Spin susceptibility and magnetic short-range order in the Hubbard model

TL;DR

This paper develops a theoretical approach to calculate the spin susceptibility in the Hubbard model, revealing a doping-dependent transition in magnetic short-range order that aligns with experimental observations in cuprates.

Contribution

The authors extend the slave-boson functional-integral approach to include magnetic short-range order via an effective Ising model, providing a new method to analyze spin susceptibility in the Hubbard model.

Findings

Identifies a transition from no SRO to antiferromagnetic SRO at specific doping levels.

Shows susceptibility increases with doping and exhibits a cusp at the transition point.

Results agree with experimental data on LSCO, with a maximum susceptibility near 25 ext% doping.

Abstract

The uniform static spin susceptibility in the paraphase of the one-band Hubbard model is calculated within a theory of magnetic short--range order (SRO) which extends the four-field slave-boson functional-integral approach by the trans- formation to an effective Ising model and the self-consistent incorporation of SRO at the saddle point. This theory describes a transition from the paraphase without SRO for hole dopings $\delta > \delta_{c_2}$ to a paraphase with anti- ferromagnetic SRO for $\delta_{c_1} < \delta < \delta_{c_2}$. In this region the susceptibility consists of interrelated `itinerant' and `local' parts and increases upon doping. The zero--temperature susceptibility exhibits a cusp at $\delta_{c_2}$ and reduces to the usual slave-boson result for larger dopings. Using the realistic value of the on--site Coulomb repulsion $U=8t$ for LSCO, the peak position ($\delta_{c_2} = 0.26$) as well as the doping dependence reasonably agree with low--temperature susceptibility experiments showing a maximum at a hole doping of about 25\%.