Continuum limit of finite density many-body ground states with MERA

Scalable classical algorithms for studying ground states of strongly-interacting quantum many-body systems in the continuum are of great practical importance for developments in material science, quantum chemistry, and non-perturbative quantum field theory. In this work we explore the use of Multiscale Entanglement Renormalization Ansatz (MERA) as a tensor network tool to represent ground states with a finite density of particles in the continuum. The MERA ansatz naturally represents an isometric map between coarse-grained wavefunctions at different scales of discretization. We present an energy minimization scheme to obtain the ground state, and demonstrate that the continuum limit can be reached in a number of relevant models. Firstly, we show that the ansatz can efficiently represent ground states of one dimensional free bosonic models in the continuum with inhomogenous potentials. Next, we study the Lieb-Liniger model, a one-dimensional integrable model of interacting bosonic fields. We demonstrate that the ground states at finite particle-density can be efficiently obtained in our framework, even in the strongly-interacting (fermionic) Tonks-Girardeau limit. We finally discuss potential applications of this method and ansatz to models of interacting fermions and in higher dimensions.