Applications of projected entangled-pair states to two-dimensional spin systems

The density matrix renormalization group and the class of states it operates on, matrix-product states, have been widely accepted to be among the most powerful methods for simulations of one-dimensional quantum systems. They allow reliable approximations to the ground states of many quantum systems and have recently been extended to allow the simulation of time evolution and finite-temperature states. Generalizations to two-dimensional systems have therefore long been sought after. Several classes of tensor-network states that extend the concepts of matrix-product states to higher dimensions have been proposed. The common underlying property is that by construction, they capture the scaling of ground-state entanglement for large classes of systems and are therefore expected to approximate the properties of ground states accurately. In this presentation, we focus on a specific class of states, namely projected entangled-pair states on infinite lattices. We first assess the accuracy of these states for non-frustrated spin systems by comparing with Quantum Monte Carlo results. Furthermore, we present applications to frustrated quantum spin systems in two dimensions.