The European Physical Journal Special Topics

, Volume 226, Issue 11, pp 2549–2564 | Cite as

Exact diagonalization as an impurity solver in dynamical mean field theory

  • Yi Lu
  • Maurits W. Haverkort
Open Access
Regular Article
Part of the following topical collections:
  1. Dynamical Mean-Field Approach with Predictive Power for Strongly Correlated Materials


The dynamical mean-field theory (DMFT) maps a correlated lattice problem onto an impurity problem of a single correlated site coupled to an uncorrelated bath. Most implementations solve the DMFT equations using quantum Monte-Carlo sampling on the imaginary time and frequency (Matsubara) axis. We will here review alternative methods using exact diagonalization, i.e., representing the many-body ground state of the impurity as a sum over Slater determinants and calculating Green’s functions using iterative Lanczos procedures. The advantage being that these methods have no sign problem, can handle involved multi-orbital Hamiltonians (low crystal symmetry, spin-orbit coupling) and – when working completely on the real axis – do not need a mathematically ill-posed analytical continuation. The disadvantage of traditional implementations of exact diagonalization has been the exponential scaling of the calculation problem as a function of number of bath discretization points. In the last part we will review how recent advances in exact diagonalization can evade the exponential barrier thereby increasing the number of bath discretization points to reach the thermodynamic limit.


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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.Max-Planck-Institute for Solid State ResearchStuttgartGermany
  2. 2.Max-Planck-Institute for Chemical Physics of SolidsDresdenGermany
  3. 3.Institute for theoretical physics, Heidelberg UniversityHeidelbergGermany

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