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DOE OSTI2022

The cosine-sine decomposition with different-orbitals-for-different-spins determinants

We report the spin decomposition of a spin-contaminated different-orbitals-for-different-spins (DODS) wave function is formulated in terms of the Krylov space of the $\hat{S}^2$ ||operator. The number of determinants that contribute to the various projected spin eigenfunctions vertical | $\psi ; S, M \rangle$ depends on the sparsity of the orbital overlap matrix X between the α and β spatial orbitals. The cosine-sine decomposition (CSD) procedure may be applied to this overlap matrix, and the resulting redundant orbital transformations may be applied to the α and β spatial orbitals. This produces a sparse X' matrix in the transformed basis in which each row or column has either one or two nonzero elements. This sparse X' matrix simplifies the spin-decomposition procedure in three ways:1) it reduces the number of contributing determinants within the Krylov basis functions and within the projected spin functions, 2) it reduces the effective orbital dimension through elimination of the frozen core and frozen virtual orbitals, and 3) it simplifies the spin-decomposition procedure in both the original and transformed bases by limiting the Krylov space dimension. These simplifications all reduce the computational effort for the spin-decomposition process. This procedure is implemented within a string-based DODS determinant formulation and applied to spin projection of unrestricted Hartree-Fock determinants.

unrestricted Hartree-Fock↗

DOE OSTI2022

Magnetic ground states of honeycomb lattice Wigner crystals

Lattice Wigner crystal states stabilized by long-range Coulomb interactions have recently been realized in two-dimensional moiré materials. We employ large-scale unrestricted Hartree-Fock techniques to unveil the magnetic phase diagrams of honeycomb lattice Wigner crystals. For the three lattice filling factors with the largest charge gaps, $n=2/3,1/2,1/3$, the magnetic phase diagrams contain multiple phases, including ones with non-collinear and non-coplanar spin arrangements. We discuss magnetization evolution with external magnetic field, which has potential as an experimental signature of exotic spin states. Our theoretical results could potentially be validated in moiré materials formed from group VI transition metal dichalcogenide twisted homobilayers.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Spin-orbital liquids and insulator-metal transitions on the pyrochlore lattice

The two orbital Hubbard model, with the electrons additionally coupled to a complex magnetic background, arises in the pyrochlore molybdates. The background involves local moments Hund's coupled to the electrons, driving double exchange ferromagnetism, and antiferromagnetic (AF) tendency arising from competing superexchange. The key scales include the Hubbard repulsion and the superexchange, both of which can be tuned in these materials. They control the phase transition from a ferromagnetic metal to a spin glass metal and then to a spin glass (Mott) insulator. We provide a comprehensive description of the ground state of this model using an unrestricted Hartree-Fock scheme implemented via a simulated annealing procedure and establish the metal-insulator transition line for varying Hubbard interaction and superexchange. The electrons see an effective disorder, due to orbital frustration, already in the ferromagnetic phase. The disorder is further enhanced by antiferromagnetic coupling and the resulting magnetic disorder. As a result, increasing AF coupling shifts the metal-insulator transition to lower Hubbard interaction and gives it an additional "Anderson" character. In conclusion, we provide detailed results on the magnetic and orbital correlations, the density of states, and the optical conductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Moiré Kanamori-Hubbard model for transition metal dichalcogenide homobilayers

Ab initio and continuum model studies predicted that the Γ valley transition metal dichalcogenide (TMD) homobilayers could simulate the conventional multiorbital Hubbard model on the moiré honeycomb lattice. Here, in this work, we perform the Wannierization starting from the continuum model and show that a more general moiré Kanamori-Hubbard model emerges, beyond the extensively studied standard multiorbital Hubbard model, which can be used to investigate the many-body physics in the Γ valley TMD homobilayers. Using the unrestricted Hartree-Fock and Lanczos techniques, we study these half-filled multiorbital moiré bands. By constructing the phase diagrams we predict the presence of an antiferromagnetic state and in addition we found unexpected and dominant states, such as a S = 1 ferromagnetic insulator and a charge density wave state. Our theoretical predictions made using this model can be tested in future experiments on the Γ valley TMD homobilayers.

