标题： 有限$T$下六角晶格上的Hubbard相互作用 显示英文标题

标题： Hubbard interaction at finite $T$ on a hexagonal lattice

摘要： 时间有限体积在低维系统如石墨烯的蒙特卡洛模拟中产生显著影响，石墨烯是一种二维六边形系统，以其独特的电子性质和众多潜在应用而闻名。 在本工作中，我们研究了具有由耦合$U$表征的哈伯德型相互作用的六边形片上的费米子行为。 该系统表现出零或接近零能量的激发态，这些激发态对有限温度效应非常敏感。 我们计算了低能激发态的自能和有效质量的修正，得出一个包含时间有限体积的量化条件。 然后对零温及有限温度情况进行分析。 我们的研究结果表明，一阶$\mathcal{O}(U)$贡献缺失，导致非平凡的修正从$\mathcal{O}(U^2)$开始。 我们将计算结果与从小晶格的混合蒙特卡洛模拟中获得的精确和数值结果进行了验证。 显示英文摘要

摘要： The temporal finite volume induces significant effects in Monte Carlo simulations of systems in low dimensions, such as graphene, a 2-D hexagonal system known for its unique electronic properties and numerous potential applications. In this work, we explore the behavior of fermions on a hexagonal sheet with a Hubbard-type interaction characterized by coupling $U$. This system exhibits zero or near zero-energy excitations that are highly sensitive to finite temperature effects. We compute corrections to the self-energy and the effective mass of low-energy excitations, arriving at a quantization condition that includes the temporal finite volume. These analyses are then conducted for both zero and finite temperatures. Our findings reveal that the first-order $\mathcal{O}(U)$ contributions are absent, leading to non-trivial corrections starting at $\mathcal{O}(U^2)$. We validate our calculations against exact and numerical results obtained from Hybrid Monte Carlo simulations on small lattices.