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Methodology of Analytic and Computational Studies on Quantum Systems

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Abstract

The concept of “separation of procedures” and the ST-transformation are briefly reviewed together with the equivalence theorem that a d-dimensional quantum system with finite-range interactions is equivalent to the corresponding (d+1)-dimentional classical system with finite-range interactions. This theorem yields the introduction of the quantum transfer-matrix method. Thermo quantum dynamics is formulated using the quantum transfer-matrix method. This new formulation has the great merit that the thermal average 〈Q〉 for any observable Q in the thermodynamic limit is expressed as an expectation value over a temperature-dependent state vector in the single (conjugate) Hilbert space in the contrast to the usage of the double Hilbert space in thermo field dynamics.

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  1. Department of Applied Physics, Science University of Tokyo, 1–3, Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, Japan

    Masuo Suzuki

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  1. Masuo Suzuki
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Suzuki, M. Methodology of Analytic and Computational Studies on Quantum Systems. Journal of Statistical Physics 110, 945–956 (2003). https://doi.org/10.1023/A:1022128423037

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