Diagrammatic Quantum Monte Carlo Solution of Two dimensional Cooperon-Fermion model

We investigate the two-dimensional Cooperon-fermion model in the strong coupling limit with continuous-time diagrammatic determinant quantum monte carlo (DDQMC). We obtained the same Kosterlitz-Thouless transition temperature $T_{c}$ for the fermion's off-diagonal long range order $\chi_{OD}$ ({\boldmath $k$}=0,$\omega=0)$ and cooperon's Greens function $G^{b}$({\boldmath $k$}=0,$\omega=0)$ as expected. The renormalized cooperon's band (band gap and mass) is examined carefully. The delocalization of the cooperons enhances the diamagnetism. When applied to study the diamagnetism of pseudogap state in high-T$_{c}$ cuprate, the results we obtained is in good agreement with recent torque magnetization measurements.