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Ground-state-based model reduction with unitary circuits

Here, we present a method to numerically obtain low-energy effective models based on a unitary transformation of the ground state. The algorithm finds a unitary circuit that transforms the ground state of the original model to a projected wavefunction with only the low-energy degrees of freedom. The effective model can then be derived using the unitary transformation encoded in the circuit. We test our method on the one-dimensional and two-dimensional square-lattice Hubbard model at half-filling, and obtain more accurate effective spin models than the standard perturbative approach.

Hubbard model

First-Principles Framework for the Prediction of Intersystem Crossing Rates in Spin Defects: The Role of Electron Correlation

Optically active spin defects in solids are promising platforms for quantum technologies. In this work, we present a first-principles framework to investigate intersystem crossing processes, which represent crucial steps in the optical spin-polarization cycle used to address spin defects. Considering the nitrogen-vacancy center in diamond as a case study, we demonstrate that our framework effectively captures electron correlation effects in the calculation of many-body electronic states and their spin-orbit coupling and electron-phonon interactions, while systematically addressing finite-size effects. We validate our predictions by carrying out measurements of fluorescence lifetimes, finding excellent agreement between theory and experiments. The framework presented here provides a versatile and robust tool for exploring the optical cycle of varied spin defects entirely from first principles.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates La 3 ⁢Ni 2 ⁢O 7

Motivated by the recently proposed alternating single-layer trilayer stacking structure for the nickelate La 3 ⁢Ni 2 ⁢O 7 , we comprehensively study this system using ab initio and random-phase approximation techniques. Here, our analysis unveils similarities between this novel La 3⁢ Ni 2 ⁢O 7 structure and other Ruddlesden-Popper nickelate superconductors, such as a similar charge-transfer gap value and orbital-selective behavior of the eg orbitals. Pressure primarily increases the bandwidths of the Ni e g bands, suggesting an enhancement of the itinerant properties of those e g states. By changing the cell volume ratio V/V 0 from 0.9 to 1.10, we found that the bilayer structure in La 3 ⁢Ni 2 ⁢O 7 always has lower energy than the single-layer trilayer stacking La 3 ⁢Ni 2 ⁢O 7 . In addition, we observe a “self-doping” effect (compared to the average 1.5 electrons per eg orbital per site of the entire structure) from the trilayer to the single-layer sublattices and this effect will be enhanced by overall electron doping. Moreover, we find a leading d x 2 -y 2 -wave pairing state that is restricted to the single layer. Because the effective coupling between the single layers is very weak, due to the nonsuperconducting trilayer in-between, this suggests that the superconducting transition temperature T c in this structure should be much lower than in the bilayer structure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Correlation effects on coupled electronic and structural properties of doped rare-earth trihydrides

Rare-earth trihydride (𝑅⁢H 3 ) compounds exhibit intriguing coupled electronic and structural properties as a function of doping, hydrogen vacancies, and thermodynamic conditions. Theoretical studies of these materials typically rely on density functional theory (DFT), including the use of small supercells that may underestimate strong correlation effects and structural distortions which in turn may influence their metallicity. Here, we elucidate the roles of lattice distortions and correlation effects on the electronic properties of pristine and doped 𝑅⁢H 3 compounds by adopting DFT +U and quantum Monte Carlo (QMC) methods. Linear-response constrained DFT (LR-cDFT) methods find Hubbard U ≈ 2 eV for 𝑅 𝑑 orbitals and U ≈ 6 eV for H 𝑠 ⁡/N 𝑝 /O 𝑝 orbitals. The small U on Lu 𝑑 orbitals is consistent with QMC calculations on LuH 3 and LuH 2.875 ⁢N 0.125 . In pure face-centered-cubic (FCC) 𝑅⁢H 3 (𝑅 = Lu,Y) compounds, neither DFT nor DFT +U with the self-consistently determined U is enough to create a band gap, however a supercell with hydrogen distortions creates a small gap whose magnitude increases when performing DFT +U with self-consistently determined U values. Furthermore, correlation effects, in turn, have a moderate influence on the coupled structural and electronic properties of doped 𝑅⁢H 3 compounds and may be important when considering the competition between structural distortions and superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Monte Carlo Explicitly Correlated Second-Order Many-Body Green’s Function Calculations of Semiconductor Band Gaps

A systematically converging series of ab initio, post-density-functional, size-consistent, electron-correlated approximations is desired for predictive computing of felectronic band structures of insulating, semiconducting, and metallic solids. A series that meets all of these desiderata (except the applicability to metals) is ab initio many-body Green's function theory based on Gaussian-type-orbital (GTO) basis sets. Here, its leading-order approximation, the second-order Green's function (GF2) method in the diagonal and frequency-independent approximations with the aug-cc-pVDZ basis set, is applied to the fundamental band gaps of three semiconductors (diamond, silicon, and silicon carbide in the zincblende structure) using cluster models. Corrections are made to the basis-set-incompleteness errors by the explicit-correlation (F12) ansatz (GF2-F12) for the valence band edges. The crystals are modeled as surface-passivated clusters of increasing sizes, whose wave functions are expanded by up to 2709 GTO basis functions. Immense computational costs of these calculations are overcome by the highly scalable stochastic algorithm of the Monte Carlo GF2-F12 method, whose operation cost per state increases only as a cubic power of system size, which has a tiny memory footprint and easily achieves near-perfect parallel efficiency on thousands of CPUs or on hundreds of GPUs. The correlated, F12-corrected highest-occupied and lowest-unoccupied molecular-orbital energy (HOMO-LUMO) gap is 5.78 ± 0.07 eV for C 87 H 76 as compared with the experimental value of the fundamental (indirect) band gap of bulk diamond at 5.48 eV. The correlated, F12-corrected HOMO-LUMO gaps for Si 75 H 76 and Si 32 C 43 H 76 are 2.56 ± 0.15 eV and 3.50 ± 0.12 eV, respectively, which are expected to decrease further with increasing cluster sizes. As a result, the experimental fundamental (indirect) band gaps of bulk silicon and silicon carbide are 1.17 eV and 2.42 eV, respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Novel Relativistic Electronic Structure Theories for Actinide-Containing Compounds

Actinides of importance to basic energy sciences contain electrons moving at speed comparable to the speed of light. Reliable computational simulation of these electrons and hence actinide chemistry requires accurate description of relativistic effects. The present project advances computational actinide chemistry with development of new methodologies, algorithms, and computer programs in relativistic quantum chemistry, as well as applications to actinide chemistry and spectroscopy. A new “electrons-only” exact two-component approach has been developed to provide efficient treatments of relativistic effects, while maintaining chemical accuracy. New computational algorithms developed here extend the applicability of relativistic electron-correlation methods to larger molecules. The method-development work in this project also features the first implementation of analytic gradient technique for relativistic electron-correlation methods, which provides significantly enhanced ability to compute properties for molecules containing actinides. The applicability and usefulness of these new methods and computer programs have been demonstrated in calculations of actinide-containing molecules to facilitate understanding of actinide chemistry and spectroscopy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH