Quantum Monte Carlo simulation study of two-dimensional Hubbard model

The physical properties of strongly correlated fermionic systems, described by the two-dimensional Hubbard model with nearest neighbour hopping have been studied using the path integral formulation along with quantum Monte Carlo simulation technique. The partition function of the fermionic system is evaluated within the usual path integral formulation treating beta, the inverse temperature as imaginary time and dividing it into small discrete intervals. The singlet and triplet pairing correlation functions, nearest-neighbour charge density correlations, local squared magnetic moment, double occupancy and total energy are studied as a function of interaction strength for various band fillings at different temperatures. This study leads to the conclusions that the singlet pairing correlation decreases with increasing interaction strength. The triplet pairing correlations for parallel spins show abrupt behaviour The extended singlet pairing correlation and triplet pairing correlations for anti-parallel spins show the slightly functuating behaviour at finite temperatures. The enhancement of local squared magnetic moment and decrement of double occupancy and increment of total energy with U at finite temperatures for half-filled, one-third-filled and one-fourth-filled bands are also noted.