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ds2-5-body-link" href="https://www.academia.edu/19177912/Extended_coupled_cluster_treatment_of_correlations_in_quantum_magnets">Extended coupled-cluster treatment of correlations in quantum magnets</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="39389182" href="https://independent.academia.edu/NorbertLigterink">Norbert Ligterink</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="5859577" href="https://independent.academia.edu/RaymondBishop">Raymond Bishop</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review B, 1999</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Extended coupled-cluster treatment of correlations in quantum 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href="https://www.academia.edu/30380885/MAGNETIC_COUPLINGS_IN_THE_HUBBARD_MODEL">MAGNETIC COUPLINGS IN THE HUBBARD MODEL</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="3580807" href="https://duth.academia.edu/PavlosMihas">Pavlos Mihas</a></div><p class="ds-related-work--abstract ds2-5-body-sm">The half-filled Hubbard model can be analyzed in terms of quasi-electron and spin wave excitations; the latter are described by í µí°» í µí°» = − 1 2 ∑ í µí°½ í µí±í µí± í µí°» í µí½ í µí² í µí½ í µí² í µí±í µí± The quantities J mn were calculated and the resulting thermodynamic quantities in the one-dimensional (1D) case are in very good agreement with exact results. We outline here our approximate treatment of the Hubbard [1] hamiltonian, í µí°» ̂ = ∑ ∈ 0 í µí± ̂ í µí±í µí¼ í µí±í µí¼ + ∑ í µí± í µí±í µí±í µí¼ í µí±í µí±í µí¼ í µí»¼ í µí±í µí¼ + í µí± í µí±í µí¼ + í µí± ∑ í µí± ̂ í µí±↑ í µí± ̂ í µí°½↓ í µí± and we summarize our results. For simplicity we take V jjΣ equal to a constant V when the lattice sites i,j are nearest neighbors and zero otherwise. The unperturbed (U= 0) half bandwidth B is proportional to V; e.g. when the site {i} forms a simple cubic lattice B = 6V. In the binary, self-consistent, static approximation (see, e.g., Cyrot's [2] work) one replaces the term í µí±í µí± ̂ í µí±↑ í µí± ̂ í µí± ↓ by í µí± í µí±í µí¼ í µí± ̂ í µí±í µí¼ ; e iς is a random variable which takes the values U(n-μ)/2 and U(n + μ)/2 each with probability 1 2 ;n is the average number of electrons per site and μ is a quantity to be determined self-consistently by the condition í µí¼ = ⟨í µí± ̅ í µí±↑ ⟩ í µí±= í µí±¢ − ⟨ í µí± ̅ í µí± ↓ ⟩ í µí± =í µí±¢ where the bar indicates quantum mechanical average and ⟨ ⟩ í µí±= í µí±¢ denotes configurational average under the condition thatí µí± í µí±↑ = U(n — μ)/2 and í µí± í µí±↓ = U(n + μ)/2.. The quantity μ can be interpreted as the magnitude of a local moment, which can take two values ±μ. We call ρ(E) the average density of states corresponding to the effective hamiltonian resulting from the substitution of í µí±í µí± ̂ í µí±↑ í µí± ̂ í µí±↓ by í µí± í µí±í µí¼ í µí± ̂ í µí± í µí¼ .</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"MAGNETIC COUPLINGS IN THE HUBBARD MODEL","attachmentId":50830622,"attachmentType":"pdf","work_url":"https://www.academia.edu/30380885/MAGNETIC_COUPLINGS_IN_THE_HUBBARD_MODEL","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/30380885/MAGNETIC_COUPLINGS_IN_THE_HUBBARD_MODEL"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="96477260" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/96477260/Linked_cluster_series_expansion_for_the_spin_one_Heisenberg_model_with_easy_axis_anisotropy_specific_heat">Linked-cluster series expansion for the spin-one Heisenberg model with easy-axis anisotropy: specific heat</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="4414854" href="https://independent.academia.edu/ChrisWentworth4">Chris Wentworth</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Physics: Condensed Matter, 1989</p><p class="ds-related-work--abstract ds2-5-body-sm">The linked-cluster series expansion technique is used to calculate the specific heat series of the spin-one Heisenberg model with easy-axis anisotropy on the FCC lattice. Series coefficients through sixth order in the interaction parameter are obtained. Examples of the temperature dependence of the specific heat in both ferromagnetic and paramagnetic phase are given. Comparison is made with the mean-field approximation and with a Green function theory.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Linked-cluster series expansion for the spin-one Heisenberg model with easy-axis anisotropy: specific heat","attachmentId":98365507,"attachmentType":"pdf","work_url":"https://www.academia.edu/96477260/Linked_cluster_series_expansion_for_the_spin_one_Heisenberg_model_with_easy_axis_anisotropy_specific_heat","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" 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href="https://www.academia.edu/4584976/Renormalization_group_calculation_for_the_two_dimensional_square_Ising_model_in_a_transverse_magnetic_field">Renormalization-group calculation for the two-dimensional square Ising model in a transverse magnetic field</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="5754141" href="https://independent.academia.edu/jorgehirsch">jorge hirsch</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review B, 1979</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Renormalization-group calculation for the two-dimensional square Ising model in a transverse magnetic 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href="https://www.academia.edu/113532218/Quantum_correlated_cluster_mean_field_theory_applied_to_the_transverse_Ising_model">Quantum correlated cluster mean-field theory applied to the transverse Ising model</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="45106150" href="https://independent.academia.edu/JonasMaziero">Jonas Maziero</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E, 2016</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Quantum correlated cluster mean-field theory applied to the transverse Ising model","attachmentId":110468238,"attachmentType":"pdf","work_url":"https://www.academia.edu/113532218/Quantum_correlated_cluster_mean_field_theory_applied_to_the_transverse_Ising_model","alternativeTracking":true}"><span 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lattices</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="283577552" href="https://independent.academia.edu/JozefStrecka">Jozef Strecka</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv (Cornell University), 2013</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the nature of intermediate magnetization plateaus in the spin-1/2 Ising-Heisenberg and Heisenberg models on two-dimensional triangulated lattices","attachmentId":111432630,"attachmentType":"pdf","work_url":"https://www.academia.edu/114853076/On_the_nature_of_intermediate_magnetization_plateaus_in_the_spin_1_2_Ising_Heisenberg_and_Heisenberg_models_on_two_dimensional_triangulated_lattices","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" 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B, Condensed matter, 1987</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Square-lattice Ising model in a weak uniform magnetic field: Renormalization-group analysis","attachmentId":52242684,"attachmentType":"pdf","work_url":"https://www.academia.edu/31968929/Square_lattice_Ising_model_in_a_weak_uniform_magnetic_field_Renormalization_group_analysis","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/31968929/Square_lattice_Ising_model_in_a_weak_uniform_magnetic_field_Renormalization_group_analysis"><span class="ds2-5-text-link__content">View PDF</span><span 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