(Spin-)density-functional theory for open-shell systems: Exact magnetization density functional for the half-filled Hubbard trimer

Ullrich, Carsten A.

doi:10.1103/PhysRevA.100.012516

Title: (Spin-)density-functional theory for open-shell systems: Exact magnetization density functional for the half-filled Hubbard trimer

Abstract

Based on the Hohenberg-Kohn theorem of density-functional theory (DFT), all observable quantities of systems of interacting electrons can be expressed as functionals of the ground-state density. This includes, in principle, the spin polarization (magnetization) of open-shell systems; the explicit form of the magnetization as a functional of the total density is, yet, unknown. In practice, open-shell systems are always treated with spin-DFT, where the basic variables are the spin densities. In this work, the relation between DFT and spin-DFT for open-shell systems is illustrated and the exact magnetization density functional is obtained for the half-filled Hubbard trimer. Errors arising from spin-restricted and -unrestricted exact-exchange Kohn-Sham calculations are analyzed and partially cured via the exact magnetization functional.

Authors:

Ullrich, Carsten A. ^[1]

Univ. of Missouri, Columbia, MO (United States)

Publication Date:: Thu Jul 25 00:00:00 EDT 2019

Research Org.:: Univ. of Missouri, Columbia, MO (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1545508

Alternate Identifier(s):: OSTI ID: 1545424

Grant/Contract Number:: SC0019109

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review A

Additional Journal Information:: Journal Volume: 100; Journal Issue: 1; Journal ID: ISSN 2469-9926

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 74 ATOMIC AND MOLECULAR PHYSICS; Density-functional theory; noncollinear magnetism; Hubbard model

Citation Formats


                    Ullrich, Carsten A. (Spin-)density-functional theory for open-shell systems: Exact magnetization density functional for the half-filled Hubbard trimer.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevA.100.012516.

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                    Ullrich, Carsten A. (Spin-)density-functional theory for open-shell systems: Exact magnetization density functional for the half-filled Hubbard trimer.  United States.  https://doi.org/10.1103/PhysRevA.100.012516

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                    Ullrich, Carsten A. Thu .  
"(Spin-)density-functional theory for open-shell systems: Exact magnetization density functional for the half-filled Hubbard trimer".  United States.  https://doi.org/10.1103/PhysRevA.100.012516.  https://www.osti.gov/servlets/purl/1545508.

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@article{osti_1545508,

  title        = {(Spin-)density-functional theory for open-shell systems: Exact magnetization density functional for the half-filled Hubbard trimer},

  author       = {Ullrich, Carsten A.},

  abstractNote = {Based on the Hohenberg-Kohn theorem of density-functional theory (DFT), all observable quantities of systems of interacting electrons can be expressed as functionals of the ground-state density. This includes, in principle, the spin polarization (magnetization) of open-shell systems; the explicit form of the magnetization as a functional of the total density is, yet, unknown. In practice, open-shell systems are always treated with spin-DFT, where the basic variables are the spin densities. In this work, the relation between DFT and spin-DFT for open-shell systems is illustrated and the exact magnetization density functional is obtained for the half-filled Hubbard trimer. Errors arising from spin-restricted and -unrestricted exact-exchange Kohn-Sham calculations are analyzed and partially cured via the exact magnetization functional.},

  doi          = {10.1103/PhysRevA.100.012516},

  journal      = {Physical Review A},

  number       = 1,

  volume       = 100,

  place        = {United States},

  year         = {Thu Jul 25 00:00:00 EDT 2019},

  month        = {Thu Jul 25 00:00:00 EDT 2019}

}

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https://doi.org/10.1103/PhysRevA.100.012516

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Cited by: 4 works

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Figures / Tables:

FIG. 1: Total ground-state energies of the linear and triangular asymmetric half-filled Hubbard trimer with V₁ = 1, V₂ = 0, and V₃ = 2, comparing exact results with XX and XXr Kohn-Sham calculations.

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Works referencing / citing this record:

Exchange-correlation magnetic fields in spin-density-functional theory
journal, September 2019

Pluhar, Edward A.; Ullrich, Carsten A.
Physical Review B, Vol. 100, Issue 12
DOI: 10.1103/physrevb.100.125135

Exchange-correlation magnetic fields in spin-density-functional theory
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DOI: 10.48550/arxiv.1907.08724

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Title: (Spin-)density-functional theory for open-shell systems: Exact magnetization density functional for the half-filled Hubbard trimer

Abstract

Citation Formats

Figures / Tables:

Density Functional Theory book, January 2011

A local exchange-correlation potential for the spin polarized case. i journal, July 1972

Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism journal, May 1976

Potential in spin-density-functional theory of noncollinear magnetism determined by the many-electron ground state journal, April 2007

Spin in density-functional theory journal, August 2012

Challenges for Density Functional Theory journal, December 2011

Perspective: Fifty years of density-functional theory in chemical physics journal, May 2014

Inhomogeneous Electron Gas journal, November 1964

Self-Consistent Equations Including Exchange and Correlation Effects journal, November 1965

Some Fundamental Issues in Ground-State Density Functional Theory: A Guide for the Perplexed journal, March 2009

