发表机构
Brookhaven National Laboratory; University of Chicago; Argonne National Laboratory（布鲁海文国家实验室; 芝加哥大学; 阿贡国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过费米子规范变换实现了Bose-Hubbard模型的精确费米子对偶，推广至软核相互作用，并验证了无能隙相与相变由紧致玻色子共形场论支配，为强关联系统研究提供新途径。
AI 中文摘要
近期发展已通过规范变换确立了具有$\mathbb{Z}_2$对称性的精确玻色化和费米化作为对偶关系。在本工作中，我们将费米子规范变换（实现广义Jordan-Wigner变换）应用于具有全局$U(1)$对称性的Bose-Hubbard（BH）模型，并推导出由玻色子和费米子构成的费米子复合体的精确对偶描述。在一维情形下，该对偶将扩展硬核BH模型与无自旋Fermi-Hubbard模型之间的精确映射推广至覆盖软核相互作用。在低能下，该映射归结为sine-Gordon模型与Thirring模型之间众所周知的等价关系。在无能隙相中，费米子复合体关联函数的振荡波矢由其密度决定，这为Luttinger定理提供了新的体现。我们利用密度矩阵重正化群（DMRG）计算验证了该精确对偶，并证明无能隙相和相变由紧致玻色子共形场论所支配。我们的构造自然推广至一般玻色子系统和更高维度，为研究光晶格中的Bose-Fermi混合物及其他强关联量子系统开辟了新途径。
英文摘要
Recent developments have established exact bosonization and fermionization with a $\mathbb{Z}_2$ symmetry as dualities through gauging. In this work, we apply fermionic gauging, which realizes generalized Jordan-Wigner transformations, to the Bose-Hubbard (BH) model with a global $U(1)$ symmetry and derive an exact dual description in terms of fermionic composites, built from bosons and fermions. In 1D, this duality generalizes the exact mapping between the extended hard-core BH model and the spinless Fermi-Hubbard model to include soft-core bosons. At low energies, the mapping reduces to the well-known equivalence between the sine-Gordon model and the Thirring model. The oscillation wave vector of the fermionic composite correlation function in the gapless phase is fixed by their density, providing a novel manifestation of Luttinger's theorem. We verify the exact duality using density matrix renormalization group (DMRG) calculations and demonstrate that the gapless phase and the phase transition are governed by the compact boson conformal field theory. Our construction naturally extends to generic bosonic systems and higher dimensions, opening new avenues for studying Bose-Fermi mixtures in optical lattices and other strongly correlated quantum systems.
Commentsv2: revised; 25 pages, 7 figures
