Numerical Study Of Superconductivity And Exciton Condensation In The Two-Dimensional Correlated Electron System

Superconductivity and exciton condensation in the low-dimensional correlated electron systems are the hot topics in condensed matter physics.In this thesis,we mainly study two typical two-dimensional correlated electron systems by the constrained-path Monte Carlo method.In the single-layered cuprates,we study the difference of superconducting critical temperatures between La2-x(Sr/Ba)xCuO4 and HgBa2CuO4+x by a two-orbital model that considers both dx2-v2 and dz2 orbitals.Based on previous results on exciton state,we systematically study the local exciton and exciton condensation in the bilayer Hubbard model.In the two-orbital model,the results show that the d-wave pairing correlation of electrons on dx2-v2 orbital is stronger in the Hg system than in the La system,which is identified by a key parameter ?E representing the energy difference between the dx2-v2 and dz2 orbitals.However,the value of nearest neighbor spin correlation has little difference in these two superconductors,which could not explain the pronounced change of the d-wave pairing correlation in these two systems.Further analysis indicates that the holes on the dx2-v2 orbital increase with increasing ?E,leading to a higher superconducting critical temperature in the Hg system with larger ?E.Our results provide a new theoretical understanding on the superconducting property in the single-layered cuprates.Based on the interlayer tunneling ? defined by Louk,we study the bilayer Hubbard model.We find that the formation of local exciton is suppressed by Hubbard U and electron(hole)doping density.In order to describe the exciton condensation,we define the exciton correlation function P(R),which is more suitable for the limit where t? approaches zero.One results show that the long-range exciton correlation P(R>2)is lowered with increasing interlayer interaction V for the Nx = 6 cluster at large doping when the onsite repulsion U=2t,while the behavior is reversed around very low doping.At U=4t,P(R>2)is suppressed in the whole doping region.The scaling of P(R>2)as a function of lattice size shows that the long-range part correlation of exciton is finite in the thermodynamic limit around the very low doping and U=2t.This result demonstrates that there may exist exciton condensation in the bilayer Hubbard model at weak electron correlation.