Continuous matrix-product states in inhomogeneous systems with long-range interactions

We develop the continuous matrix-product states approach for description of inhomogeneous one-dimensional quantum systems with long-range interactions. The method is applied to the exactly-solvable Calogero-Moser model. We show the high accuracy of reproducing the ground-state properties of the many-body system and discuss potential errors that can originate from the approximation of the nonlocal interaction potentials with singularities.