Valence-Bond Quantum Monte Carlo Algorithms Defined on Trees

Abstract

We present a new class of algorithms for performing valence-bond quantum Monte Carlo of quantum spin models. Valence-bond quantum Monte Carlo is a T=0 Monte Carlo method based on sampling of a set of operator-strings that can be viewed as forming a tree-like structure. The algorithms presented here utilize the notion of a worm that moves up and down this tree and changes the associated operator-string. In quite general terms we derive a set of equations whose solutions correspond to a new class of algorithms. As specific examples of this class of algorithms we focus on two cases. The bouncing worm algorithm, for which updates are always accepted by allowing the worm to bounce up and down the tree and the driven worm algorithm, where a single parameter controls how far up the tree the worm reaches before turning around. The latter algorithm involves only a single bounce where the worm turns from going up the tree to going down. The presence of the control parameter necessitates the introduction of an acceptance probability for the update.

Final version, 13 pages, 11 figures

References in corpus (4)

• Loop updates for variational and projector quantum Monte Carlo simulations in the valence-bond basis
• Some formal results for the valence bond basis
• Reptation quantum Monte Carlo for lattice Hamiltonians with a directed-update scheme
• Generalization of the singlet sector valence bond loop algorithm to antiferromagnetic ground states with total spin $S_{tot}=1/2$