We present a comprehensive study of the two-dimensional 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 $\mathbf{Q}=(\pi ,\pi )$, $(0,\pi )$, and (0,0) we find incommensurate phases where the ordering wave vectors $\mathbf{Q}=(Q,Q)$ 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.

• Received 10 January 2020
• Revised 10 March 2020
• Accepted 15 April 2020

DOI:https://doi.org/10.1103/PhysRevB.101.235137