AI 中文总结
研究三角晶格单空穴无限U哈伯德模型，通过将多体问题简化为两体空穴 - 磁振子散射问题确定临界点，数值计算证实螺旋基态等，建立了三角晶格长冈铁磁体的首个量子不稳定性并提供磁学基线。
AI 中文摘要
我们研究了具有最近邻和次近邻跳跃\(t_1\)和\(t_2\)的三角晶格上的单空穴无限U哈伯德模型。令人沮丧的\(t_2\)通过里夫希茨转变使长冈铁磁性失稳，在\(t_{2,c}/t_1 = -0.182\)时转变为长波长共面螺旋态。我们通过将多体问题简化为有效的两体空穴 - 磁振子散射问题来解析确定临界点，其中硬核空穴 - 磁振子约束得到精确处理。数值计算证实了螺旋基态，并揭示了在里夫希茨位移动量\(\mathbf{K}=-\mathbf{Q}^*\)处具有准粒子权重\(Z\simeq0.92\)的相干自旋极化子。这些结果建立了三角晶格长冈铁磁体的首个量子不稳定性，并为有限掺杂下磁振子介导的配对提供了磁学基线。
英文摘要
We study the single-hole infinite-$U$ Hubbard model on the triangular lattice with nearest- and next-nearest-neighbor hoppings $t_1$ and $t_2$. A frustrating $t_2$ destabilizes Nagaoka ferromagnetism through a Lifshitz transition to a long-wavelength coplanar spiral at $t_{2,c}/t_1=-0.182$. We determine the critical point analytically by reducing the many-body problem to an effective two-body hole--magnon scattering problem in which the hard-core hole--magnon constraint is treated exactly. Numerical calculations confirm the spiral ground state and reveal a coherent spin polaron with quasiparticle weight $Z\simeq0.92$ at the Lifshitz-shifted momentum $\mathbf{K}=-\mathbf{Q}^*$. These results establish the first quantum instability of the triangular-lattice Nagaoka ferromagnet and provide the magnetic baseline for magnon-mediated pairing at finite doping.
Comments4+11 pages, 3+3 figures
