Pseudoparticle vertex solver for quantum impurity models

Kim AJ, Li J, Eckstein M, Werner P (2022)

Publication Type: Journal article

Publication year: 2022


Book Volume: 106

Article Number: 085124

Journal Issue: 8

DOI: 10.1103/PhysRevB.106.085124


We present a quantum impurity solver based on a pseudoparticle framework, which combines diagrammatic resummations for a three-point vertex with diagrammatic Monte Carlo sampling of a four-point vertex. This recently proposed approach (A. J. Kim, arXiv:2112.15549) is generalized here to fermionic impurity problems and we discuss the technical details of the implementation, including the time-stepping approach, the Monte Carlo updates, and the routines for checking the two-particle irreducibility of the four-point vertex. We also explain how the vertex information can be efficiently stored using a Dubiner basis representation. The convergence properties of the algorithm are demonstrated with applications to exactly solvable impurity models and dynamical mean field theory simulations of the single-orbital Hubbard model. It is furthermore shown that the algorithm can handle a two-orbital problem with off-diagonal hybridizations, which would cause a severe sign problem in standard hybridization-expansion Monte Carlo simulations. Since the vertex-based algorithm successfully handles sign-oscillating integrals in equilibrium and samples only connected diagrams, it may be a promising approach for real-time simulations.

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Kim, A.J., Li, J., Eckstein, M., & Werner, P. (2022). Pseudoparticle vertex solver for quantum impurity models. Physical Review B, 106(8).


Kim, Aaram J., et al. "Pseudoparticle vertex solver for quantum impurity models." Physical Review B 106.8 (2022).

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