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Dynamical exchange-correlation potential formalism for spin- 12 Heisenberg and Hubbard chains : The antiferromagnetic/half-filled case

Zhao, Zhen LU ; Verdozzi, Claudio LU and Aryasetiawan, Ferdi LU (2023) In Physical Review B 108(23).
Abstract

The exchange-correlation potential formalism previously introduced and applied to the one-dimensional Hubbard model has been extended to spin systems and applied to the case of the one-dimensional antiferromagnetic spin-12 Heisenberg model. Within the spin exchange-correlation potential formulation, a sum rule for spin systems is derived. The exchange-correlation potential for the Heisenberg model is extrapolated from exact diagonalization results of small antiferromagnetic Heisenberg clusters. This procedure is also employed to revisit and computationally improve the previous investigation of the exchange-correlation potential of the half-filled Hubbard model, which was based on the exchange-correlation potential of the dimer.... (More)

The exchange-correlation potential formalism previously introduced and applied to the one-dimensional Hubbard model has been extended to spin systems and applied to the case of the one-dimensional antiferromagnetic spin-12 Heisenberg model. Within the spin exchange-correlation potential formulation, a sum rule for spin systems is derived. The exchange-correlation potential for the Heisenberg model is extrapolated from exact diagonalization results of small antiferromagnetic Heisenberg clusters. This procedure is also employed to revisit and computationally improve the previous investigation of the exchange-correlation potential of the half-filled Hubbard model, which was based on the exchange-correlation potential of the dimer. Numerical comparisons with exact benchmark calculations for both the Heisenberg and the Hubbard models indicate that, starting from the exchange-correlation potential of a finite cluster, the extrapolation procedure yields a one-particle spectral function with favorable accuracy at a relatively low computational cost. In addition, a comparison between the ground-state energies for the one-dimensional Hubbard and Heisenberg models displays how the well-known similarity in behavior of the two models at large interactions manifests itself within the exchange-correlation potential formalism.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review B
volume
108
issue
23
article number
235132
publisher
American Physical Society
external identifiers
  • scopus:85179759069
ISSN
2469-9950
DOI
10.1103/PhysRevB.108.235132
language
English
LU publication?
yes
id
fc8e8cef-f5bd-49bc-ba56-13cd3eb768c6
date added to LUP
2024-01-03 12:26:30
date last changed
2024-01-03 12:27:58
@article{fc8e8cef-f5bd-49bc-ba56-13cd3eb768c6,
  abstract     = {{<p>The exchange-correlation potential formalism previously introduced and applied to the one-dimensional Hubbard model has been extended to spin systems and applied to the case of the one-dimensional antiferromagnetic spin-12 Heisenberg model. Within the spin exchange-correlation potential formulation, a sum rule for spin systems is derived. The exchange-correlation potential for the Heisenberg model is extrapolated from exact diagonalization results of small antiferromagnetic Heisenberg clusters. This procedure is also employed to revisit and computationally improve the previous investigation of the exchange-correlation potential of the half-filled Hubbard model, which was based on the exchange-correlation potential of the dimer. Numerical comparisons with exact benchmark calculations for both the Heisenberg and the Hubbard models indicate that, starting from the exchange-correlation potential of a finite cluster, the extrapolation procedure yields a one-particle spectral function with favorable accuracy at a relatively low computational cost. In addition, a comparison between the ground-state energies for the one-dimensional Hubbard and Heisenberg models displays how the well-known similarity in behavior of the two models at large interactions manifests itself within the exchange-correlation potential formalism.</p>}},
  author       = {{Zhao, Zhen and Verdozzi, Claudio and Aryasetiawan, Ferdi}},
  issn         = {{2469-9950}},
  language     = {{eng}},
  number       = {{23}},
  publisher    = {{American Physical Society}},
  series       = {{Physical Review B}},
  title        = {{Dynamical exchange-correlation potential formalism for spin- 12 Heisenberg and Hubbard chains : The antiferromagnetic/half-filled case}},
  url          = {{http://dx.doi.org/10.1103/PhysRevB.108.235132}},
  doi          = {{10.1103/PhysRevB.108.235132}},
  volume       = {{108}},
  year         = {{2023}},
}