Spin-current density-functional theory for a correct treatment of spin-orbit interactions and its application to topological phase transitions journal, November 2018

Density functionals and model Hamiltonians: Pillars of many-particle physics journal, July 2013

Density-functional theory for systems with noncollinear spin: Orbital-dependent exchange-correlation functionals and their application to the Hubbard dimer journal, July 2018

Density-functional study of the Mott gap in the Hubbard model journal, November 2002

Simple parameterization for the ground-state energy of the infinite Hubbard chain incorporating Mott physics, spin-dependent phenomena and spatial inhomogeneity journal, July 2012

The Hubbard dimer: a density functional case study of a many-body problem journal, September 2015

Corrigendum: The Hubbard dimer: a density functional case study of a many-body problem (2015 J. Phys.: Condens. Matter 27 393001) journal, November 2016

Linear response time-dependent density functional theory of the Hubbard dimer journal, July 2018

Testing density-functional approximations on a lattice and the applicability of the related Hohenberg-Kohn-like theorem journal, January 2018

Melting a Hubbard dimer: benchmarks of ‘ALDA’ for quantum thermodynamics journal, October 2018

Thermodynamic Properties of the One-Dimensional Half-Filled-Band Hubbard Model journal, March 1972

Spin electric effects in molecular antiferromagnets journal, July 2010

Hubbard Trimer with Spin–Orbit Coupling: Hartree–Fock Solutions, (Non)Collinearity, and Anisotropic Spin Hamiltonian journal, February 2019

DFT Calculations on the Spin-Crossover Complex Fe(salen)(NO): A Quest for the Best Functional journal, November 2007

Can DFT Accurately Predict Spin Densities? Analysis of Discrepancies in Iron Nitrosyl Complexes journal, August 2011

Benchmarks and Reliable DFT Results for Spin Gaps of Small Ligand Fe(II) Complexes journal, March 2018

Quantifying Density Errors in DFT journal, October 2018

Finding Density Functionals with Machine Learning journal, June 2012

Inhomogeneous Electron Gas journal, March 1973

Understanding and reducing errors in density functional calculations text, January 2012

The Hubbard Dimer: A density functional case study of a many-body problem text, January 2015

Landscape of an exact energy functional text, January 2015

Density-functional theory for systems with noncollinear spin: orbital-dependent exchange-correlation functionals and their application to the Hubbard dimer text, January 2018

Quantifying Density Errors in DFT text, January 2018

Exchange-correlation magnetic fields in spin-density-functional theory journal, September 2019

Exchange-correlation magnetic fields in spin-density-functional theory text, January 2019

Density Functional Theory
book, January 2011

A local exchange-correlation potential for the spin polarized case. i
journal, July 1972

Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism
journal, May 1976

Potential in spin-density-functional theory of noncollinear magnetism determined by the many-electron ground state
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Spin in density-functional theory
journal, August 2012

Challenges for Density Functional Theory
journal, December 2011

Perspective: Fifty years of density-functional theory in chemical physics
journal, May 2014

Inhomogeneous Electron Gas
journal, November 1964

Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965

Some Fundamental Issues in Ground-State Density Functional Theory: A Guide for the Perplexed
journal, March 2009

Spin-current density-functional theory for a correct treatment of spin-orbit interactions and its application to topological phase transitions
journal, November 2018

Density functionals and model Hamiltonians: Pillars of many-particle physics
journal, July 2013

Density-functional theory for systems with noncollinear spin: Orbital-dependent exchange-correlation functionals and their application to the Hubbard dimer
journal, July 2018

Density-functional study of the Mott gap in the Hubbard model
journal, November 2002

Simple parameterization for the ground-state energy of the infinite Hubbard chain incorporating Mott physics, spin-dependent phenomena and spatial inhomogeneity
journal, July 2012

The Hubbard dimer: a density functional case study of a many-body problem
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Corrigendum: The Hubbard dimer: a density functional case study of a many-body problem (2015 J. Phys.: Condens. Matter 27 393001)
journal, November 2016

Linear response time-dependent density functional theory of the Hubbard dimer
journal, July 2018

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journal, January 2018

Melting a Hubbard dimer: benchmarks of ‘ALDA’ for quantum thermodynamics
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Thermodynamic Properties of the One-Dimensional Half-Filled-Band Hubbard Model
journal, March 1972

Spin electric effects in molecular antiferromagnets
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Hubbard Trimer with Spin–Orbit Coupling: Hartree–Fock Solutions, (Non)Collinearity, and Anisotropic Spin Hamiltonian
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DFT Calculations on the Spin-Crossover Complex Fe(salen)(NO): A Quest for the Best Functional
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Can DFT Accurately Predict Spin Densities? Analysis of Discrepancies in Iron Nitrosyl Complexes
journal, August 2011

Benchmarks and Reliable DFT Results for Spin Gaps of Small Ligand Fe(II) Complexes
journal, March 2018

Quantifying Density Errors in DFT
journal, October 2018

Finding Density Functionals with Machine Learning
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Inhomogeneous Electron Gas
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Understanding and reducing errors in density functional calculations
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The Hubbard Dimer: A density functional case study of a many-body problem
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Landscape of an exact energy functional
text, January 2015

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