Application of Path Integral Methods: The Renormalization Group Approach

Shuji Watanabe, Masatoshi Imada

Yoshiki Imai, Yuichi Otsuka, Masatoshi Imada

The path-integral renormalization group method is an efficient tool for computing electronic structure of strongly correlated electron systems. Combined with the conventional density functional approaches as a hybrid scheme, it offers a first-principles method for complex materials with involved electron correlation effects. We assess the efficiency and applicability of the hybrid scheme by examining applications to Sr(2)VO(4) and YVO(3).

Masatoshi Imada

Path‐integral renormalization‐group (PIRG) method is a rapidly developing tool for computing ground state properties of interacting quantum systems on lattices, particularly models for strongly correlated electrons such as the Hubbard model. It has served in clarifying phase diagrams of the Hubbard model containing quantum spin liquid phase. PIRG has also been implemented as a low‐energy solver of the effective Hamiltonian for realistic systems. This makes it possible to construct a scheme of first‐principles calculation by the hybrid approach combined with the density functional theory.

Shinichiro Akiyama, Y. Kuramashi

We investigate the metal-insulator transition of the ($1+1$)-dimensional Hubbard model in the path-integral formalism with the tensor renormalization group method. The critical chemical potential ${\ensuremath{\mu}}_{\mathrm{c}}$ and the critical exponent $\ensuremath{\nu}$ are determined from the $\ensuremath{\mu}$ dependence of the electron density in the thermodynamic limit. Our results for ${\ensuremath{\mu}}_{\mathrm{c}}$ and $\ensuremath{\nu}$ show consistency with an exact solution based on the Bethe ansatz. Our encouraging results indicate the applicability of the tensor renormalization group method to the analysis of higher-dimensional Hubbard models.