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Journal of the Physical Society of Japan

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

Masatoshi Imada, Minoru Takahashi

Published Feb 15, 1987• 5 citations
Publisher
DOI
10.1143/jpsj.56.838

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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.
Based on the mapping introduced by the classical-map hypernetted-chain (CHNC) method, classical numerical simulations, Monte Carlo and molecular dynamics, have been applied to the twodimensional electron fluid and the results are compared with those of quantum Monte Carlo simulations hitherto reported. It is shown that polarization properties of the ground state obtained by the diffusion Monte Carlo method are reproduced within the accuracy of quantum simulations by both of two mapping functions for the quantum temperature which have been proposed within the CHNC method. These results may serve as the basis of numerical simulations based on the CHNC method which are applicable to finite non-periodic systems like quantum dots and systems at finite temperatures.
We formulate a new quantum many body simulation method for a general quantum fluid at any given temperature. Unlike path integral Monte Carlo our method evolves in imaginary time the density matrix from its initial delta function condition to its final thermal form at time time equal to the inverse temperature. It does this with a molecular dynamics scheme on a classical Hamiltonian that has the same functional form as the one of the quantum mechanical Hamiltonian according to the properties of the continuous representation of John R. Klauder. We then end up with the thermal density matrix that can be used to extract thermal averages of observables using the Monte Carlo method equally well in any statistics.