Dynamical Mean-Field Theory Simulations with the Adaptive Sampling Configuration Interaction Method

In the pursuit of accurate descriptions of strongly correlated quantum many-body systems, dynamical mean-field theory (DMFT) has been an invaluable tool for elucidating the spectral properties and quantum phases of both phenomenological models and ab initio descriptions of real materials. Key to the DMFT process is the self-consistent map of the original system into an Anderson impurity model, the ground state of which is computed using an impurity solver. The power of the method is thus limited by the complexity of the impurity model the solver can handle. Simulating realistic systems generally requires many correlated sites. By adapting the recently proposed adaptive sampling configuration interaction (ASCI) method as an impurity solver, we enable much more efficient zero temperature DMFT simulations. The key feature of the ASCI method is that it selects only the most relevant Hilbert space degrees of freedom to describe the ground state. This reduces the numerical complexity of the calculation, which will allow us to pursue future DMFT simulations with more correlated impurity sites than in previous works. Here we present the ASCI-DMFT method and example calculations on the one-dimensional and two-dimensional Hubbard models that exemplify its efficient convergence and timing properties. We show that the ASCI approach is several orders of magnitude faster than the current best published ground state DMFT simulations, which allows us to study the bath discretization error in simulations with small clusters, as well as to address cluster sizes beyond the current state of the art. Our approach can also be adapted for other embedding methods such as density matrix embedding theory and self-energy embedding theory.Comment: 12 pages, 11 figures, supplemental informatio

Quantum Eigenvector Continuation for Chemistry Applications

A typical task for classical and quantum computing in chemistry is finding a potential energy surface (PES) along a reaction coordinate, which involves solving the quantum chemistry problem for many points along the reaction path. Developing algorithms to accomplish this task on quantum computers has been an active area of development, yet finding all the relevant eigenstates along the reaction coordinate remains a difficult problem, and determining PESs is thus a costly proposal. In this paper, we demonstrate the use of a eigenvector continuation -- a subspace expansion that uses a few eigenstates as a basis -- as a tool for rapidly exploring potential energy surfaces. We apply this to determining the binding PES or torsion PES for several molecules of varying complexity. In all cases, we show that the PES can be captured using relatively few basis states; suggesting that a significant amount of (quantum) computational effort can be saved by making use of already calculated ground states in this manner.Comment: 13 pages, 8 figures, 3 pages of appendi

A Parallel, Distributed Memory Implementation of the Adaptive Sampling Configuration Interaction Method

Many-body simulations of quantum systems is an active field of research that involves many different methods targeting various computing platforms. Many methods commonly employed, particularly coupled cluster methods, have been adapted to leverage the latest advances in modern high-performance computing.Selected configuration interaction (sCI) methods have seen extensive usage and development in recent years. However development of sCI methods targeting massively parallel resources has been explored only in a few research works. In this work, we present a parallel, distributed memory implementation of the adaptive sampling configuration interaction approach (ASCI) for sCI. In particular, we will address key concerns pertaining to the parallelization of the determinant search and selection, Hamiltonian formation, and the variational eigenvalue calculation for the ASCI method. Load balancing in the search step is achieved through the application of memory-efficient determinant constraints originally developed for the ASCI-PT2 method. Presented benchmarks demonstrate parallel efficiency exceeding 95\% for the variational ASCI calculation of Cr$_2$ (24e,30o) with $10^6, 10^7$, and $3*10^8$ variational determinants up to 16,384 CPUs. To the best of the authors' knowledge, this is the largest variational ASCI calculation to date.Comment: 32 pages, 4 figure

Strong Correlation Through Selected Configuration Interaction: From Molecules to Extended Systems

