Ground States of Heisenberg Spin Clusters from a Cluster-Based Projected Hartree–Fock Approach

Tabrizi, Shadan Ghassemi; Jiménez-Hoyos, Carlos A.

doi:10.3390/condmat8010018

Cited by 5 publications

(2 citation statements)

References 49 publications

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“…When those correlations are strong, however, the HF treatment is inadequate. Cluster mean-field (cMF − ) theory generalizes this basic idea but provides a more nuanced and flexible framework. It also uses a wave function which is correct for non-interacting constituents, but where in HF these constituents are the individual electrons, cMF uses multielectronic fragments.…”

Section: Introductionmentioning

confidence: 99%

Linear Combinations of Cluster Mean-Field States Applied to Spin Systems

Papastathopoulos-Katsaros,

Henderson,

Scuseria

2024

J. Chem. Theory Comput.

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We present an innovative cluster-based method employing linear combinations of diverse cluster mean-field states and apply it to describe the ground state of strongly correlated spin systems. In cluster mean-field theory, the ground state wave function is expressed as a factorized tensor product of optimized cluster states. While our prior work concentrated on a single cMF tiling, this study removes that constraint by combining different tilings of cMF states. Selection criteria, including translational symmetry and spatial proximity, guide this process. We present benchmark calculations for the one-and two-dimensional J 1 − J 2 and XXZ Heisenberg models. Our findings highlight two key aspects. First, the method offers a semiquantitative description of the 0.4 ≲ J 2 /J 1 ≲ 0.6 regime of the J 1 − J 2 model�a particularly challenging regime for existing methods. Second, our results demonstrate the capability of our method to provide qualitative descriptions for all the models and regimes considered, establishing it as a valuable reference. However, the inclusion of additional (weak) correlations is necessary for quantitative agreement, and we explore methods to incorporate these extra correlations.

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Section: Introductionmentioning

confidence: 99%

Linear Combinations of Cluster Mean-Field States Applied to Spin Systems

Papastathopoulos-Katsaros,

Henderson,

Scuseria

2024

J. Chem. Theory Comput.

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show abstract

“…When those correlations are strong, however, the HF treatment is inadequate. Cluster meanfield (cMF [1][2][3][4][5][6][7][8][9] ) theory generalizes this basic idea but provides a more nuanced and flexible framework. It also uses a wave function which is correct for non-interacting constituents, but where in HF these constituents are the individual electrons, cMF uses multi-electronic fragments.…”

Section: Introductionmentioning

confidence: 99%

Coupled Cluster and Perturbation Theories Based on a Cluster Mean-Field Reference Applied to Strongly Correlated Spin Systems

Papastathopoulos-Katsaros

Hoyos

Henderson

et al. 2022

J. Chem. Theory Comput.

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We introduce perturbation and coupled-cluster theories based on a cluster mean-field reference for describing the ground state of strongly correlated spin systems. In cluster mean-field, the ground state wave function is written as a simple tensor product of optimized cluster states. The cluster language and the mean-field nature of the ansatz allow for a straightforward improvement which uses perturbation theory and coupled-cluster to account for intercluster correlations. We present benchmark calculations on the 1D chain and 2D square J 1–J 2 Heisenberg model, using cluster mean-field, perturbation theory, and coupled-cluster. We also present an extrapolation scheme that allows us to compute thermodynamic limit energies accurately. Our results indicate that, with sufficiently large clusters, the correlated methods (cPT2, cPT4, and cCCSD) can provide a relatively accurate description of the Heisenberg model in the regimes considered, which suggests that the methods presented can be used for other strongly correlated systems. Some ways to improve upon the methods presented in this work are discussed.

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Symmetry-projected cluster mean-field theory applied to spin systems

Papastathopoulos-Katsaros,

Henderson,

Scuseria

2023

The Journal of Chemical Physics

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We introduce Sz spin-projection based on cluster mean-field theory and apply it to the ground state of strongly correlated spin systems. In cluster mean-fields, the ground state wavefunction is written as a factorized tensor product of optimized cluster states. In previous work, we have focused on unrestricted cluster mean-field, where each cluster is Sz symmetry adapted. We here remove this restriction by introducing a generalized cluster mean-field (GcMF) theory, where each cluster is allowed to access all Sz sectors, breaking Sz symmetry. In addition, a projection scheme is used to restore global Sz, which gives rise to the Sz spin-projected generalized cluster mean-field (SzGcMF). Both of these extensions contribute to accounting for inter-cluster correlations. We benchmark these methods on the 1D, quasi-2D, and 2D J1 − J2 and XXZ Heisenberg models. Our results indicate that the new methods (GcMF and SzGcMF) provide a qualitative and semi-quantitative description of the Heisenberg lattices in the regimes considered, suggesting them as useful references for further inter-cluster correlations, which are discussed in this work.

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Ground States of Heisenberg Spin Clusters from a Cluster-Based Projected Hartree–Fock Approach

Cited by 5 publications

References 49 publications

Linear Combinations of Cluster Mean-Field States Applied to Spin Systems

Linear Combinations of Cluster Mean-Field States Applied to Spin Systems

Coupled Cluster and Perturbation Theories Based on a Cluster Mean-Field Reference Applied to Strongly Correlated Spin Systems

Symmetry-projected cluster mean-field theory applied to spin systems

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