arXiv subjects

Agam Shayit

Publications and source records attributed to Agam Shayit.

5 recordsLinked to original sources

arXiv2026

Quaternion Dirac--Coulomb--Breit Integral Transformation for Relativistic Four-Component Correlated Electronic Structure Theory

High-accuracy correlated four-component relativistic electronic structure methods are typically formulated in terms of integrals over molecular orbital (MO). Consequently, an efficient and scalable strategy is required to deal with the complexity of transforming relativistic two-electron integrals from the atomic orbital (AO) to the MO basis. The transformation bottleneck is particularly acute for approaches that include Breit interaction integrals, whose computational and memory demands further exacerbate the transformation cost. To overcome this challenge, we develop a quaternion-based, AO-driven direct integral transformation scheme. The method operates on scalar AO integrals and combines quaternion density-based contractions with direct Cauchy-Schwarz screening to systematically exploit integral locality. As a result, the proposed framework substantially lowers the practical computational scaling and provides an efficient, memory-conscious, and highly parallelizable pathway for the routine inclusion of relativistic Dirac-Coulomb-Breit integrals in large-scale four-component correlated calculations.

physics.chem-ph↗

arXiv2026

Definitive Assessment of the Accuracy, Variationality, and Convergence of Relativistic Coupled Cluster and Density Matrix Renormalization Group in 100-Orbital Space

Accuracy, variationality, and convergence underpin the reliability of modern electronic structure methods, yet definitive benchmarks in the relativistic regime remain elusive due to the absence of numerically exact full configuration interaction (CI) references. Recent algorithmic advances in the CI framework, enabled by the small-tensor-product (STP) decomposition approach, have dramatically extended the tractable size of the configuration space, making numerically exact CI calculations feasible in large active spaces previously beyond reach. In this work, we employ the recently developed STP-CI framework to perform large-scale numerically exact CI calculations and directly benchmark relativistic coupled cluster and density matrix renormalization group methods. Definitive benchmarking of approximate relativistic electronic structure methods is ensured through the application of the gap theorem, which provides rigorous error bounds on the CI reference and establishes a controlled standard for assessing accuracy, variationality, and convergence.

physics.chem-ph↗

arXiv2025

Numerically Exact Configuration Interaction at Quadrillion-Determinant Scale

The combinatorial scaling of configuration interaction (CI) has long restricted its applicability to only the simplest molecular systems. Here, we report the first numerically exact CI calculation exceeding one quadrillion ($10^{15}$) determinants, enabled by categorical compression within the small-tensor-product distributed active space (STP-DAS) framework. As a demonstration, we converged the relativistic complete active space CI (CASCI) ground state of HBrTe involving over $10^{15}$ complex-valued 2-spinor determinants in under 34.5 hours (time-to-completion) using 1000 nodes, representing the largest CASCI calculation reported to date. Additionally, we achieved $\boldsymbol{\sigma}$-build times of just 5 minutes for systems with approximately 150 billion complex-valued 2-spinor determinants using only a few compute nodes. Extensive benchmarks confirm that the method retains numerical exactness with drastically reduced resource demands. Compared to previous state-of-the-art CI calculations, this work represents a 3-orders-of-magnitude increase in CI space, a 6-orders-of-magnitude increase in FLOP count, and a 6-orders-of-magnitude improvement in computational speed. By introducing a numerically exact, categorically compressed representation of the CI expansion vectors and reformulating the $\boldsymbol{\sigma}$-build accordingly, we eliminate memory bottlenecks associated with storing excitation lists and CI vectors while significantly reducing computational cost. A compression-compatible preconditioner further enhances performance by generating compressed CI expansion vectors throughout Davidson iterations. This work establishes a new computational frontier for numerically exact CI methods, enabling chemically and physically accurate simulations of strongly correlated, spin-orbit coupled systems previously thought to be beyond reach.

physics.chem-ph↗

arXiv2025

Chirality-Driven Magnetization Emerges from Relativistic Four-Current Dynamics

Chirality-induced spin selectivity (CISS) is a striking quantum phenomenon in which electron transport through chiral molecules leads to spin polarization -- even in the absence of external magnetic fields or magnetic components. Although observed in systems such as DNA, helicenes, proteins, and polymers, the fundamental physical origin of CISS remains unresolved. Here, we introduce a time-dependent relativistic four-current framework, in which charge and current densities evolve according to the time-dependent variational principle. Real-time relativistic four-current simulations enable direct analysis of helical currents and induced magnetization dynamics. Applied to helicenes -- axially chiral molecules lacking stereocenters -- our simulations reveal curvature-induced helical electron currents that generate spontaneous magnetic fields aligned along the molecular axis. These fields are handedness-dependent and reach magnitudes of $10^{-1}$ Tesla per single helicene strand. Our results suggest that CISS may arise from intrinsic, relativistic curvature-induced helical currents and the associated magnetic fields within chiral molecules. This four-current mechanism offers a self-contained explanation for the driving force underlying spin selectivity, independent of interfacial effects or unphysically enhanced spin-orbit coupling. Furthermore, our results provide a new perspective that offers a unifying framework with the potential to reconcile many existing hypotheses and theoretical models, while also suggesting several testable predictions that can be examined experimentally.

cond-mat.mes-hall↗

arXiv2021

Vacuum energy density and pressure inside a soft wall

In the study of quantum vacuum energy and the Casimir effect, it is desirable to model the conductor by a potential of the form $V(z)=z^\alpha$. This "soft wall" model was proposed so as to avoid the violation of the principle of virtual work under ultraviolet regularization that occurs for the standard Dirichlet wall. The model was formalized for a massless scalar field, and the expectation value of the stress tensor has been expressed in terms of the reduced Green function of the equation of motion. In the limit of interest, $\alpha \gg 1$, which approximates a Dirichlet wall, a closed-form expression for the reduced Green function cannot be found, so piecewise approximations incorporating the perturbative and WKB expansions of the Green function, along with interpolating splines in the region where neither expansion is valid, have been developed. After reviewing this program, in this article we apply the scheme to the wall with $\alpha=6$ and use it to compute the renormalized energy density and pressure inside the cavity for various values of the conformal parameter. The consistency of the results is verified by comparison to their numerical counterparts and verification of the trace anomaly and the conservation law. Finally, we use the approximation scheme to reproduce the energy density inside the quadratic wall, which was previously calculated exactly but with some uncertainty.

hep-th↗