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

Recently, Syljuasen and Sandvik proposed a new framework for constructing algorithms of quantum Monte Carlo simulation. While it includes new classes of powerful algorithms, it is not straightforward to find an efficient algorithm for a given model. Based on their framework, we propose an algorithm that is a natural extension of the conventional loop algorithm with the split-spin representation. A complete table of the vertex density and the worm-scattering probability is presented for the general XXZ model of an arbitrary S with a uniform magnetic field.Comment: 12 pages, 7 figures, insert a word "squared" in the first line of the caption of Fig.7 and correct the label of vertical axis of Fig.

Quantum Monte Carlo with Directed Loops

We introduce the concept of directed loops in stochastic series expansion and path integral quantum Monte Carlo methods. Using the detailed balance rules for directed loops, we show that it is possible to smoothly connect generally applicable simulation schemes (in which it is necessary to include back-tracking processes in the loop construction) to more restricted loop algorithms that can be constructed only for a limited range of Hamiltonians (where back-tracking can be avoided). The "algorithmic discontinuities" between general and special points (or regions) in parameter space can hence be eliminated. As a specific example, we consider the anisotropic S=1/2 Heisenberg antiferromagnet in an external magnetic field. We show that directed loop simulations are very efficient for the full range of magnetic fields (zero to the saturation point) and anisotropies. In particular for weak fields and anisotropies, the autocorrelations are significantly reduced relative to those of previous approaches. The back-tracking probability vanishes continuously as the isotropic Heisenberg point is approached. For the XY-model, we show that back-tracking can be avoided for all fields extending up to the saturation field. The method is hence particularly efficient in this case. We use directed loop simulations to study the magnetization process in the 2D Heisenberg model at very low temperatures. For LxL lattices with L up to 64, we utilize the step-structure in the magnetization curve to extract gaps between different spin sectors. Finite-size scaling of the gaps gives an accurate estimate of the transverse susceptibility in the thermodynamic limit: chi_perp = 0.0659 +- 0.0002.Comment: v2: Revised and expanded discussion of detailed balance, error in algorithmic phase diagram corrected, to appear in Phys. Rev.

Entanglement and Spontaneous Symmetry Breaking in Quantum Spin Models

It is shown that spontaneous symmetry breaking does not modify the ground-state entanglement of two spins, as defined by the concurrence, in the XXZ- and the transverse field Ising-chain. Correlation function inequalities, valid in any dimensions for these models, are presented outlining the regimes where entanglement is unaffected by spontaneous symmetry breaking

Directed Loop Updates for Quantum Lattice Models

This article outlines how the quantum Monte Carlo directed loop update recently introduced can be applied to a wide class of quantum lattice models. Several models are considered: Spin-S XXZ models with longitudinal and transverse magnetic fields, boson models with two-body interactions, and 1D spinful fermion models. Expressions are given for the parameter regimes were very efficient "no-bounce" quantum Monte Carlo algorithms can be found.Comment: 18 pages, 19 figure