Systematic speedup of path integrals of a generic N fold discretized theory
Abstract
We present and discuss a detailed derivation of an analytical method that systematically improves the convergence of path integrals of a generic N fold discretized theory. We develop an explicit procedure for calculating a set of effective actions S^{(p)} , for p=1,2,3,… which have the property that they lead to the same continuum amplitudes as the starting action, but converge to that continuum limit ever faster. Discretized amplitudes calculated using the p level effective action differ from the continuum limit by a term of order 1/N^{p} . We obtain explicit expressions for the effective actions for levels p⩽9 . We end by analyzing the speedup of Monte Carlo simulations of two different models: an anharmonic oscillator with quartic coupling and a particle in a modified PöschlTeller potential.
 Publication:

Physical Review B
 Pub Date:
 August 2005
 DOI:
 10.1103/PhysRevB.72.064302
 arXiv:
 arXiv:condmat/0508546
 Bibcode:
 2005PhRvB..72f4302B
 Keywords:

 05.30.d;
 05.10.Ln;
 03.65.Db;
 Quantum statistical mechanics;
 Monte Carlo methods;
 Functional analytical methods;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Physics  Computational Physics
 EPrint:
 10 pages, 5 figures, biblio info corrected