Fluctuation corrections to the free energy of strongly correlated electron systems

We determine the free energy of strongly correlated electron systems in the example of the Hubbard model by calculating the contribution of spin and charge fluctuations to the Gutzwiller approximation mean-field result. We employ the slave-boson formulation of Kotliar and Ruckenstein in its spin-rotation-invariant form in the usual continuous-time approximation of the functional integral representation, corrected by “high-frequency contributions” ( SRIKR + ). In contrast to all previous attempts to calculate the fluctuation contribution to the free energy within the spin-rotation-invariant Kotliar-Ruckenstein slave-boson representation (SRIKR) scheme our result preserves the noninteracting limit. We show that the correct form of the kinetic energy renormalization is essential. The results for the ground-state energy in the paramagnetic phase are in very good agreement with state-of-the-art results obtained by methods such as density matrix embedding theory, quantum Monte Carlo, and others. The leading low-temperature behavior of the free energy allows us to extract the quasiparticle effective mass, in particular its enhancement near a continuous phase transition into an ordered state. Our work demonstrates that the SRIKR + method is competitive with the best available alternative methods and equips the slave-boson approach with an improved synoptic power to explore strongly correlated electron systems.