Exactly Solvable Quantum Impurity Model with Inverse-Square Interactions

Abstract

We construct an exactly solvable quantum impurity model which consists of spin-1/2 conduction fermions and the spin-1/2 magnetic moment. The ground state is a Gutzwiller projected Fermi sea with non-orthonormal modes and its wave function in the site-occupation basis is a Jastrowtype homogeneous polynomial. The parent Hamiltonian has all-to-all inverse-square hopping terms between the conduction fermions and inverse-square spin-exchange terms between the conduction fermions and the magnetic moments. The low-lying energy levels, spin-spin correlation function, and von Neumann entanglement entropy of our model demonstrate that it exhibits the essential aspects of spin-1/2 Kondo physics. The machinery developed in this work can generate many other exactly solvable quantum impurity models.

Quantum impurity models from conformal field theory

“…The analytical calculations presented above have only proved that |Ψ is an eigenstate of H. Following our previous SU(2) results [49], we also expect that it is the ground state.…”

“…It was proved in Ref. [49] that this term has an inverse-square form in real space. To be specific, it can be written as…”

“…Exact solutions provide valuable insights into quantum impurity physics and serve as benchmarks for other analytical and numerical techniques. In our previous work [49], we proposed an exactly solvable quantum impurity model consists of one SU(2) spin and spin-1/2 conduction fermions whose parent Hamiltonian contains inverse-square hopping and spin exchange terms. It can be defined on finite-size lattices and the lowest eigenstates for an odd number of conduction fermions can be written down.…”

“…Firstly, the one impurity SU(2) model in Ref. [49] is generalized to SU(N) cases with an arbitrary N . The simplest SU(N) Kondo model was proposed by Coqblin and Schrieffer in 1969 [3] but lacks experimental relevance for a long time.…”

“…which means that A m and A m,m are sufficient for our purpose. After some lengthy calculations [49], their final values are rather simple…”