Sea-Boson Analysis of the Infinite-U Hubbard Model

TL;DR

This paper develops a sea-boson based Hamiltonian for the infinite-U Hubbard model, accurately capturing spin, charge velocities, and quasiparticle residue in one and two dimensions, confirming previous theoretical predictions.

Contribution

It introduces a quadratic sea-boson Hamiltonian that reproduces known properties of the infinite-U Hubbard model and extends the analysis to two dimensions.

Findings

Accurate spin and charge velocities in 1D from the sea-boson Hamiltonian.

Quasiparticle residue Z_F ≈ 0.79 near half-filling in 2D.

Divergence of magnetic susceptibility near half-filling.

Abstract

By expanding the projection operator in powers of the density fluctuations, we conjecture a hamiltonian purely quadratic in the sea-bosons that reproduces the right spin and charge velocities and exponent for the $ U = \infty $ case in one dimension known from the work of Schulz. Then we argue that by simply promoting wavenumbers to wave vectors we are able to study the two dimensional case. We find that the quasiparticle residue takes a value $ Z_{F} = 0.79 $ close to half-filling where it is the smallest. This is in exact agreement with the prediction by Castro-Neto and Fradkin nearly ten years ago. We also compute the magnetic suceptibility and find that it diverges close to half-filling consistent with Nagakoka's theorem.