Evaluation of the two-particle propagator for the Hubbard model with the help of the Hubbard-I approximation

Abstract

Abstract. The Hubbard-I approximation is generalized to allow for direct evaluation of the equal-time anomalous two-electron propagator for Hubbard model on twodimensional square lattice. This propagator is compared against the quantum Monte Carlo data obtained by Aimi and Imada [J. Phys. Soc. Jpn. 76, 113708 (2007)] in the limit of strong electron-electron interaction. The Hubbard-I predictions are in a good qualitative agreement with the Monte Carlo results. In particular, d-wave correlations decay as cr −3 ("free electron" behaviour), if separation r exceeds 2-3 lattice constants. However, the Hubbard-I approximation underestimates coefficient c by a factor of about three. We conclude that the Hubbard-I approximation, despite its simplicity and artefacts, captures the qualitative behaviour of the two-particle propagator for the Hubbard model, at least for moderate values of r.

Electronic phase separation: Recent progress in the old problem

“…Moreover, the Hubbard I approximation was used for the direct evaluation of the equal-time anomalous two-electron propagator for the Hubbard model on a two-dimensional square lattice [196]. The results were compared with the quantum Monte Carlo calculations reported in Ref.…”

Phase separation of hydrogen atoms adsorbed on graphene and the smoothness of the graphene-graphane interface

“…The applicability of Hubbard-I and related approaches has been tested in many cases (see, e.g., Refs. 17,20,21). In the Hubbard-I approach,F pp is approximated by the product…”

“…The applicability of Hubbard-I and related approaches has been tested in many cases (see, e.g., Refs. 15,18,19). In the Hubbard-I approach, Fpp is approximated by the product This closes the system of equations (13), whose solution may be written explicitly as…”

О Дираковской Массе Хаббардовских Фермионов В Сильно Коррелированном Топологическом Сверхпроводнике Высокого Порядка

“…В режиме U → ∞ приближение Хаббард-I может рассматриваться как хорошее первое приближение, на фоне которого можно учесть корреляционные поправки (см., например, [19][20][21][22][23]). При этом некоторые спектральные [24] и сверхпроводящие [25,26] свойства сильно коррелированных систем удовлетворительно описываются в рамках отмеченного приближения.…”