Uncovering phase transitions that underpin the flat-planes in the tilted Hubbard model using subsystems and entanglement measures.

The failure of many approximate electronic structure methods can be traced to their erroneous description of fractional charge and spin redistributions in the asymptotic limit toward infinity, where violations of the flat-plane conditions lead to delocalization and static correlation errors. Although the energetic consequences of the flat-planes are known, the underlying quantum phase transitions that occur when (spin)charge is redistributed have not been characterized. In this study, we use open subsystems to redistribute (spin)charges in the tilted Hubbard model by imposing suitable Lagrange constraints on the Hamiltonian. We computationally recover the flat-plane conditions and quantify the underlying quantum phase transitions using quantum entanglement measures. The resulting entanglement patterns quantify the phase transition that gives rise to the flat-plane conditions and quantify the complexity required to accurately describe charge redistributions in strongly correlated systems. Our study indicates that entanglement patterns can uncover those phase transitions that have to be modeled accurately if the delocalization and static correlation errors of approximate methods are to be reduced.

GQCP: The Ghent Quantum Chemistry Package.

The Ghent Quantum Chemistry Package (GQCP) is an open-source electronic structure software package that aims to provide an intuitive and expressive software framework for electronic structure software development. Its high-level interfaces (accessible through C++ and Python) have been specifically designed to correspond to theoretical concepts, while retaining access to lower-level intermediates and allowing structural run-time modifications of quantum chemical solvers. GQCP focuses on providing quantum chemical method developers with the computational "building blocks" that allow them to flexibly develop proof of principle implementations for new methods and applications up to the level of two-component spinor bases.

Extending Conceptual Density Functional Theory toward First-Order Reduced Density Matrices: An Open Subsystems Viewpoint on the Fukui Matrix.

As a matrix extension of the Fukui function, a reactivity descriptor grounded within Conceptual Density Functional Theory, the Fukui matrix extends Frontier Molecular Orbital Theory to correlated regimes with its eigendecomposition in Fukui occupations and Fukui naturals. Despite successful applications, the questions remain as to whether replacing a quantity derived from a purely density-based framework by its matrix extension is theoretically well-founded and what chemical information is contained in the corresponding eigendecomposition. In this study, we show that the matrix extension of the Fukui function is only well-defined if one also generalizes the external potential to become nonlocal, leading to the introduction of Conceptual First-Order Reduced Density Matrix Functional Theory. By interpreting the Anderson impurity model from an interacting open subsystem perspective, we show how Fukui occupations and Fukui naturals reflect the influence of an increasing (static) correlation and which characteristic patterns we should expect within a molecular context. This study represents a step in generalizing Conceptual Density Functional Theory beyond its density-based perspective.

Analyzing the Behavior of Spin Phases in External Magnetic Fields by Means of Spin-Constrained States.

During molecular dissociation in the presence of an external uniform magnetic field, electrons flip their spin antiparallel to the magnetic field because of the stabilizing influence of the spin Zeeman operator. Although generalized Hartree-Fock descriptions furnish the optimal mean-field energetic description of such bond-breaking processes, they are allowed to break Sz symmetry, leading to intricate and unexpected spin phases and phase transitions. In this work, we show that the behavior of these molecular spin phases can be interpreted in terms of spin phase diagrams constructed by constraining states to target expectation values of projected spin. The underlying constrained states offer a complete electronic characterization of the spin phases and spin phase transitions, as they can be analyzed using standard quantum chemical tools. Because the constrained states effectively span the entire phase space, they could provide an excellent starting point for post-Hartree-Fock methods aimed at gaining more electron correlation or regaining spin symmetry.

Quantifying Delocalization and Static Correlation Errors by Imposing (Spin)Population Redistributions through Constraints on Atomic Domains.

The failure of many density functional approximations can be traced to their behavior under fractional (spin)population redistributions in the asymptotic limit toward infinite bonding distances, which should obey the flat-plane conditions. However, such errors can only be characterized sufficiently in terms of those redistributions if exact energies are available for many possible (spin)population redistributions at different bonding distances. In this study, we propose to model such redistributions by imposing (spin)populations on atomic domains by constraining full configuration interaction wave functions. The resulting N-representable descriptions of small hydrogen chains at different bonding distances allow us to computationally illustrate the effects of the flat-plane conditions in the limit to infinite bond distances, leading to more chemical insight into those flat-plane conditions. As the proposed methodology is able to capture the effects of the flat plane conditions, it could be used to generate the reference data that is required to measure the extent to which approximate methods violate the requirements of the exact functional, leading to a quantification of the delocalization and static correlation error of such methods.