Wilson's ratio for strongly correlated electrons

The (Sommerfeld-)Wilson ratio is an important quantity to characterise strongly correlated Fermi liquids.

Chapter 5 of Hewson's book The Kondo Problem to Heavy Fermions describes the Fermi liquid theory of the Anderson single impurity model. One can derive the identity

which relates the impurity spin susceptibility, charge susceptibility, and the specific heat coefficient gamma.

In the Kondo regime the charge susceptibility is zero and this leads to the fact that the Wilson ratio has the universal value of exactly two.

It is interesting that one can derive the same identity for the exact (Bethe ansatz) solution to the Hubbard model in one dimension. See equation (7) in this paper by Tatsuya Usuki, Norio Kawakami, and Ayao Okiji. As a result one finds the Wilson ratio is always less than 2. As the band filling tends towards one-half the Mott insulator is approached, the charge susceptibility diverges and the Wilson ratio W tends to zero. See the Figure below.