Strong coupling quantum impurity solver on the real and imaginary axis

Kristjan Haule

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arXiv · 2311.09412

Strong coupling quantum impurity solver on the real and imaginary axis

Kristjan Haule

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Abstract

The diagramatic Monte Carlo method has so far been primarily used in connection with the weak coupling expansion. Here we show that the strong coupling expansion offers a significant advantage: it can be efficiently implemented on both the real and the imaginary axis at finite temperature. Using the example of a quantum impurity solver for the Dynamical Mean Field Theory (DMFT) problem, we illustrate rapid convergence with respect to the expansion order. We derive a closed-form expression for the Feynman diagrams of arbitrary order on the real axis. Employing these Feynman rules, we implement the bold hybridization-expansion quantum Monte Carlo (BHQMC) impurity solver and compare its performance to state-of-the-art results from Numerical Renormalization Group calculations of the Mott transition within DMFT applied to the Hubbard model. We demonstrate its power in providing a very precise frequency dependent scattering rate at finite temperature, enabling accurate spectroscopy calculations and delivering benchmark results for transport within DMFT.

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Kristjan Haule. 2023-11-15. Strong coupling quantum impurity solver on the real and imaginary axis. https://arxiv.org/abs/2311.09412

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