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arXiv:2311.09412

Strong Coupling Quantum Impurity Solver on the Real and Imaginary Axes

Yueyi Wang, Kristjan Haule

Published Nov 15, 2023• 1 citation
arXivHTMLPDF

Abstract

The diagrammatic Monte Carlo method has so far been used mainly for weak-coupling expansions. Here we show that the strong-coupling expansion offers a key advantage: it can be implemented efficiently on both the real and imaginary frequency axes at finite temperature. Using a quantum-impurity solver for dynamical mean-field theory (DMFT) as an example, we find rapid convergence with expansion order. We derive closed-form real-axis Feynman rules for diagrams of arbitrary order, and implement them in a bold hybridization-expansion quantum Monte Carlo (BHQMC) impurity solver. Benchmarking against state-of-the-art numerical renormalization group (NRG) results for the DMFT Mott transition of the Hubbard model, we obtain a highly accurate frequency-dependent scattering rate at finite temperature. This enables reliable spectroscopy and provides benchmark transport results within DMFT and cluster-DMFT.

DOI
10.48550/arxiv.2311.09412

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We show how to use diagrammatic techniques to compute the weak-coupling perturbation series of the self-consistent solution to a dynamical mean field theory (DMFT) problem. This approach constitutes an alternative to using diagrammatic techniques directly as an impurity solver. It allows one to bypass the need of multiple perturbative series resummations within the DMFT self-consistency loop. It can be applied at or out of equilibrium, with any diagrammatic formalism, such as real times, imaginary times, or Matsubara frequencies formalisms. As a proof of principle, we illustrate our method with the half-filled Hubbard model on the Bethe lattice in the DMFT approximation, using quantum quasi Monte Carlo (QQMC) to obtain the impurity perturbation series on the real time axis.
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