Dual Boson Diagrammatic Monte Carlo Approach Applied to the Extended Hubbard Model

Physical Review B (submitted), (2020)

Dual Boson Diagrammatic Monte Carlo Approach Applied to the Extended Hubbard Model

M. Vandelli, V. Harkov, E. A. Stepanov, J. Gukelberger, E. Kozik, A. Rubio, A. I. Lichtenstein

In this work we introduce the Dual Boson Diagrammatic Monte Carlo technique for strongly interacting electronic systems. This method combines the strength of dynamical mean-filed theory for non-perturbative description of local correlations with the systematic account of non-local corrections in the Dual Boson theory by the diagrammatic Monte Carlo approach. It allows us to get a numerically exact solution of the dual boson theory at the two-particle local vertex level for the extended Hubbard model. We show that it can be eciently applied to description of single particle observables in a wide range of interaction strengths. We compare our exact results for the self-energy with the ladder Dual Boson approach and determine a physical regime, where description of collective electronic e ects requires more accurate consideration beyond the ladder approximation. Additionally, we find that the order-by-order analysis of the perturbative diagrammatic series for the single-particle Green’s function allows to estimate the transition point to the charge density wave phase.

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Preprint - 6.5 MB
We acknowledge financial support from the European Research Council (ERC-2015-AdG-694097) and the Cluster of Excellence Advanced Imaging of Matter (AIM) EXC 2056 - 390715994. Additional support by the Max Planck Institute, the Simons Foundation and the North-German Supercomputing Alliance (HLRN) under the Project No. hhp00042 is also acknowledged.

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