The European Physical Journal Special Topics

, Volume 226, Issue 11, pp 2499–2523 | Cite as

Quantum Monte Carlo impurity solvers for multi-orbital problems and frequency-dependent interactions

  • H. Shinaoka
  • F. Assaad
  • N. Blümer
  • P. Werner
Open Access
Part of the following topical collections:
  1. Dynamical Mean-Field Approach with Predictive Power for Strongly Correlated Materials


The solution of an auxiliary quantum impurity system is the computationally expensive step in dynamical mean field theory simulations of lattice models and materials. In this review, we discuss Monte Carlo based impurity solvers, which are suitable for a wide range of applications. In particular, we present an efficient implementation of the hybridization expansion approach, which enables the simulation of multiorbital impurity problems with off-diagonal and complex hybridizations, and dynamically screened (retarded) density-density interactions. As a complementary approach, we discuss an impurity solver based on the determinant Monte Carlo method, which scales favorably with inverse temperature and hence provides access to the very low temperature regime. The usefulness of these state-of-the-art impurity solvers is demonstrated with applications to the downfolding problem, i.e., the systematic derivation of dynamically screened interactions for low-energy effective models, and to pyrochlore iridates, where the spin-orbit coupling leads to complex hybridization functions in a multi-orbital system. As a benchmark for cluster extensions of dynamical mean field theory, we also present results from lattice Monte Carlo simulations for the momentum dependence of the pseudo-gap in the half-filled two-dimensional Hubbard model.


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© The Author(s) 2017

Open Access This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Department of PhysicsSaitama UniversitySaitamaJapan
  2. 2.Institut für Theoretische Physik und Astrophysik, Universität WürzburgWürzburgGermany
  3. 3.Katholische Universität Eichstätt-Ingolstadt Ostenstr. 24EichstättGermany
  4. 4.Department of PhysicsUniversity of FribourgFribourgSwitzerland

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