Qubit parametrization of the variational discrete action theory at N =3 for the multi-orbital Hubbard model

The variational discrete action theory (VDAT) at N =3 is a potent tool for accurately capturing Mott and Hund physics at zero temperature in d= ∞ at a cost comparable to the Gutzwiller approximation, which is recovered by VDAT at N =2 . Here we develop an exact reparameterization of the gauge constrained algorithm of VDAT at N =3 for the multi-orbital Hubbard model with general density-density interactions in d= ∞ , yielding an explicit variational trial energy. The variational parameters consist of the momentum density distribution, the shape of the fermi sea, and the pure state of a qubit system with a dimension of the local Hilbert space, and are restricted by two constraints per spin orbital. We refer to this development as the qubit parameterization. Restricting the variational parameters for N =3 recovers the qubit trial energy for N =2 , which is equivalent to the slave spin mean-field theory. A key feature of the N =3 qubit trial energy is that the momentum density distribution can be analytically optimized, greatly simplifying the minimization of the trial energy. To illustrate the power of the qubit parameterization, we demonstrate how the Hund's coupling affects the nature of the metal-insulator transition in the two orbital Hubbard model. Additionally, we provide an analytical solution for the ground state properties of the single band Hubbard model with a special density of states.