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 one-dimensional spinful fermion models. Expressions are given for the parameter regimes where very efficient “no-bounce” quantum Monte Carlo algorithms can be found.