  We propose a new class of tensor-network states, which we name projected
entangled simplex states (PESS), for studying the ground-state properties of
quantum lattice models. These states extend the pair-correlation basis of
projected entangled pair states (PEPS) to a simplex. PESS are an exact
representation of the simplex solid states and provide an efficient trial wave
function that satisfies the area law of entanglement entropy. We introduce a
simple update method for evaluating the PESS wave function based on
imaginary-time evolution and the higher-order singular-value decomposition of
tensors. By applying this method to the spin-1/2 antiferromagnetic Heisenberg
model on the kagome lattice, we obtain accurate and systematic results for the
ground-state energy, which approach the lowest upper bounds yet estimated for
this quantity.
