The Single Histogram Method and the Quantum Harmonic Oscillator: Accuracy Limits

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dc.creatorOquendo, W. F.
dc.creatorMunoz, J. D.
dc.date2004-10-27
dc.date2005-08-16
dc.date.accessioned2026-07-07T03:01:44Z
dc.date.available2026-07-07T03:01:44Z
dc.descriptionIn a recent work, M. Troyer, F. Alet and S. Wessel \cite{brazilean} proposed a way to extend histogram methods to quantum systems in the World Line Quantum Monte Carlo (WLQMC) formulation. The strategy, also proposed in \cite{josedaniel}, allows to compute quantum averages on a narrow temperature range from a single Monte Carlo run at fixed temperature. This is achieved by fixing $N$, the number of temporal divisions in the Trotter-Suzuki expansion of WLQMC, and by changing $ε$$=$$1/(N \kb T)$. In this work we apply this strategy to construct a single histogram Monte Carlo method for a canonical ensemble of one-dimensional quantum harmonic oscillators and we explore its accuracy limits. We obtain that fixing $N$ imposses a limit of minimal temperature to the properly performance of the method, which is $T_{min}$$=$$1.9(2)N^{-0.80(6)}$ in our example. This limit is a consequence of the fact that the Trotter-Suzuki expansion fails for large $ε$ values, and, therefore, should be taken into account in all applications of this histogram method for quantum systems.
dc.description5 pages, 4 figures, 1 table,(gzipped tar file)
dc.identifierhttps://arxiv.org/abs/cond-mat/0410710
dc.identifierhttp://arxiv.org/abs/cond-mat/0410710
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/25157
dc.subjectStatistical Mechanics
dc.subjectStrongly Correlated Electrons
dc.titleThe Single Histogram Method and the Quantum Harmonic Oscillator: Accuracy Limits
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