Löwdin's symmetry dilemma within Green functions theory for the one‐dimensional Hubbard model. Issue 2 (28th January 2021)

• Record Type: Journal Article
• Authors: Joost, J.‐P.; Schlünzen, N.; Hese, S.; Bonitz, M.; Verdozzi, C.; Schmitteckert, P.; Hopjan, M.
• Other Names: Dornheim Tobias guestEditor.; Manfredi Giovanni guestEditor.; Bonitz Michael guestEditor.
• Is Part Of: Contributions to plasma physics. Volume 62:Issue 2(2022)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-01-28
• Subjects: DMRG simulations -- Green functions -- Hubbard model -- symmetry breaking; Plasma (Ionized gases) -- Periodicals; Electronic journals; 530.44
• DOI: 10.1002/ctpp.202000220
• Languages: English
• ISSNs: 0863-1042

Abstract

Abstract: The energy gap of correlated Hubbard clusters is well studied for one‐dimensional systems using analytical methods and density‐matrix‐renormalization‐group (DMRG) simulations. Beyond 1D, however, exact results are available only for small systems by quantum Monte Carlo. For this reason and, due to the problems of DMRG in simulating 2D and 3D systems, alternative methods such as Green functions combined with many‐body approximations (GFMBA), that do not have this restriction, are highly important. However, it has remained open whether the approximate character of GFMBA simulations prevents the computation of the Hubbard gap. Here we present new GFMBA results that demonstrate that GFMBA simulations are capable of producing reliable data for the gap which agrees well with the DMRG benchmarks in 1D. An interesting observation is that the accuracy of the gap can be significantly increased when the simulations give up certain symmetry restriction of the exact system, such as spin symmetry and spatial homogeneity. This is seen as manifestation and generalization of the "symmetry dilemma" introduced by Löwdin for Hartree–Fock wave function calculations.