TY - JOUR

T1 - Path integrals in the theory of condensed helium

AU - Ceperley, D. M.

PY - 1995

Y1 - 1995

N2 - One of Feynman's early applications of path integrals was to superfluid 4He. He showed that the thermodynamic properties of Bose systems are exactly equivalent to those of a peculiar type of interacting classical "ring polymer." Using this mapping, one can generalize Monte Carlo simulation techniques commonly used for classical systems to simulate boson systems. In this review, the author introduces this picture of a boson superfluid and shows how superfluidity and Bose condensation manifest themselves. He shows the excellent agreement between simulations and experimental measurements on liquid and solid helium for such quantities as pair correlations, the superfluid density, the energy, and the momentum distribution. Major aspects of computational techniques developed for a boson superfluid are discussed: the construction of more accurate approximate density matrices to reduce the number of points on the path integral, sampling techniques to move through the space of exchanges and paths quickly, and the construction of estimators for various properties such as the energy, the momentum distribution, the superfluid density, and the exchange frequency in a quantum crystal. Finally the path-integral Monte Carlo method is compared to other quantum Monte Carlo methods.

AB - One of Feynman's early applications of path integrals was to superfluid 4He. He showed that the thermodynamic properties of Bose systems are exactly equivalent to those of a peculiar type of interacting classical "ring polymer." Using this mapping, one can generalize Monte Carlo simulation techniques commonly used for classical systems to simulate boson systems. In this review, the author introduces this picture of a boson superfluid and shows how superfluidity and Bose condensation manifest themselves. He shows the excellent agreement between simulations and experimental measurements on liquid and solid helium for such quantities as pair correlations, the superfluid density, the energy, and the momentum distribution. Major aspects of computational techniques developed for a boson superfluid are discussed: the construction of more accurate approximate density matrices to reduce the number of points on the path integral, sampling techniques to move through the space of exchanges and paths quickly, and the construction of estimators for various properties such as the energy, the momentum distribution, the superfluid density, and the exchange frequency in a quantum crystal. Finally the path-integral Monte Carlo method is compared to other quantum Monte Carlo methods.

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U2 - 10.1103/RevModPhys.67.279

DO - 10.1103/RevModPhys.67.279

M3 - Article

AN - SCOPUS:11944260941

VL - 67

SP - 279

EP - 355

JO - Reviews of Modern Physics

JF - Reviews of Modern Physics

SN - 0034-6861

IS - 2

ER -