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  Exact diagonalization as an impurity solver in dynamical mean field theory

Lu, Y., & Haverkort, M. W. (2017). Exact diagonalization as an impurity solver in dynamical mean field theory. European Physical Journal - Special Topics, 226(11), 2549-2564. doi:10.1140/epjst/e2017-70042-4.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002D-AF10-F Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002D-AF12-B
Genre: Journal Article

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 Creators:
Lu, Yi1, Author
Haverkort, Maurits W.2, Author              
Affiliations:
1External Organizations, ou_persistent22              
2Maurits Haverkort, Physics of Correlated Matter, Max Planck Institute for Chemical Physics of Solids, Max Planck Society, ou_1863455              

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 Abstract: 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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Language(s): eng - English
 Dates: 2017-07-102017-07-10
 Publication Status: Published in print
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Title: European Physical Journal - Special Topics
  Abbreviation : Eur. Phys. J. Spec. Top.
Source Genre: Journal
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Publ. Info: Berlin, Heidelberg : Springer
Pages: - Volume / Issue: 226 (11) Sequence Number: - Start / End Page: 2549 - 2564 Identifier: ISSN: 1951-6355
CoNE: /journals/resource/1000000000277330