Date Awarded


Document Type


Degree Name

Doctor of Philosophy (Ph.D.)




Shiwei Zhang

Committee Member

Shiwei Zhang

Committee Member

Junping Shi

Committee Member

Kostas Orginos

Committee Member

Seth Aubin


The Hubbard model is a "paradigmatic" model in the realm of condensed matter physics. Recently a work with various state-or-art methods established the ground state stripe order near 1/8 doping and strong on-site interaction. Therefore, in this thesis, we determine the spin and charge order of ground state of 2D doped Hubbard model in its simplest form (with only on site repulsion and nearest-neighbor hoping) with various doping and small to medium interaction. At half-filling, the ground state is known to be an antiferromagnetic Mott insulator. Doping Mott insulators is believed to be relevant to the superconductivity observed in cuprates. We employ one of the state-of-art method, the auxiliary field quantum monte-carlo (AFQMC) with self-consistently optimized gauge constraints, to systematically study this model. With carefully finite size scaling, we map out the ground state phase diagram in terms of spin and charge order. The result shows a modulated antiferromagnetic (AFM) order present from near half-filling to about 1/5 doping. The doped Hubbard model is believed to be relevant to high temperature superconductivity in cuprates. We employ AFQMC together with the density matrix renormalization group (DMRG) method to study the superconducting order parameter in the ground state of the Hubbard model when a next-nearest-order hopping, $t'$, is included. Our algorithmic advances include a more robust procedure for self-consistent constraint in AFQMC and twist average boundary conditions which can handle finite size effects much more effectively. We compute the superconducting order parameter in the ground state for a number of parameter sets ($t'$, doping) and discuss its interplay with magnetic and charge orders.



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