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Löwdin's symmetry dilemma within Green functions theory for the one-dimensional Hubbard model

Joost, J.-P. ; Schlünzen, N. ; Hese, S. ; Bonitz, M. ; Verdozzi, C. LU ; Schmitteckert, P. and Hopjan, M. LU (2021) In Contributions to Plasma Physics
Abstract

The energy gap of correlated Hubbard clusters is well studied for one-dimensional systems using analytical methods and density-matrix-renormalization-group (DMRG) simulations. Beyond 1D, however, exact results are available only for small systems by quantum Monte Carlo. For this reason and, due to the problems of DMRG in simulating 2D and 3D systems, alternative methods such as Green functions combined with many-body approximations (GFMBA), that do not have this restriction, are highly important. However, it has remained open whether the approximate character of GFMBA simulations prevents the computation of the Hubbard gap. Here we present new GFMBA results that demonstrate that GFMBA simulations are capable of producing reliable data... (More)

The energy gap of correlated Hubbard clusters is well studied for one-dimensional systems using analytical methods and density-matrix-renormalization-group (DMRG) simulations. Beyond 1D, however, exact results are available only for small systems by quantum Monte Carlo. For this reason and, due to the problems of DMRG in simulating 2D and 3D systems, alternative methods such as Green functions combined with many-body approximations (GFMBA), that do not have this restriction, are highly important. However, it has remained open whether the approximate character of GFMBA simulations prevents the computation of the Hubbard gap. Here we present new GFMBA results that demonstrate that GFMBA simulations are capable of producing reliable data for the gap which agrees well with the DMRG benchmarks in 1D. An interesting observation is that the accuracy of the gap can be significantly increased when the simulations give up certain symmetry restriction of the exact system, such as spin symmetry and spatial homogeneity. This is seen as manifestation and generalization of the “symmetry dilemma” introduced by Löwdin for Hartree–Fock wave function calculations.

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author
; ; ; ; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
DMRG simulations, Green functions, Hubbard model, Symmetry breaking
in
Contributions to Plasma Physics
article number
e202000220
pages
14 pages
publisher
Wiley-Blackwell
external identifiers
  • scopus:85099859498
ISSN
0863-1042
DOI
10.1002/ctpp.202000220
language
English
LU publication?
yes
id
5fe61e4f-8c9d-4d1b-8360-3751adb751a5
date added to LUP
2021-02-08 10:49:57
date last changed
2022-08-26 17:31:29
@article{5fe61e4f-8c9d-4d1b-8360-3751adb751a5,
  abstract     = {{<p>The energy gap of correlated Hubbard clusters is well studied for one-dimensional systems using analytical methods and density-matrix-renormalization-group (DMRG) simulations. Beyond 1D, however, exact results are available only for small systems by quantum Monte Carlo. For this reason and, due to the problems of DMRG in simulating 2D and 3D systems, alternative methods such as Green functions combined with many-body approximations (GFMBA), that do not have this restriction, are highly important. However, it has remained open whether the approximate character of GFMBA simulations prevents the computation of the Hubbard gap. Here we present new GFMBA results that demonstrate that GFMBA simulations are capable of producing reliable data for the gap which agrees well with the DMRG benchmarks in 1D. An interesting observation is that the accuracy of the gap can be significantly increased when the simulations give up certain symmetry restriction of the exact system, such as spin symmetry and spatial homogeneity. This is seen as manifestation and generalization of the “symmetry dilemma” introduced by Löwdin for Hartree–Fock wave function calculations.</p>}},
  author       = {{Joost, J.-P. and Schlünzen, N. and Hese, S. and Bonitz, M. and Verdozzi, C. and Schmitteckert, P. and Hopjan, M.}},
  issn         = {{0863-1042}},
  keywords     = {{DMRG simulations; Green functions; Hubbard model; Symmetry breaking}},
  language     = {{eng}},
  month        = {{01}},
  publisher    = {{Wiley-Blackwell}},
  series       = {{Contributions to Plasma Physics}},
  title        = {{Löwdin's symmetry dilemma within Green functions theory for the one-dimensional Hubbard model}},
  url          = {{http://dx.doi.org/10.1002/ctpp.202000220}},
  doi          = {{10.1002/ctpp.202000220}},
  year         = {{2021}},
}