Magnetically bound nature of a holon-doublon pair in two-dimensional photoexcited Mott insulators

Abstract

We revisit the holon-doublon binding problem in two-dimensional (2D) photoexcited Mott insulators. Low-energy photoexcited states in Mott insulators are described as a pair state of a doublon and a holon. The most basic question is whether its bound state is formed in the lowest-energy state, and negative and positive responses have been discussed in the past. In this study we begin with the 2D Hubbard model, and transform it into the first effective model, which is based on the $t/U$ expansion, with $U$ and $t$ being the Hubbard $U$ and the electron hopping energy, respectively. We find that quantitative reliability is assured for $U/t\ensuremath{\gtrsim}10$. Furthermore, we transform it into a second effective model that selects essential states in the low-energy region. In both effective models we distinguish two magnetic terms, namely, the spin-exchange interaction and the three-site transfer, and parametrize the two terms with the parameters ${J}_{\mathrm{ex}}$ and ${J}_{3\mathrm{site}}$. By changing the parameters apart from the restriction given by the Hubbard model, any positive ${J}_{\mathrm{ex}}$ value with ${J}_{3\mathrm{site}}=0$ yields a finite amount of binding, whereas a finite value of ${J}_{3\mathrm{site}}$ suppresses the binding significantly, still leaving the Hubbard case of $U=10t$ in the vicinity of the bound-unbound boundary.