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Dynamical cluster quantum Monte Carlo studies on the square and triangular lattice Hubbard model

Using large-scale dynamical cluster quantum Monte Carlo simulations, we investigate the novel properties such as metal-insulator transition, quantum critical point, marginal-Fermi liquid, unconventional superconductivity, etc, of Hubbard model on two dimensional square [1,2] and triangular [3] lattices.

In the square lattice case, the control parameters are hole doping, temperature T and next-nearneighbor hopping t'/t. We find that at t'/t>0, a line of finite temperature classical critical points converges to the quantum critical point at t'=0 and T=0; at t'/t<=0, we identify a line of Lifshitz transition points associated with a change of the Fermi surface topology. At the Lifshitz transition points, a van Hove singularity in the density of states crosses the Fermi level. Above the Lifshitz points at finite temperature, marginal Fermi liquid separates the pseudogap in the underdope and Fermi liquid in the overdope regions [1]. We furthermore explore the evolution of the d-wave superconducting dome in t’/t<=0 region of the phase diagram, and find out the superconducting dome is enhanced as t' goes to negative values [2].

In the triangular lattice case, we explore the Mott transition at half-filling as well as the superconducting instability in the hole-hoped side of the phase diagram [3]. Due to the interplay of electronic correlations, geometric frustration, and Fermi surface topology, in the hole-doped side, we find a doubly degenerate singlet pairing state at interaction strength close to the bare bandwidth. This superconducting state is mediated by antiferromagnetic spin fluctuations and might of a chiral, d+id pairing symmetry. Our findings have relevance to the superconductivity in water-intercalated sodium cobaltates Na x CoO 2 .yH 2 O, as well as the superconducting phases of the organic compounds \kappa-(ET) 2 X and Pd(dmit) 2 .

1. “Lifshitz Transition in the Two Dimensional Hubbard Model”, K. S. Chen, Z. Y. Meng, T. Pruschke, J. Moreno
and M. Jarell, Phys. Rev. B 86, 165136 (2012).

2. "Evolution of the Superconductivity Dome in the two dimensional Hubbard Model", K. S. Chen, Z. Y. Meng,
S. Yang, T. Pruschke, J. Moreno and M. Jarell, arXiv:1308.5946.

3. “Unconventional superconductivity on the triangular lattice Hubbard Model”, K. S. Chen, Z. Y. Meng,
U. Yu, S. Yang, M. Jarrell and J. Moreno, Phys. Rev. B 88, 041103(R) (2013).