Diagrammatic Monte Carlo for Correlated Fermions

Abstract

We show that Monte Carlo sampling of the Feynman diagrammatic series (DiagMC) can be used for tackling hard fermionic quantum many-body problems in the thermodynamic limit by presenting accurate results for the repulsive Hubbard model in the correlated Fermi liquid regime. Sampling Feynman's diagrammatic series for the single-particle self-energy we can study moderate values of the on-site repulsion ($U/t\sim 4$) and temperatures down to $T/t=1/40$. We compare our results with high temperature series expansion and with single-site and cluster dynamical mean-field theory.

4 pages, 5 figures, stylistic changes

References in corpus (7)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• The ALPS project release 1.3: open source software for strongly correlated systems
• Fermi-Polaron: Diagrammatic Monte Carlo for Divergent Sign-Alternating Series
• Continuous-time auxiliary field Monte Carlo for quantum impurity models
• Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
• Local Order and the gapped phase of the Hubbard model: a plaquette dynamical mean field investigation
• Four-loop lattice-regularized vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory

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