Title page for ETD etd-10122011-115219

Type of Document Dissertation
Author Yang, Shuxiang
Author's Email Address yangphysics@gmail.com
URN etd-10122011-115219
Title Next Generation Multi-Scale Quantum Simulations for Strongly Correlated Materials
Degree Doctor of Philosophy (Ph.D.)
Department Physics & Astronomy
Advisory Committee
Advisor Name Title
Jarrell, Mark Committee Chair
Moreno, Juana Committee Member
Pullin, Jorge Committee Member
Ramanujam, Jagannathan Committee Member
Zhang, Jiandi Committee Member
Tom, Michael Dean's Representative
  • Hubbard model
  • Strongly correlated system
  • Minus sign problem
  • parquet
  • Dynamical cluster approaximation
  • dual fermion
  • quantum Monte Carlo
  • Multi-Scale Many-body approach
Date of Defense 2011-08-22
Availability unrestricted
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


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.

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