Optimizing Bath Fitting in Dynamical Mean-Field Theory Using Machine Learning

Taeung Kim, Jeongmoo Lee, Ara Go

Louis-François Arsenault, Alejandro López‐Bezanilla, O. Anatole von Lilienfeld +2 more

Carlos Mejuto-Zaera, Leonardo Zepeda-Núñez, Michael Lindsey +3 more

We introduce a nested optimization procedure using semidefinite relaxation for the fitting step in Hamiltonian-based cluster dynamical mean-field theory methodologies. We show that the proposed method is more efficient and flexible than state-of-the-art fitting schemes, which allows us to treat as large a number of bath sites as the impurity solver at hand allows. We characterize its robustness to initial conditions and symmetry constraints, thus providing conclusive evidence that in the presence of a large bath our semidefinite relaxation approach can find the correct set of bath parameters without needing to include a priori knowledge of the properties that are to be described. We believe this method will be of great use for Hamiltonian-based calculations, simplifying and improving one of the key steps in cluster dynamical mean-field theory calculations.

Taegeun Song, Roser Valentí, Hunpyo Lee

We develop a novel analytic continuation method for self-energies on the Matsubara domain as computed by quantum Monte Carlo simulations within dynamical mean field theory (QMC+DMFT). Unlike a maximum entropy (maxEn) procedure employed for the last thirty years, our approach is based on a machine learning (ML) technique in combination with the iterative perturbative theory impurity solver of the dynamical mean field theory self-consistent process (IPT+DMFT). The input and output training datasets for ML are simultaneously obtained from IPT+DMFT calculations on Matsubara and real frequency domains, respectively. The QMC+DMFT self-energy on real frequencies is determined from the -- usually noisy -- input QMC+DMFT self-energy on the Matsubara domain and the trained ML kernel. Our approach is free from both, bias of ML training datasets and from fitting parameters present in the maxEn method. We demonstrate the efficiency of the method on the testbed frustrated Hubbard model on the square lattice.

Roger G. Melko

Erik Koch, Giorgio Sangiovanni, O. Gunnarsson

We analyze cellular dynamical mean-field theory (CDMFT) and the dynamical cluster approximation (DCA). We derive exact sum-rules for the hybridization functions and give examples for dynamical mean-field theory, CDMFT, and DCA. For impurity solvers based on a Hamiltonian, these sum rules can be used to monitor convergence of the bath-parametrization. We further discuss how the symmetry of the cluster naturally leads to a decomposition of the bath Green matrix into irreducible components, which can be parametrized independently, and give an explicit recipe for finding the optimal bath parametrization. As a benchmark we revisit the one-dimensional Hubbard model. We carefully analyze the evolution of the density as a function of chemical potential and find that, close to the Mott transition, convergence with cluster size is unexpectedly slow. Going from one to two dimensions we find that fitting the bath becomes in general significantly more difficult, requiring a large number of bath sites. For such large baths our symmetry-adapted approach should prove crucial for finding a reliable bath-parametrization.