Permutation sampling in Path Integral Monte Carlo

Journal of Low Temperature Physics

Volumn 141, Issue 1-2, 2005, Pages 27-46

  Boninsegni, Massimo ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Bose condensation; Quantum simulations; Superfluid helium

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SIMULATION; CONDENSATION; MONTE CARLO METHODS; THERMODYNAMIC PROPERTIES;

BOSE CONDENSATION; PATH INTEGRAL MONTE CARLO (PIMC) SIMULATIONS; QUANTUM SIMULATIONS;

SUPERFLUID HELIUM;

EID: 25144452903     PISSN: 00222291     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10909-005-7513-0     Document Type: Article

References (15)

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2. D. M. Ceperley and E. L. Pollock 1986 Phys. Rev. Lett. 56 351
3. See, for instance, D. M, Ceperley, in Monte Carlo and Molecular Dynamics of Condensed Matter Systems, K. Binder and G. Ciccotti, eds., Editrice Compositori Bologna, Italy, (1996).
4. Our permutation sampling algorithm is equally applicable to fermions, although it does not solve the sign problem.
5. S. A. Chin 1997 Phys, Lett. A 226 344
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7. See, for instance, J. M. Thijssen, Computational Physics, Cambridge University Press Cambridge, UK (1999), pp. 278-280.
8. L for any given particle, due to the presence of permutations. Therefore, it is necessary that path entanglement, arising from permutations, be properly taken into account. That means that, on proceeding past the Lth position, one must be sure to reconnect the path of the particle, back at the first slice, in a way that is consistent with the current permutation of particle labels.
9. E. L. Pollock and D. M. Ceperley 1984 Phys. Rev. B 30 2555 10.1103/ PhysRevB.30.2555
10. 2, where b̄ = (a + c)/2.
11. We emphasize that all distances in (17) are computed by taking the periodic image of each particle that is closest to particle ν. Thus, as a result of permutation sampling, paths cross over into adjacent simulation cells. This aspect is crucial in estimating the superfluid density, or imaginary time diffusion of individual particles. (for details; see Ref. 1).
12. R. A. Aziz V. P. S. Nain J. S. Carley W. L. Taylor and G. T. McConville 1979 J. Chem. Phys. 70 4330 10.1063/1.438007
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14. For "permute" type moves, we define the optimal value of s that for which the rate of acceptance of attempted permutations is greatest.
15. E. L. Pollock and D. M. Ceperley 1987 Phys. Rev. B 36 8343 10.1103/ PhysRevB.36.8343