Finite-size effects in canonical and grand-canonical quantum Monte Carlo simulations for fermions

Zhenjiu Wang, Fakher F. Assaad, and Francesco Parisen Toldin
Phys. Rev. E 96, 042131 – Published 16 October 2017

Abstract

We introduce a quantum Monte Carlo method at finite temperature for interacting fermionic models in the canonical ensemble, where the conservation of the particle number is enforced. Although general thermodynamic arguments ensure the equivalence of the canonical and the grand-canonical ensembles in the thermodynamic limit, their approach to the infinite-volume limit is distinctively different. Observables computed in the canonical ensemble generically display a finite-size correction proportional to the inverse volume, whereas in the grand-canonical ensemble the approach is exponential in the ratio of the linear size over the correlation length. We verify these predictions by quantum Monte Carlo simulations of the Hubbard model in one and two dimensions in the grand-canonical and the canonical ensemble. We prove an exact formula for the finite-size part of the free energy density, energy density and other observables in the canonical ensemble and relate this correction to a susceptibility computed in the corresponding grand-canonical ensemble. This result is confirmed by an exact computation of the one-dimensional classical Ising model in the canonical ensemble, which for classical models corresponds to the so-called fixed-magnetization ensemble. Our method is useful for simulating finite systems which are not coupled to a particle bath, such as in nuclear or cold atom physics.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
2 More
  • Received 1 August 2017

DOI:https://doi.org/10.1103/PhysRevE.96.042131

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Zhenjiu Wang*, Fakher F. Assaad, and Francesco Parisen Toldin

  • Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany

  • *Zhenjiu.Wang@physik.uni-wuerzburg.de
  • assaad@physik.uni-wuerzburg.de
  • francesco.parisentoldin@physik.uni-wuerzburg.de

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 96, Iss. 4 — October 2017

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×