2-dimensional systems↗

DOE OSTI2023

Weak-coupling theory of neutron scattering as a probe of altermagnetism

Inelastic neutron scattering provides a powerful probe of the magnetic excitations of quantum magnets. Altermagnets have recently emerged as a new class of magnets with vanishing net magnetization characteristic of antiferromagnets and with a spin-split electronic structure typical of ferromagnets. Here we introduce a minimal Hubbard model with two-sublattice orthorhombic anisotropy as a framework to study altermagnetism. Using unrestricted Hartree-Fock calculations, we find an altermagnetic state for this model that evolves from a metallic state to an insulating state with increasing Hubbard-U Coulomb repulsion. We then examine the inelastic neutron scattering response in these states using random-phase approximation calculations of the dynamic spin susceptibility χ"(q,ω). We find that the magnetic excitation spectrum depends on its chirality for q along certain directions in reciprocal space, an observation that may be used in inelastic neutron scattering experiments as a probe of altermagnetism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Atomic isotropic hyperfine properties for second row elements (Al–Cl)

Isotropic hyperfine properties have been obtained for the second row elements Al–Cl using a systematic composite approach consisting of a sequence of core/valence correlation consistent basis sets, up through aug-cc-pCV7Z, along with configuration interaction and coupled cluster methods. The best nonrelativistic final values for the atomic ground states (in MHz) are -1.80 27 Al ( 2 P o 1/2 ), -24.31 29 Si ( 3 P 0 ), 63.70 31 P ( 4 So 3/2 ), 20.77 33 S ( 3 P 2 ), and 35.42 35 Cl ( 2 P o 3/2 ). We find a large K shell contribution to the spin density at the nucleus that is almost canceled by the L and M shell contributions. The spin density in atomic units is approximately linear with respect to the atomic number.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

A static quantum embedding scheme based on coupled cluster theory

Here, we develop a static quantum embedding scheme that utilizes different levels of approximations to coupled cluster (CC) theory for an active fragment region and its environment. To reduce the computational cost, we solve the local fragment problem using a high-level CC method and address the environment problem with a lower-level Møller–Plesset (MP) perturbative method. This embedding approach inherits many conceptual developments from the hybrid second-order Møller–Plesset (MP2) and CC works by Nooijen [J. Chem. Phys. 111, 10815 (1999)] and Bochevarov and Sherrill [J. Chem. Phys. 122, 234110 (2005)]. We go beyond those works here by primarily targeting a specific localized fragment of a molecule and also introducing an alternative mechanism to relax the environment within this framework. We will call this approach MP-CC. We demonstrate the effectiveness of MP-CC on several potential energy curves and a set of thermochemical reaction energies, using CC with singles and doubles as the fragment solver, and MP2-like treatments of the environment. The results are substantially improved by the inclusion of orbital relaxation in the environment. Using localized bonds as the active fragment, we also report results for N=N bond breaking in azomethane and for the central C–C bond torsion in butadiene. We find that when the fragment Hilbert space size remains fixed (e.g., when determined by an intrinsic atomic orbital approach), the method achieves comparable accuracy with both a small and a large basis set. Additionally, our results indicate that increasing the fragment Hilbert space size systematically enhances the accuracy of observables, approaching the precision of the full CC solver.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

The approximate second order coupled-cluster method based on a size-consistent Brillouin–Wigner partitioning

We present a variant of the approximate second order coupled-cluster method (CC2) with a two-parameter size-consistent Brillouin–Wigner (BW-s) partitioning instead of a Møller–Plesset (MP) partitioning for the unperturbed Hamiltonian, which we refer to as BWs-CC2. The computational complexity of this model scales identically to CC2 with molecular size. Conventional CC2 and its regularized BWs-CC2 variants, as well as conventional MP2 and two of its regularized BW-s2 variants, were assessed on a 535 element database spanning thermochemistry, non-covalent interactions, barrier heights, and isomerization energies. To ensure a well-defined model chemistry, the assessment was performed using internally stable spin-polarized Hartree–Fock (HF) orbitals in the finite aug-cc-pVQZ basis without counterpoise corrections. As a result of using stable orbitals, contrary to conventional wisdom, we find that CC2 substantially outperforms MP2 on molecules with significantly spin contaminated reference orbitals without a significant increase in error on systems with a spin-pure reference, showing the value of its single substitutions. While no single choice of regularization parameters can be optimal for all datasets, we find that BWs-CC2 generally outperforms both CC2 and BW-s2 with a single judicious parameter choice. Additional tests on dipole moments and bond lengths of diatomics provide further support for the utility of this choice. Furthermore, the main outliers and poorest performing cases are associated with large amounts of spin-contamination in the HF reference, which is indicative of systems with either strong correlation or extensive artificial symmetry breaking. Overall, these findings argue that the perception of the quality of the CC2 ground state should be reevaluated and that it can be further improved upon by the soundly based BWs-CC2 variant with the recommended parameter choice.

Correlation energy↗