently by strongly reducing the slowing down effects.

Communications in Theoretical Physics•Jun 15, 1994•0 citations

Blockspin Cluster Algorithms for Quantum Spin Systems

U.‐J. Wiese, H. -p. Ying

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 maped 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 problems of slowing down from which standard algorithms are suffering. Two-dimensional quantum spin systems are relevant for the description of the undoped anti-ferromagnetic precursor insulators of high-Tc superconductors. Presumably understanding the physics of the superconductors requires an understanding of their precursor insulators. This already is a nontrivial problem, which most likely does not allow for a complete analytic solution. Therefore it is natural to use a numerical approach to compute the properties of these materials. At present different

•Jan 1, 2008•30 citations

BLOCKSPIN SCHEME AND THE CLUSTER-UPDATING ALGO-RITHMS FOR THE QUANTUM SPIN SYSTEMS

Ying He-Ping, U. J. WIESB

In this paper, we proposed a blockspin scheme and developed the usual cluster-updating algorithms for the one-and two-dimensional quantum spin systems, saying s=1/2 isotropic Hei-senberg models. The results for he ferro-and antiferro-magnet chains showed that the criti-cal slowing down (CSD) was indeed eliminated, and so it offered a possibility to improve the estimations in the lower-temperature region. We expect that the algorithms could also be ap-plied to the anisotropic or/and the higher-spin cases, as will as some other interesting models, such as eight-vortex lattice model and low-dimensional Fermi-systems.

Acta Physica Sinica•Jan 1, 1993•0 citations

Blockspin scheme and cluster algorithm for quantum spin systems

U.‐J. Wiese, H.-P. Ying

Nuclear Physics B - Proceedings Supplements•Mar 1, 1993•1 citation

Cluster method for the Ashkin-Teller model

Shai Wiseman, Eytan Domany

A cluster Monte Carlo algorithm for the Ashkin-Teller (AT) model is constructed according to the guidelines of a general scheme for such algorithms. Its dynamical behavior is tested for the square-lattice AT model. We perform simulations on the line of critical points along which the exponents vary continuously, and find that critical slowing down is significantly reduced. We find continuous variation of the dynamical exponent z along the line, following the variation of the ratio of specific-heat and correlation-length exponents \ensuremath{\alpha}/\ensuremath{\nu}, in a manner which satisfies the Li-Sokal bound ${\mathit{z}}_{\mathrm{cluster}}$\ensuremath{\ge}\ensuremath{\alpha}/\ensuremath{\nu}, that was so far proved only for Potts models.

arXiv:hep-lat/9310015•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Nov 1, 1993•55 citations

Blockspin cluster algorithms for quantum spin systems

U.‐J. Wiese, H.-P. Ying

arXiv:cond-mat/9204014•Physics Letters A•Aug 1, 1992•27 citations
We present a numerical study using a cluster algorithm for the 1-d S=1/2S=1/2S=1/2 quantum Heisenberg models. The dynamical critical exponent for anti-ferromagnetic chains is z=0.0(1)z=0.0(1)z=0.0(1) such that critical slowing down is eliminated.
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 maped 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 problems of slowing down from which standard algorithms are suffering. Two-dimensional quantum spin systems are relevant for the description of the undoped anti-ferromagnetic precursor insulators of high-Tc superconductors. Presumably understanding the physics of the superconductors requires an understanding of their precursor insulators. This already is a nontrivial problem, which most likely does not allow for a complete analytic solution. Therefore it is natural to use a numerical approach to compute the properties of these materials. At present different
In this paper, we proposed a blockspin scheme and developed the usual cluster-updating algorithms for the one-and two-dimensional quantum spin systems, saying s=1/2 isotropic Hei-senberg models. The results for he ferro-and antiferro-magnet chains showed that the criti-cal slowing down (CSD) was indeed eliminated, and so it offered a possibility to improve the estimations in the lower-temperature region. We expect that the algorithms could also be ap-plied to the anisotropic or/and the higher-spin cases, as will as some other interesting models, such as eight-vortex lattice model and low-dimensional Fermi-systems.
A cluster Monte Carlo algorithm for the Ashkin-Teller (AT) model is constructed according to the guidelines of a general scheme for such algorithms. Its dynamical behavior is tested for the square-lattice AT model. We perform simulations on the line of critical points along which the exponents vary continuously, and find that critical slowing down is significantly reduced. We find continuous variation of the dynamical exponent z along the line, following the variation of the ratio of specific-heat and correlation-length exponents \ensuremath{\alpha}/\ensuremath{\nu}, in a manner which satisfies the Li-Sokal bound zcluster{\mathit{z}}_{\mathrm{cluster}}zcluster​\ensuremath{\ge}\ensuremath{\alpha}/\ensuremath{\nu}, that was so far proved only for Potts models.