Quantum Monte Carlo method for pairing phenomena: Super-counter-fluid of two-species Bose gases in optical lattices

We study the super-counter-fluid(SCF) states in the two-component hardcore Bose-Hubbard model on the square lattice, using the quantum Monte Carlo method based on the worm(directed loop) algorithm. Since the SCF state is a state of a pair-condensation characterized by $< a^{\dagger} b > \neq 0, < a > = 0$, and $< b > = 0$, where $a$ and $b$ are the order parameters of the two components, it is important to study behaviors of the pair-correlation function $< a_{i} b_{i}^{\dagger} a_{j}^{\dagger} b_{j} >$. For this purpose, we propose a choice of the worm head for calculating the pair-correlation function. From this pair-correlation, we confirm the Kosterlitz-Thouless(KT) charactor of the SCF phase. The simulation efficiency is also improved in the SCF phase.