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Bulletin of the American Physical Society

Hubbard model analysis with dynamical mean-field theory and selective configuration interaction

Carlos Mejuto-Zaera, Norm M. Tubman, K. Birgitta Whaley

Published Mar 4, 2019• 0 citations
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The development of polynomial cost solvers for correlated quantum impurity models, with controllable errors, is a central challenge in quantum many-body physics, where these models find applications ranging from nanoscience to the dynamical mean-field theory (DMFT). Here, we describe how configuration interaction (CI) approximations to exact diagonalization (ED) may be used as solvers in DMFT. CI approximations retain the main advantages of ED, such as the ability to treat general interactions and off-diagonal hybridizations and to obtain real spectral information, but are of polynomial cost. Furthermore, their errors can be controlled by monitoring the convergence of physical quantities as a function of the CI hierarchy. Using benchmark DMFT applications, such as single-site DMFT of the one-dimensional Hubbard model and $2\ifmmode\times\else\texttimes\fi{}2$ cluster DMFT of the two-dimensional Hubbard model, we show that CI approximations allow us to obtain near-exact ED results for a tiny fraction of the cost. This is true over the entire range of interaction strengths including ``difficult'' regimes, such as in the pseudogap phase of the two-dimensional Hubbard model. We use the ability of CI approximations to treat large numbers of orbitals to demonstrate convergence of the bath representation in the $2\ifmmode\times\else\texttimes\fi{}2$ cluster DMFT using a 24-bath orbital representation. CI approximations thus form a promising route to extend ED to problems that are currently difficult to study using other solvers such as continuous-time quantum Monte Carlo, including impurity models with large numbers of orbitals and general interactions.
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. In this Letter, we present the ASCI-DMFT method and use the one- and two-dimensional Hubbard models to 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. Our approach can also be adapted for other embedding methods such as density matrix embedding theory and self-energy embedding theory.
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.