Applying matrix product operators to model systems with long-range interactions

An algorithm is presented which computes a translationally invariant matrix product state approximation of the ground state of an infinite one-dimensional (1D) system. It does this by embedding sites into an approximation of the infinite environment of the chain, allowing the sites to relax and then merging them with the environment in order to refine the approximation. By making use of matrix product operators, our approach is able to directly model any long-range interaction that can be systematically approximated by a series of decaying exponentials. We apply these techniques to compute the ground state of the Haldane-Shastry model [Phys. Rev. Lett. 60, 635 (1988) and Phys. Rev. Lett. 60, 639 (1988)] and present the results.