Stochastic Series Expansion Algorithm for t-J Model Doped by a Single Hole

In Quantum Monte Carlo (QMC) simulations, Stochastic Series Expansion (SSE) algorithm has been successfully applied to study quantum magnetism, such as the isotropic Heisenberg model. The directed loop algorithm improves the loop update strategy and can give an efficient simulation to the anisotropic XXZ model. In our work, we develop an algorithm based on the directed loop algorithm to study the t-J model doped by a single hole. Because of the hole hopping term, the model will have a sign problem if the interaction in XY direction is anti-ferromagnetic, while sign-problem-free for ferromagnetic XY interactions. Moreover, the ferromagnetic partition function corresponds to the absolute-weight sum of the case with sign-problem. It has recently been shown that such a free energy difference can be captured by the average sign in QMC simulations.