Skip to main content
eScholarship
Open Access Publications from the University of California

Scholarly Works (7 results)

  • Thesis
  • Peer Reviewed
UC Berkeley Electronic Theses and Dissertations (2021)

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.

    Cover page: Strong Correlation Through Selected Configuration Interaction: From Molecules to Extended Systems
    • Article
    • Peer Reviewed
    UC Berkeley Previously Published Works (2019)
    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- 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.
      Cover page: Dynamical mean field theory simulations with the adaptive sampling configuration interaction method
      • Article
      • Peer Reviewed
      LBL Publications (2023)
      The many-body simulation of quantum systems is an active field of research that involves several 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, the development of sCI methods targeting massively parallel resources has been explored only in a few research works. Here, we present a parallel, distributed memory implementation of the adaptive sampling configuration interaction approach (ASCI) for sCI. In particular, we will address the 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. The presented benchmarks demonstrate near optimal speedup for ASCI calculations of Cr2 (24e, 30o) with 106, 107, and 3 × 108 variational determinants on up to 16 384 CPUs. To the best of the authors' knowledge, this is the largest variational ASCI calculation to date.
        Cover page: A parallel, distributed memory implementation of the adaptive sampling configuration interaction methodCreative Commons 'BY' version 4.0 license
        • Article
        • Peer Reviewed
        LBL Publications (2022)
        Iron-sulfur clusters comprise an important functional motif in the catalytic centers of biological systems, capable of enabling important chemical transformations at ambient conditions. This remarkable capability derives from a notoriously complex electronic structure that is characterized by a high density of states that is sensitive to geometric changes. The spectral sensitivity to subtle geometric changes has received little attention from correlated, large active space calculations, owing partly to the exceptional computational complexity for treating these large and correlated systems accurately. To provide insight into this aspect, we report the first Complete Active Space Self Consistent Field (CASSCF) calculations for different geometries of the [Fe(II/III)4S4(SMe)4]-2 clusters using two complementary, correlated solvers: spin-pure Adaptive Sampling Configuration Interaction (ASCI) and Density Matrix Renormalization Group (DMRG). We find that the previously established picture of a double-exchange driven magnetic structure, with minute energy gaps (<1 mHa) between consecutive spin states, has a weak dependence on the underlying geometry. However, the spin gap between the singlet and the spin state 2S + 1 = 19, corresponding to a maximal number of Fe-d electrons being unpaired and of parallel spin, is strongly geometry dependent, changing by a factor of 3 upon slight deformations that are still within biologically relevant parameters. The CASSCF orbital optimization procedure, using active spaces as large as 86 electrons in 52 orbitals, was found to reduce this gap compared to typical mean-field orbital approaches. Our results show the need for performing large active space calculations to unveil the challenging electronic structure of these complex catalytic centers and should serve as accurate starting points for fully correlated treatments upon inclusion of dynamical correlation outside the active space.
          Cover page: The Effect of Geometry, Spin, and Orbital Optimization in Achieving Accurate, Correlated Results for Iron–Sulfur Cubanes
          • Article
          • Peer Reviewed
          LBL Publications (2021)
          Iron-sulfur clusters comprise an important functional motif of the catalytic centers of biological systems, capable of enabling important chemical transformations at ambient conditions. This remarkable capability derives from a notoriously complex electronic structure that is characterized by a high density of states that is sensitive to geometric changes. The spectral sensitivity to subtle geometric changes has received little attention from fully-correlated calculations, owing partly to the exceptional computational complexity for treating these large and correlated systems accurately. To provide insight into this aspect, we report the first Complete Active Space Self Consistent Field (CASSCF) calculations for different geometries of cubane-based clusters using two complementary, fully-correlated solvers: spin-pure Adaptive Sampling Configuration Interaction (ASCI) and Density Matrix Renormalization Group (DMRG). We find that the previously established picture of a double-exchange driven magnetic structure, with minute energy gaps (< 1 mHa) between consecutive spin states, has a weak dependence on the underlying geometry. However, the spin gap between the lowest singlet and the highest spin states is strongly geometry dependent, changing by an order of magnitude upon slight deformations that are still within biologically relevant parameters. The CASSCF orbital optimization procedure, using active spaces as large as 86 electrons in 52 orbitals, was found to reduce this gap by a factor of two compared to typical mean-field orbital approaches. Our results clearly demonstrate the need for performing highly correlated calculations to unveil the challenging electronic structure of these complex catalytic centers.
            Cover page: The Effect of Geometry, Spin and Orbital Optimization in Achieving Accurate, Fully-Correlated Results for Iron-Sulfur Cubanes
            • Article
            • Peer Reviewed
            UC Berkeley Previously Published Works (2021)
            In this work we present a detailed analysis of variational quantum phase estimation (VQPE), a method based on real-time evolution for ground and excited state estimation on near-term hardware. We derive the theoretical ground on which the approach stands, and demonstrate that it provides one of the most compact variational expansions to date for solving strongly correlated Hamiltonians. At the center of VQPE lies a set of equations, with a simple geometrical interpretation, which provides conditions for the time evolution grid in order to decouple eigenstates out of the set of time evolved expansion states, and connects the method to the classical filter diagonalization algorithm. Further, we introduce what we call the unitary formulation of VQPE, in which the number of matrix elements that need to be measured scales linearly with the number of expansion states, and we provide an analysis of the effects of noise which substantially improves previous considerations. The unitary formulation allows for a direct comparison to iterative phase estimation. Our results mark VQPE as both a natural and highly efficient quantum algorithm for ground and excited state calculations of general many-body systems. We demonstrate a hardware implementation of VQPE for the transverse field Ising model. Further, we illustrate its power on a paradigmatic example of strong correlation (Cr2 in the SVP basis set), and show that it is possible to reach chemical accuracy with as few as ~50 timesteps.
              Cover page: Real time evolution for ultracompact Hamiltonian eigenstates on quantum hardware
              • Article
              • Peer Reviewed
              UC Berkeley Previously Published Works (2022)
              In this work we present a detailed analysis of variational quantum phase estimation (VQPE), a method based on real-time evolution for ground- and excited-state estimation on near-term hardware. We derive the theoretical ground on which the approach stands, and demonstrate that it provides one of the most compact variational expansions to date for solving strongly correlated Hamiltonians, when starting from an appropriate reference state. At the center of VQPE lies a set of equations, with a simple geometrical interpretation, which provides conditions for the time evolution grid in order to decouple eigenstates out of the set of time-evolved expansion states, and connects the method to the classical filter-diagonalization algorithm. Furthermore, we introduce what we call the unitary formulation of VQPE, in which the number of matrix elements that need to be measured scales linearly with the number of expansion states, and we provide an analysis of the effects of noise that substantially improves previous considerations. The unitary formulation allows for a direct comparison to iterative phase estimation. Our results mark VQPE as both a natural and highly efficient quantum algorithm for ground- and excited-state calculations of general many-body systems. We demonstrate a hardware implementation of VQPE for the transverse field Ising model. Furthermore, we illustrate its power on a paradigmatic example of strong correlation (Cr2 in the def2-SVP basis set), and show that it is possible to reach chemical accuracy with as few as approximately 50 time steps.
                Cover page: Real-Time Evolution for Ultracompact Hamiltonian Eigenstates on Quantum Hardware
                Top