The theoretical description of many-body systems, be it molecular or extended, from first principles has been one of the principal goals of the physical sciences since the advent of quantum mechanics. This is unfortunately an exceptionally complicated endeavour, especially so in the so called ``strongly correlated'' systems. These are characterized by their qualitative behavior being dominated by particle-particle interactions, which precludes their accurate description using effective one-body approaches, such as Kohn-Sham density-functional theory. As a consequence of their remarkable complexity, strongly correlated materials present a wide palette of exciting collective phenomena of huge technological interest. Paradigmatic examples are high temperature superconductors based on transition metal oxides or pnictides, materials presenting colossal magnetoresistance, or iron/molybdenum based catalytic centers in biological systems. With the ample range of potential applications in mind, from energy conversion and storage to the development of new principles for information processing devices, great interdisciplinary effort, combining condensed matter physics, quantum chemistry and materials science, has been dedicated over the last decades to devising and applying accurate theoretical and numerical approaches for the description and prediction of electronic properties arising from strong correlation.Unfortunately, due to the rich variety of physical and chemical principles which can result in strongly correlated behavior, there is currently no single method which can be successfully applied to all correlated many-body systems. On the contrary, a broad toolkit composed of analytical theories and computational approaches has been developed over the years, each based on a different heuristic to simplify the solution of the problem, and therefore each being applicable accurately on a different class of many-body system. In this thesis, we have refined and developed one such tool in the many-body toolbox: the adaptive sampling configuration interaction (ASCI) method. This is an exceptionally efficient selective configuration interaction approach, originally formulated to provide accurate ground state energies of molecular systems with a moderate computational cost. Here, we further extend the ASCI framework to compute accurate spectral properties, accessible through the one-body Green's function, allowing us to study excited state properties as well as to apply ASCI to extended systems by using it as impurity solver within the dynamical mean-field theory (DMFT). This makes ASCI noticeably versatile, and we employ it to contribute to open problems in quantum computation, molecular physics and computational condensed matter theory. This wide applicability shows ASCI to be a useful new addition to the many-body theory tool-set. In particular the ASCI-DMFT approach introduced here holds great promise for the \emph{ab initio} study of strongly correlated materials

Strong Correlation Through Selected Configuration Interaction: From Molecules to Extended Systems

The theoretical description of many-body systems, be it molecular or extended, from first principles has been one of the principal goals of the physical sciences since the advent of quantum mechanics. This is unfortunately an exceptionally complicated endeavour, especially so in the so called ``strongly correlated'' systems. These are characterized by their qualitative behavior being dominated by particle-particle interactions, which precludes their accurate description using effective one-body approaches, such as Kohn-Sham density-functional theory. As a consequence of their remarkable complexity, strongly correlated materials present a wide palette of exciting collective phenomena of huge technological interest. Paradigmatic examples are high temperature superconductors based on transition metal oxides or pnictides, materials presenting colossal magnetoresistance, or iron/molybdenum based catalytic centers in biological systems. With the ample range of potential applications in mind, from energy conversion and storage to the development of new principles for information processing devices, great interdisciplinary effort, combining condensed matter physics, quantum chemistry and materials science, has been dedicated over the last decades to devising and applying accurate theoretical and numerical approaches for the description and prediction of electronic properties arising from strong correlation.Unfortunately, due to the rich variety of physical and chemical principles which can result in strongly correlated behavior, there is currently no single method which can be successfully applied to all correlated many-body systems. On the contrary, a broad toolkit composed of analytical theories and computational approaches has been developed over the years, each based on a different heuristic to simplify the solution of the problem, and therefore each being applicable accurately on a different class of many-body system. In this thesis, we have refined and developed one such tool in the many-body toolbox: the adaptive sampling configuration interaction (ASCI) method. This is an exceptionally efficient selective configuration interaction approach, originally formulated to provide accurate ground state energies of molecular systems with a moderate computational cost. Here, we further extend the ASCI framework to compute accurate spectral properties, accessible through the one-body Green's function, allowing us to study excited state properties as well as to apply ASCI to extended systems by using it as impurity solver within the dynamical mean-field theory (DMFT). This makes ASCI noticeably versatile, and we employ it to contribute to open problems in quantum computation, molecular physics and computational condensed matter theory. This wide applicability shows ASCI to be a useful new addition to the many-body theory tool-set. In particular the ASCI-DMFT approach introduced here holds great promise for the \emph{ab initio} study of strongly correlated materials