Integrable impurities in Hubbard chain with the open boundary condition

TL;DR

This paper solves the Kondo problem with two impurities in an open boundary Hubbard chain, deriving exact results for ground state energy corrections, specific heat, susceptibility, and Kondo temperature, highlighting the effects of boundary impurities.

Contribution

It introduces an integrable model for impurities at the boundaries of the Hubbard chain and provides exact analytical expressions for physical quantities.

Findings

Finite size correction of ground state energy due to impurities

Explicit formulas for low temperature specific heat contributions

Kondo temperature inversely proportional to electron density

Abstract

The Kondo problem of two impurities in 1D strongly correlated electron system within the framework of the open boundary Hubbard chain is solved and the impurities, coupled to the ends of the electron system, are introduced by their scattering matrices with electrons so that the boundary matrices satisfy the reflecting integrability condition. The finite size correction of the ground state energy is obtained due to the impurities. Exact expressions for the low temperature specific heat contributed by the charge and spin parts of the magnetic impurities are derived. The Pauli susceptibility and the Kondo temperature are given explicitly. The Kondo temperature is inversely proportional to the density of electrons.