Dynamical $t/U$ Expansion of the Doped Hubbard Model

TL;DR

This paper develops a new theoretical framework using a $U(1)$ slave spin representation and a dynamical $t/U$ expansion to analyze the doped Hubbard model, capturing key phenomena like spin-charge separation and Nagaoka ferromagnetism.

Contribution

It introduces a novel $U(1)$ slave spin approach and a dynamical $t/U$ expansion that effectively describe low-energy physics and emergent ferromagnetic interactions in the doped Hubbard model.

Findings

Reproduces mean-field results at lowest order of expansion.

Derives an effective $t-J$ model with self-consistent spinon and slave spin coupling.

Identifies a persistent ferromagnetic exchange channel in the infinite $U$ limit.

Abstract

We construct a new $U(1)$ slave spin representation for the single band Hubbard model in the large-$U$ limit. The mean-field theory in this representation is more amenable to describe both the spin-charge-separation physics of the Mott insulator at half-filling and the strange metal behavior at finite doping. By employing a dynamical Green's function theory for slave spins, we calculate the single-particle spectral function of electrons, and the result is comparable to that in dynamical mean field theories. We then formulate a dynamical $t/U$ expansion for the doped Hubbard model that reproduces the mean-field results at the lowest order of expansion. To the next order of expansion, it naturally yields an effective low-energy theory of a $t-J$ model for spinons self-consistently coupled to n $XXZ$ model for the slave spins. We show that the superexchange $J$ is renormalized by doping, in agreement with the Gutzwiller approximation. Surprisingly, we find a new ferromagnetic channel of exchange interactions which survives in the infinite $U$ limit, as a manifestation of the Nagaoka ferromagnetism.