AI 中文总结
研究一维哈伯德模型，结合玻色化与精确对角化，发现剔除一种自旋粒子会产生具有特定性质的涌现模块化卢廷格液体，揭示了相互作用一维费米子系统的普适模块化结构。
AI 中文摘要
我们研究一维排斥哈伯德模型的自旋分块纠缠哈密顿量。通过将玻色化方法与精确对角化结合，我们发现剔除一种自旋粒子会产生一种模块化卢廷格液体，其性质与原物理系统存在根本差异。该模块化谱完全无色散，且具有与动量无关的纠缠能隙；其本征态呈现由单一有效卢廷格参数支配的代数关联，该参数等于电荷与自旋卢廷格参数的几何均值。所得纠缠谱呈现出与精确对角化结果高度吻合的普适分支层级。我们进一步证明，该模块化基态与无自旋卢廷格液体的基态几乎完全一致。这些结果揭示了相互作用一维费米子系统中的普适模块化结构。
英文摘要
We study the spin-partitioned entanglement Hamiltonian of the one-dimensional repulsive Hubbard model. By combining bosonization with exact diagonalization, we show that tracing out one spin species produces a modular Luttinger liquid, whose properties fundamentally differ from those of the physical system. While the modular spectrum is fully dispersionless and possesses a momentum-independent entanglement gap, its eigenstates exhibit algebraic correlations governed by a single effective Luttinger parameter equal to the geometric mean of the charge and spin Luttinger parameters. The resulting entanglement spectrum displays a universal branching hierarchy in excellent agreement with exact diagonalization. We further demonstrate that the modular ground state is nearly identical to that of the spinless Luttinger liquid. These results uncover a universal modular structure in interacting one-dimensional fermionic systems.
Comments7 pages, 4 figures
