Momentum-space finite-size corrections for quantum Monte Carlo calculations

Extended solids are frequently simulated as finite systems with periodic boundary conditions, which due to the long-range nature of the Coulomb interaction may lead to slowly decaying finite-size errors. In the case of quantum Monte Carlo simulations, which are based on real space, both real-space a...

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Bibliographic Details
Published in:Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2012-03, Vol.85 (12), Article 125125
Main Authors: Gaudoin, R., Gurtubay, I. G., Pitarke, J. M.
Format: Article
Language:English
Subjects:
Computer simulation
Condensed matter
Convergence
Decay rate
Interpolation
Mathematical analysis
Mathematical models
Monte Carlo methods
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Summary:Extended solids are frequently simulated as finite systems with periodic boundary conditions, which due to the long-range nature of the Coulomb interaction may lead to slowly decaying finite-size errors. In the case of quantum Monte Carlo simulations, which are based on real space, both real-space and momentum-space solutions to this problem exist. Here, we describe a hybrid method which using real-space data models the spherically averaged structure factor in momentum space. We show that (i) by integration our hybrid method exactly maps onto the real-space model periodic Coulomb-interaction (MPC) method and (ii) therefore our method combines the best of both worlds (real space and momentum space). One can use known momentum-resolved behavior to improve convergence where MPC fails (e.g., at surfacelike systems). In contrast to pure momentum-space methods, our method only deals with a simple single-valued function and hence better lends itself to interpolation with exact small-momentum data as no directional information is needed. By virtue of integration, the resulting finite-size corrections can be written as an addition to MPC.
ISSN:1098-0121
1550-235X
DOI:10.1103/PhysRevB.85.125125