Reduced basis surrogates for quantum spin systems based on tensor networks.

Within the reduced basis methods approach, an effective low-dimensional subspace of a quantum many-body Hilbert space is constructed in order to investigate, e.g., the ground-state phase diagram. The basis of this subspace is built from solutions of snapshots, i.e., ground states corresponding to particular and well-chosen parameter values. Here, we show how a greedy strategy to assemble the reduced basis and thus to select the parameter points can be implemented based on matrix-product-state calculations. Once the reduced basis has been obtained, observables required for the computation of phase diagrams can be computed with a computational complexity independent of the underlying Hilbert space for any parameter value. We illustrate the efficiency and accuracy of this approach for different one-dimensional quantum spin-1 models, including anisotropic as well as biquadratic exchange interactions, leading to rich quantum phase diagrams.

Surrogate models for quantum spin systems based on reduced-order modeling.

We present a methodology to investigate phase diagrams of quantum models based on the principle of the reduced basis method (RBM). The RBM is built from a few ground-state snapshots, i.e., lowest eigenvectors of the full system Hamiltonian computed at well-chosen points in the parameter space of interest. We put forward a greedy strategy to assemble such a small-dimensional basis, i.e., to select where to spend the numerical effort needed for the snapshots. Once the RBM is assembled, physical observables required for mapping out the phase diagram (e.g., structure factors) can be computed for any parameter value with a modest computational complexity, considerably lower than the one associated to the underlying Hilbert space dimension. We benchmark the method in two test cases, a chain of excited Rydberg atoms and a geometrically frustrated antiferromagnetic two-dimensional lattice model, and illustrate the accuracy of the approach. In particular, we find that the ground-state manifold can be approximated to sufficient accuracy with a moderate number of basis functions, which increases very mildly when the number of microscopic constituents grows-in stark contrast to the exponential growth of the Hilbert space needed to describe each of the few snapshots. A combination of the presented RBM approach with other numerical techniques circumventing even the latter big cost, e.g., tensor network methods, is a tantalizing outlook of this work.

Quantum Chemistry Common Driver and Databases (QCDB) and Quantum Chemistry Engine (QCEngine): Automation and interoperability among computational chemistry programs.

Community efforts in the computational molecular sciences (CMS) are evolving toward modular, open, and interoperable interfaces that work with existing community codes to provide more functionality and composability than could be achieved with a single program. The Quantum Chemistry Common Driver and Databases (QCDB) project provides such capability through an application programming interface (API) that facilitates interoperability across multiple quantum chemistry software packages. In tandem with the Molecular Sciences Software Institute and their Quantum Chemistry Archive ecosystem, the unique functionalities of several CMS programs are integrated, including CFOUR, GAMESS, NWChem, OpenMM, Psi4, Qcore, TeraChem, and Turbomole, to provide common computational functions, i.e., energy, gradient, and Hessian computations as well as molecular properties such as atomic charges and vibrational frequency analysis. Both standard users and power users benefit from adopting these APIs as they lower the language barrier of input styles and enable a standard layout of variables and data. These designs allow end-to-end interoperable programming of complex computations and provide best practices options by default.

Black-box inhomogeneous preconditioning for self-consistent field iterations in density functional theory.

We propose a new preconditioner based on the local density of states for computing the self-consistent problem in Kohn-Sham density functional theory. This preconditioner is inexpensive and able to cure the long-range charge sloshing known to hamper convergence in large, inhomogeneous systems such as clusters and surfaces. It is based on a parameter-free and physically motivated approximation to the independent-particle susceptibility operator, appropriate for both metals and insulators. It can be extended to semiconductors by using the macroscopic electronic dielectric constant as a parameter in the model. We test our preconditioner successfully on inhomogeneous systems containing metals, insulators, semiconductors and vacuum.

A posteriori error estimation for the non-self-consistent Kohn-Sham equations.

We address the problem of rigorously bounding the errors in the numerical solution of the Kohn-Sham equations due to (i) the finiteness of the basis set, (ii) the convergence thresholds in iterative procedures, and (iii) the propagation of rounding errors in floating-point arithmetic. In this contribution, we compute fully-guaranteed bounds on the solution of the non-self-consistent equations in the pseudopotential approximation in a plane-wave basis set. We demonstrate our methodology by providing band structure diagrams of silicon annotated with error bars indicating the combined error.

Quantifying the error of the core-valence separation approximation.

For the calculation of core-excited states probed through X-ray absorption spectroscopy, the core-valence separation (CVS) scheme has become a vital tool. This approach allows us to target such states with high specificity, albeit introducing an error. We report the implementation of a post-processing step for CVS excitations obtained within the algebraic-diagrammatic construction scheme for the polarization propagator, which removes this error. Based on this, we provide a detailed analysis of the CVS scheme, identifying its accuracy to be dominated by an error balance between two neglected couplings, one between core and valence single excitations and the other between single and double core excitations. The selection of the basis set is shown to be vital for a proper description of both couplings, with tight polarizing functions being necessary for a good balance of errors. The CVS error is confirmed to be stable across multiple systems, with an element-specific spread for K-edge spectrum calculations of only about ±0.02 eV. A systematic lowering of the CVS error by 0.02 eV-0.03 eV is noted when considering excitations to extremely diffuse states, emulating ionization.

Toward quantum-chemical method development for arbitrary basis functions.

We present the design of a flexible quantum-chemical method development framework, which supports employing any type of basis function. This design has been implemented in the light-weight program package molsturm, yielding a basis-function-independent self-consistent field scheme. Versatile interfaces, making use of open standards like python, mediate the integration of molsturm with existing third-party packages. In this way, both rapid extension of the present set of methods for electronic structure calculations as well as adding new basis function types can be readily achieved. This makes molsturm well-suitable for testing novel approaches for discretising the electronic wave function and allows comparing them to existing methods using the same software stack. This is illustrated by two examples, an implementation of coupled-cluster doubles as well as a gradient-free geometry optimisation, where in both cases, arbitrary basis functions could be used. molsturm is open-sourced and can be obtained from http://molsturm.org.

Polarizable Embedding Combined with the Algebraic Diagrammatic Construction: Tackling Excited States in Biomolecular Systems.

We present a variant of the algebraic diagrammatic construction (ADC) scheme by combining ADC with the polarizable embedding (PE) model. The presented PE-ADC method is implemented through second and third order and is designed with the aim of performing accurate calculations of excited states in large molecular systems. Accuracy and large-scale applicability are demonstrated with three case studies, and we further analyze the importance of both state-specific and linear-response-type corrections to the excitation energies in the presence of the polarizable environment. We demonstrate how our combined method can be readily applied to study photoinduced biochemical processes as we model the charge-transfer (CT) excitation which is key to the photoprotection mechanism in the dodecin protein with PE-ADC(2). Through direct access to state-of-the-art excited state analysis, we find that the polarizable environment plays a decisive role by significantly increasing the CT character of the electronic excitation in dodecin. PE-ADC is thus suited to decipher photoinduced processes in complex, biomolecular systems at high precision and at reasonable computational cost.