Efficient Hybridization Fitting for Dynamical Mean-Field Theory via Semi-Definite Relaxation*

Hamiltonian-based solvers for dynamical mean-field theory (DMFT) can compute spectral properties directly in the real axis and are applicable to impurity Hamiltonians presenting general interactions. This flexibility comes at the prize of having to truncate the formally infinite bath, transforming the DMFT self-consistent condition into a non-linear optimization problem. Fulfilling the self-consistency condition exactly with a finite bath is impossible. Furthermore, the large number of degrees of freedom in the optimization problem makes it likely to fall into local minima, which may result in the DMFT calculation converging to the wrong physical solution. As a consequence, the optimization step in Hamiltonian-based DMFT can become the most difficult part of the calculation. In this work¹, we propose a nested optimization procedure using semi-definite relaxation which addresses and improves many of the issues that plague the optimization step in Hamiltonian-based DMFT.
[1]: arXiv:1907.07191