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. For the complete family of parent Hamiltonians with a ground state of Bijl-Jastrow form in free space, the dual 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 wavefunctions is also presented. We apply this exact mapping to construct eigenstates of trapped systems from free-space solutions with a variety of pair correlation functions and interparticle interactions.
Highlights
Exact solutions play an important role in physics
We have introduced an exact mapping between the ground state of a Hamiltonian in free space and the ground state of a dual Hamiltonian in the presence of a one-body trapping potential and additional many-body interactions
This mapping can be used by fixing the pair correlation function entering the Bijl-Jastrow form, as we have done to find trapped states in systems with inverse-square, contact, quadratic, and Toda-like interactions
Summary
Exact solutions play an important role in physics. Solvable models often bring novel insights, they can serve as a test bed for physical theories and a starting point for new approximations, and help benchmarking numerical methods. In the one-dimensional case, an exact treatment is possible via the Bethe ansatz approach, which expresses the wave function as a superposition of plane waves [2,3,4] This reduces the possible settings to free space (no external one-body potential), translationally invariant ring geometries with periodic boundary conditions, or settings with hard walls such as mirrors and boxlike traps [5,6]. We find the complete family of models describing indistinguishable bosons in a harmonic trapped with a ground state of Bijl-Jastrow form This construction is generalized to anharmonic external potentials and the description of quantum solids with ground-state wave functions of Nosanov-Jastrow form. This user-friendly approach works as a factory of quasisolvable models. We describe the Lieb-Liniger-Coulomb model with a trapped McGuire soliton as an exact ground state and a trapped system with Toda-Like pairwise interactions
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