We introduce string-bond states, a class of states obtained by placing strings of operators on a lattice which can be used to build an efficient variational Monte Carlo algorithm for the simulation of frustrated quantum spin systems in two and three dimension and with arbitrary boundary conditions. We discuss the properties of string-bond states and in particular how they arise as a special case of PEPS. We have implemented the algorithm on both two- and three-dimensional systems, and have found a very good agreement with QMC results. In simulating frustrated systems, the string-bond state algorithm agrees well with the results from PEPS simulations, while at the same time being much faster. It is thus the only method suitable for the simulation of frustrated systems with periodic boundary conditions and in three dimensions.
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