Slave-Boson analysis of the 2D Hubbard model

TL;DR

This paper uses the slave-boson method to analyze the 2D Hubbard model, revealing complex magnetic phases, phase transitions, and dynamic properties across various parameters.

Contribution

It applies a spin rotation invariant slave-boson approach to map the magnetic phase diagram and analyze dynamic susceptibilities in the 2D Hubbard model, including incommensurate phases.

Findings

Identification of incommensurate magnetic phases with varying wave vectors

Discontinuous changes indicating first order phase transitions

Calculation of dynamic susceptibilities and phase diagram

Abstract

We present a comprehensive study of the 2D one-band Hubbard model applying the spin rotation invariant slave-boson method. We utilize a spiral magnetic mean field and fluctuations around a paramagnetic mean field to determine the magnetic phase diagram and find the two approaches to be in good agreement. Apart from the commensurate phases characterized by ordering wave vectors $\boldsymbol Q = (\pi, \pi), (0, \pi)$, and $(0, 0)$ we find incommensurate phases where the ordering wave vectors $\boldsymbol Q = (Q, Q)$, and $(Q, \pi)$ vary continuously with filling, interaction strength or temperature. The mean field quantities magnetization and effective mass are found to change discontinuously at the phase boundaries separating the $(Q, Q)$ and $(Q, \pi)$ phases, indicating a first order transition. The band structure and Fermi surface is shown in selected cases. The dynamic spin and charge susceptibilities as well as the structure factors are calculated and discussed, including the emergence of collective modes of the zero sound and Mott insulator type. The dynamical conductivity is calculated in dependence of doping, interaction strength and temperature. Finally, a temperature-interaction strength phase diagram is established.