Abstract
We revisit the cellular dynamical mean-field theory (CDMFT) for the single-band Hubbard model on the square lattice at half filling, reaching real-space cluster sizes of up to 9×9 sites. Using benchmarks against direct lattice diagrammatic Monte Carlo at high temperature, we show that the self-energy obtained from a cluster center-focused extrapolation converges faster with the cluster size than the periodization schemes previously introduced in the literature. The same benchmark also shows that the cluster spin susceptibility can be extrapolated to the exact result at large cluster size, even though its spatial extension is larger than the cluster size.6 MoreReceived 11 March 2020Revised 14 July 2020Accepted 27 August 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.033476Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Physical SystemsStrongly correlated systemsTechniquesDynamical mean field theoryHubbard modelCondensed Matter, Materials & Applied Physics
Highlights
Even after decades of intense research, the single band Hubbard model in finite dimensions larger than one remains an unsolved cornerstone paradigm in theoretical solid state physics
Using benchmarks against direct lattice diagrammatic Monte Carlo at high temperature, we show that the self-energy obtained from a cluster center-focused extrapolation converges faster with the cluster size than the periodization schemes previously introduced in the literature
Using a systematic benchmark with the exact diagrammatic Monte Carlo (DiagMC) result at the lowest temperature for which it is obtainable, we have shown that an approximation scheme of the lattice self-energy based on the center of the cluster is superior to the conventional periodization approaches based on averages over the cluster
Summary
Even after decades of intense research, the single band Hubbard model in finite dimensions larger than one remains an unsolved cornerstone paradigm in theoretical solid state physics. The control parameter is the size of the cluster, which determines the resolution of the approximation in momentum space These approaches have found extensive use, e.g., in the study of the Hubbard model [24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41]. We solve large CDMFT clusters of up to 9 × 9 sites for the half-filled Hubbard model, and benchmark their convergence against exact results obtained with diagrammatic Monte Carlo (DiagMC) [63,64,65] in its connected determinant formulation (CDet [66] for one particle reducible quantities and DDMC [67,68,69] for one particle irreducible quantities).
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