Doctor of Philosophy (PhD)


Physics and Astronomy

Document Type



This thesis represents our effort to develop the next generation multi-scale quantum simulation methods suitable for strongly-correlated materials, where complicated phase-diagrams prevail, suggesting complicated underlying physics. We first give a detailed description of the parquet formalism. With its help, different approximate methods can be unified and a hierarchy of approximate methods with different accuracies and computational complexity can thus be designed. Next, we present a numerical solution of the parquet approximation. Results on the Hubbard model are compared to those obtained from Determinant Quantum Monte Carlo (DQMC), FLuctuation EXchange (FLEX), and self-consistent second-order approximation methods. The comparison shows a satisfactory agreement with DQMC and a significant improvement over the FLEX or the self-consistent second-order approximation. The parquet formalism can also be used to analyze the superconducting mechanism of the high-temperature superconductors. The dynamical cluster approximation (DCA) method is used to understand the proximity of the superconducting dome to the quantum critical point in the 2-D Hubbard model. At optimal doping, where Vd is revealed to be featureless, we find a power-law behavior of chi_0d(w=0), replacing the BCS logarithm behavior, and strongly enhanced T_c. After that we propose another multi-scale approach by combining the DCA and the recently introduced dual-fermion formalism. Within this approach, short and long length scale physics is addressed by the DCA cluster calculation, while intermediate length scale physics is addressed diagrammatically using dual fermions. The bare and dressed dual fermionic Green functions scale as O(1/Lc), so perturbation theory on the dual lattice converges very quickly. Lastly, we study the responses to dynamical modulation of the optical lattice potential by analyzing properties of the repulsive fermionic Hubbard model in an optical lattice. We provide numerical evidence showing the modulations by on-site local interaction cannot be ignored, and instead can even strongly contribute to the dynamical behaviors of the system in highly-doped cases.



Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Jarrell, Mark