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Physical Review Letters

Monte Carlo Calculation of the Thermodynamic Properties of a Quantum Model: A One-Dimensional Fermion Lattice Model

Hans A. De Raedt, Ad Lagendijk

Published Jan 12, 1981• 80 citations
Publisher

Abstract

Starting from a genuine discrete version of the Feynman path-integral representation for the partition function, calculations have been made of the energy, specific heat, and the static density-density correlation functions for a one-dimensional lattice model at nonzero temperatures. A Monte Carlo technique has been used to calculate the temperature-dependent properties. The results are compared with exact calculations for short chains, the Hartree-Fock approximation, and a classical model.

DOI
10.1103/physrevlett.46.77

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The thermodynamic properties of the small-polaron model are studied by means of a discrete version of the Feynman path-integral representation of the partition function. This lattice model describes a fermion interacting with a boson field. The bosons are treated analytically, the fermion contribution is calculated using a Monte Carlo method. We analyze the thermodynamic functions for the case of one-, two-, and three-dimensional polaron motion. We present strong evidence that the polaron becomes superlocalized if the interaction strength is greater than a critical value.
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The specific heat C of the one-dimensional half-filled Hubbard model is studied by Feynman path-integral quantum Monte Carlo simulations as a function of temperature (T). The strength of the electronic correlations is modified by a variable intramolecular two-electron repulsion U. For weak correlations, C shows a single maximum. For intermediate correlations C has two maxima in the T interval studied. For strong correlations only one maximum and one minimum in C are found in the T interval considered. The influence of spin and electronic excitations on the T dependence of C are discussed. The C data are correlated with calculated probabilities of single occupancy, electronic charge fluctuations, and the electronic chemical potential. \textcopyright{} 1996 The American Physical Society.
The equilibrium properties of a single quantum particle (qp) interacting with a classical gas for a wide range of temperatures that explore the system's behavior in the classical as well as in the quantum regime is investigated. Both the qp and the atoms are restricted to sites on a one-dimensional lattice. A path integral formalism developed within the context of the canonical ensemble is utilized, where the qp is represented by a closed, variable-step random walk on the lattice. Monte Carlo methods are employed to determine the system's properties. To test the usefulness of the path integral formalism, the Metropolis algorithm is employed to determine the equilibrium properties of the qp in the context of a square well potential, forcing the qp to occupy bound states. We consider a one-dimensional square well potential where all atoms on the lattice are occupied with one atom with an on-site potential except for a contiguous set of sites of various lengths centered at the middle of the lattice. Comparison of the potential energy, the energy fluctuations, and the correlation function are made between the results of the Monte Carlo simulations and the numerical calculations.
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