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The Quantum Transfer Matrix method based on the Suzuki-Trotter formulation isextended to dynamical problems. The auto-correlation functions of theTransverse Ising chain are derived by this method. It is shown that theTrotter-directional correlation function is interpreted as a Matsubara'stemperature Green function and that the auto-correlation function is given byanalytic continuation of the Green function. We propose the Trotter-directionalcorrelation function is a new measure of the quantum fluctuation and show howit works well as a demonstration.

Auto-correlation Functions and Quantum Fluctuations of the Transverse Ising Chain by the Quantum Transfer Matrix Method