QUANTUM MONTE-CARLO METHODS - RECENT DEVELOPMENTS

Recent developments of the quantum Monte Carlo methods are reviewed briefly with emphasis on basic ideas, namely the transformation of a d-dimensional quantum system to the corresponding (d + 1)-dimensional classical system. Some recent applications to quantum spin systems are summarized. In particular, numerical evidence of the Haldane gap is given. The quantum transfer-matrix method is also presented, for it is also based on the ST-transformation. The quantum Monte Carlo CAM is explained briefly. Fractal path integrals are also presented, namely a general theory of decomposition of exponential operators and symplectic integrators are explained. The negative-sign problem is also discussed.