Few Remarks on the Hubbard Model

Katarina Uzelac

Finite size scaling is applied to the one-dimensional Hubbard model with the half filled energy band at zero temperature. It is shown that, even for the scaling between small blocks of four, six and eight atoms, the essential singularity of the weak coupling limit is reproduced with remarkable accuracy, the error being less than 1% for the exponent and a few percent for the multiplicative constant. The results are discussed in comparison with the quantum renormalisation group approach, which fails to give the right exponent, and the advantages of the present method are pointed out.

Gang Su

Cary Mcilwaine Maguire

Guan-Hua Huang, Zhigang Wu

Recently, a quantum simulator for the two-dimensional Fermi-Hubbard model on an anisotropic triangular lattice has been realized, where both geometrical frustration and doping can be continuously tuned. Here, we provide a comprehensive comparison between the magnetic correlations calculated by the two-particle self-consistent (TPSC) theory and those measured in this quantum simulator, at temperatures comparable to the spin-exchange energy and Hubbard interactions comparable to the bandwidth. We find overall excellent agreements between the TPSC calculations and the measurements from the quantum simulator at all levels of frustration and doping. This is quite remarkable considering that the Hubbard model is already in the intermediate- to strong-coupling regime, for which very few methods yield reliable results. Our work showcases the potential of TPSC as a theoretical approach capable of providing reasonably accurate descriptions of the Hubbard model even at fairly strong interactions and when the frustration is present.

Huan-Qiang Zhou, Lin-Jie Jiang, Jian-Gang Tang

Ambiguities in the Lax pairs for a one-dimensional small-polaron model and the one-dimensional Hubbard model are discussed.

Élliott H. Lieb