Generalized Calogero-Sutherland models for Kondo physics in the Luttinger liquid

Abstract

We propose a series of models with inverse-square interactions, for which the ground states have an exact closed form, that describe one localized spin-$1/2$ Kondo impurity coupled to Luttinger liquids of itinerant bosons or fermions in the continuum or on a lattice. The model Hamiltonians contain two parts: a two-component Calogero-Sutherland model with open boundary condition in the continuum or a long-range $t \textendash J$-type model on the lattice, and long-range Kondo couplings between the impurity and the particles. The wave functions of the ground states in a certain basis have Jastrow product forms with powers depending on the particle statistics. It is shown that the wave functions can be expressed as chiral correlators of certain conformal field theories, which reveals that the particles are fractionalized to fully screen the Kondo impurity. This insight would be very useful in future studies on the very difficult problem of Kondo physics with interacting baths.

(5.5 + 12.5) pages, (2 + 2) figures, published version

References in corpus (6)

• Non-Abelian Anyons and Topological Quantum Computation
• The numerical renormalization group method for quantum impurity systems
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• The Berry-Tabor conjecture for spin chains of Haldane-Shastry type
• Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories
• One-Dimensional Quantum Systems with Ground-State of Jastrow Form Are Integrable