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We propose a series of exactly solvable quantum impurity models with inverse-square interactions that describe a single spin-1/2 Kondo impurity embedded in a Luttinger liquid, both in the continuum and on the lattice. The model wave functions take the form of Jastrow products and can have either fermionic or bosonic baths depending on the powers of the Jastrow factors. We show that they are exact ground states of an open boundary, two-component Calogero-Sutherland model in the continuum (or a long-range interacting t − J model on the lattice) coupled to a localized spin-1/2 impurity. The connection of these wave functions to chiral correlators of certain conformal field theories is discussed.

We show that the Klein bottle entropy [H.-H. Tu, Phys. Rev. Lett. 119, 261603 (2017)] for conformal field theories perturbed by a relevant operator is a universal function of the dimensionless coupling constant. The universal scaling of the Klein bottle entropy near criticality provides an efficient approach to extract the scaling dimension of lattice operators via data collapse. As paradigmatic examples, we validate the universal scaling of the Klein bottle entropy for Ising and Z 3 parafermion conformal field theories with various perturbations using numerical simulation with continuous matrix product operator approach.