Sequentially generated states for the study of two-dimensional systems

Matrix product states can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a family of states that extends this definition to two dimensions. Like in matrix product states, expectation values of few body observables can be efficiently evaluated and, for the case of translationally invariant systems, the correlation functions decay exponentially with the distance. We show that such states are a subclass of projected entangled pair states and investigate their suitability for approximating the ground states of local Hamiltonians.