Quantum Monte Carlo Study Of The Correlated Electron Systems In The Shastry-Sutherland Lattice

Exploring the unusual physical property and the corresponding mechanism of strong correlated electron systems is the most challenging cutting edge in the research of condensed matter physics. In recent years, people pay more attention to the quantum frustrated systems in this research field. The competition and the coexistence of various orders in these systems can cause a lot of new phenomena, and possibly make the system lie in completely different quantum fluctuation condition or ordered state, resulting in an abundant diagram. Experiments have shown peculiar physical phenomena in these system, such as the high temperature superconductivity, spin and charge excitations with energy gap, charge order and magnetic order, and so on.First, in the introduction part, we introduce several different types of correlated electron systems, including the copper-based high temperature superconductor and the iron-based high temperature superconductor, as well as organic superconductor and carbon-based superconductor. In addition, we also summarize the present understanding of the superconducting mechanism of these superconductors. Then, we introduce quantum phase transitions at different values of the frustration on the Shastry-Sutherland lattice and analyze the key issues to be addressed in this thesis. In the second chapter, we give a detailed account of the quantum Monte Carlo method which we used, i.e. the constrained path Monte Carlo method (CPMC).In the third chapter, we investigate the magnetic, charge, and superconducting properties on the Shastry-Sutherland lattice by changing the electron filling density, the value of frustration, the on-site Coulomb repulsion U, and the repulsive interaction V between nearest-neighbor sites. We find that the peak value of the spin structure factor and the charge structure factor is weakened gradually with increasing the value of frustration, which indicates that the antiferromagnetic order is suppressed by frustration. The repulsive interaction V increases the charge fluctuation between sites, resulting in a formation of charge density wave. Concerning the superconductivity, we find that the pair correlation and the corresponding vertex contribution of the extended s-wave is near to zero when the distance between electron pairs R>2, which indicate that the system does not have the extended s-wave long range order; On the other hand, the d-wave pair correlation is pronounced when R>2, which means that the system may show a d-wave superconductivity. In addition, we also find that with increasing the frustration t’, the d-wave pair correlation is suppressed.Finally, we define a new physical quantity——d-wave Block pair correlation in the fourth chapter. The computed results show that the d-wave Block pair correlation including the diagonal hopping t’and the d-wave Block pair correlation without including the diagonal hopping are weakened with the increase of t’, but the difference between these two pair correlations gradually increases. This result is consistent with the finding obtained by using the variational method, and reveals the non-uniform pairing characteristic on the Shastry-Sutherland lattice. We also find that this d-wave Block pair correlation decreases with the increase of the lattice size.