Decomposed Functional Renormalization Group Flows for Multi-band Hamiltonians

We use a singular value decomposition to decouple the functional Renormalization group (fRG) equations in the

band basis. This decomposition enables the implementation of the channel-decomposed fRG equations to arbitrary

multi-band Hamiltonians. Truncations of the flow at the band level are based on the singular value of the vertex

in each channel and thus enable the construction of efficient fRG flows for the relevant modes of the vertex. We

study the convergence of the decomposition on two-band models of the Cuprate compounds. We focus specifically on

the orbital separation and hybridization between the d_x²-y², d_z² orbitals, with the two limiting cases

corresponding to La₂CuO₄ and Ba₂CuO_3+x compounds.  We start the study of the phases in these

systems with an interaction vertex defined by the Hubbard coupling, before looking at the impact of Hund's Rule interaction

and the nearest neighbor density-density coupling on the phase diagram. For all three interaction vertices, we consider the

dependence of the self-energy and the susceptibilities on the set of singular band modes retained in each channel.

The response of the system is rich and shows strong competition between antiferromagnetic, superconducting and

charge orders depending on the value of the orbital parameters. Finally, we apply the truncated fRG to a four-band

model of the Cuprate compounds and study the evolution of phases as functions of temperature and doping.