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 $U/t\gtrsim 10$. 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.

中文翻译：

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二维光激发莫特绝缘体中全子-双布伦对的磁束缚性质

我们重新审视了二维 (2D) 光激发 Mott 绝缘体中的 holon-doublon 结合问题。莫特绝缘体中的低能光激发态被描述为双子态和全子态。最基本的问题是它的束缚态是否在最低能量状态下形成，过去已经讨论过消极和积极的反应。在这项研究中，我们从 2D Hubbard 模型开始，并将其转换为第一个有效模型，该模型基于$吨/ü$扩展，与$ü$和$吨$成为哈伯德$ü$和电子跳跃能量，分别。我们发现定量可靠性是有保证的$ü/吨\gtrsim 10$. 此外，我们将其转换为在低能区域中选择基本状态的第二个有效模型。在这两个有效模型中，我们区分了两个磁性项，即自旋交换相互作用和三点转移，并使用参数对这两个项进行参数化${Ĵ}_{\mathrm{前任}}$和${Ĵ}_{3\mathrm{地点}}$. 除了哈伯德模型给出的限制之外，通过改变参数，任何正${Ĵ}_{\mathrm{前任}}$价值与${Ĵ}_{3\mathrm{地点}}=0$产生有限量的绑定，而有限值${Ĵ}_{3\mathrm{地点}}$显着抑制绑定，仍然留下哈伯德案例$ü=10吨$在有界-无界边界附近。