Classical paths for a quadratic action with memory and exact evaluation of the path integral

Castrigiano, Domenico P. L.; Kokiantonis, N.

doi:10.1016/0375-9601(83)90588-1

Cited by 10 publications

(4 citation statements)

References 7 publications

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“…If we take V = 0 in Eq. ( 16) the M − 1 Gaussian integrals in (15) can be done analytically. The result is the exact free particle density matrix,…”

Section: Discrete Path Integral Expressionsmentioning

confidence: 99%

“…Feynman used his path integral formalism and a variational principle to develop an all coupling approximation for the polaron ground state [12]. Its extension to finite temperatures appeared first by Osaka [13,14], and more recently by Castrigiano et al [15,16,17]. Recently the polaron problem has gained new interest as it could play a role in explaining the properties of the high T c superconductors [18].…”

Section: Introductionmentioning

confidence: 99%

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Low temperature acoustic polaron localization

Fantoni

2013

Physica B: Condensed Matter

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We calculate the properties of an acoustic polaron in three dimensions in thermal equilibrium at a given low temperature using the path integral Monte Carlo method. The specialized numerical method used is described in full details, thus complementing our previous paper [R. Fantoni, Phys. Rev. B 86, 144304 (2012)], and it appears to be the first time it has been used in this context. Our results are in favor of the presence of a phase transition from a localized state to an extended state for the electron as the phonon-electron coupling constant decreases. The phase transition manifests itself with a jump discontinuity in the potential energy as a function of the coupling constant and it affects the properties of the path of the electron in imaginary time: In the weak coupling regime the electron is in an extended state whereas in the strong coupling regime it is found in a self-trapped state.

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“…If we take V = 0 in Eq. ( 16) the M − 1 Gaussian integrals in (15) can be done analytically. The result is the exact free particle density matrix,…”

Section: Discrete Path Integral Expressionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Low temperature acoustic polaron localization

Fantoni

2013

Physica B: Condensed Matter

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“…Few years later, within the path integral formalism, Feynman proposed a very powerful variational procedure to compute the ground state energy and the effective mass of the model which provide accurate results at all couplings [3]. Extension of the Feynman technique to compute properties at finite temperature appeared few years later by Osaka [4], and more recently by Castrigiano et al [5] (see also Ref. [6]).…”

Section: Introductionmentioning

confidence: 99%

“…We have checked in few significant cases that the optimal values for C and w are always close to the Feynman variational values [5], which we have used in our simulations. We exploited eq.…”

Section: Introductionmentioning

confidence: 99%

Free Energy of the Fröhlich Polaron in Two and Three Dimensions

2001

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We present a novel Path Integral Monte Carlo scheme to solve the Fröhlich polaron model. At intermediate and strong electron-phonon coupling, the polaron self-trapping is properly taken into account at the level of an effective action obtained by a preaveraging procedure with a retarded trial action. We compute the free energy at several couplings and temperatures in three and two dimensions. Our results show that the accuracy of the Feynman variational upper bound for the free energy is always better than 5% although the thermodynamics derived from it is not correct. Our estimates of the ground state energies demonstrate that the second cumulant correction to the variational upper bound predicts the self energy to better than 1% at intermediate and strong coupling.

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