Helicity Modulus and Effective Hopping in the Two-Dimensional Hubbard Model Using Slave-Boson Methods

TL;DR

This paper employs slave-boson mean-field methods to analyze the phase diagram and magnetic properties of the two-dimensional Hubbard model, revealing significant differences from Hartree-Fock approximation and aligning well with Monte Carlo results.

Contribution

It introduces a spin-rotation invariant slave-boson approach to compute the helicity modulus and effective hopping, improving upon Hartree-Fock results especially off half-filling.

Findings

Magnetic phase regions are reduced compared to HFA.

Helicity modulus at half-filling matches Monte Carlo calculations.

Off half-filling, slave-boson results outperform HFA.

Abstract

The slave-boson mean-field method is used to study the two-dimensional Hubbard model. A magnetic phase diagram allowing for paramagnetism, weak- and strong ferromagnetism and antiferromagnetism, including all continuous and first-order transitions, is constructed and compared to the corresponding phase diagram using the Hartree-Fock approximation (HFA). Magnetically ordered regions are reduced by a factor of about 3 along both the $t/U$ and density axes compared to the HFA. Using the spin-rotation invariant formulation of the slave-boson method the helicity modulus is computed and for half-filling is found to practically coincide with that found using variational Monte Carlo calculations using the Gutzwiller wave function. Off half-filling the results can be used to compare with Quantum Monte Carlo calculations of the effective hopping parameter. Contrary to the case of half-filling, the slave-boson approach is seen to greatly improve the results of the HFA when off half-filling. (Submitted to: Journal of Physics: Condensed Matter)