Exact ground states of quantum many-body systems under confinement

Abstract

Knowledge of the ground state of a homogeneous quantum many-body system can be used to find the exact ground state of a dual inhomogeneous system with a confining potential. We first identify the complete family of one-dimensional parent Hamiltonians with a ground state of Bijl-Jastrow form in free space. For each instance in this family, the dual trapped system is shown to include a one-body harmonic potential and two-body long-range interactions. The extension to anharmonic potentials and quantum solids with Nosanov-Jastrow ground-state wave functions is also presented. We apply this exact mapping to construct eigenstates of trapped systems from free-space solutions for different choices of the pair correlation functions entering the Bijl-Jastrow form. This construction is user friendly and allows one to readily rederive known instances of quasisolvable and integrable models, as well as to introduce unexplored examples. Among the latter, we describe a Lieb-Liniger-Coulomb model whose exact ground state is a McGuire soliton solution embedded in a harmonic trap.