A precise single particle density matrix functional for multi-orbital Mott physics via VDAT

The recently developed variational discrete action theory (VDAT) provides a systematic variational approach to the many-body problem, where the quality of the solution is regulated by an integer N, and increasing N monotonically approaches the exact solution. VDAT can be exactly evaluated in the d=∞ multi-orbital Hubbard model using the self-consistent canonical discrete action theory (SCDA), which requires a self-consistency condition of the integer time Green's functions. Previous work demonstrates that N=3 quantitatively captures multi-orbital Mott/Hund physics at a cost similar to the Gutzwiller approximation. Here we provide an analytic procedure to automatically satisfy the self-consistency condition of the SCDA at N=3, yielding an even more efficient algorithm with enhanced numerical stability. This analytic procedure provides a natural way to construct a single particle density matrix functional which captures Mott/Hund physics, and closed-form expressions are derived for the single band model at half filling. We present results and performance analysis for the five orbital Hubbard model in d=∞. The developments in this work will be important to applying VDAT at N=3 in strongly correlated electron materials.