Quantum Transfer Monte Carlo Method for Finite Temperature Properties and Quantum Molecular Dynamics Method for Dynamical Correlation Functions

A quantum transfer matrix method is proposed and examined. To obtain finite temperature properties, a small number of Monte Carlo samples for the trace summation is taken without the Monte Carlo sampling of the path integral. We introduce the method of a random orthonormal base in the Monte Carlo sampling. This makes it possible to investigate larger size systems than the exact diagonalization. An advantage of this method is that it does not have negative sign difficulty in the path integral as contrast to the usual quantum Monte Carlo method. A quantum molecular dynamics method is also proposed to investigate dynamical correlation functions.