发表机构
National Institute of Technology Tiruchirappalli; Assam Engineering College（国立特鲁奇拉帕利理工学院; 阿萨姆工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文用统一场玻色化技术解析研究一维Luttinger液体中杂质诱导的密度关联，统一描述Friedel振荡与Wigner晶体关联，并揭示$g=1/3$处的标度交叉。
AI 中文摘要
我们利用统一场玻色化技术（UFBT）对相互作用的一维Luttinger液体中杂质诱导的密度关联进行了解析研究。与将杂质作微扰处理的传统方法不同，UFBT在自由费米子层面上精确处理局域杂质，同时以非微扰方式处理相互作用。对于强非均匀系统，我们获得了费米子格林函数和密度-密度关联函数的闭合解析表达式，从而能够统一描述杂质诱导的$2k_F$ Friedel振荡和$4k_F$ Wigner晶体类关联。相应的标度行为被解析推导出来，揭示了在$g=1/3$处主导长程关联的交叉：对于$g>1/3$，Friedel关联占主导；而对于$g<1/3$，即足够强的排斥相互作用区域，Wigner晶体类关联变得占主导。我们发展了一种反射耦合的谐波分析，以解释杂质背散射引起的左右混合，并一致地重现由此产生的密度关联。无自旋极限也可作为自旋表述的直接约化而获得。这些结果为描述强非均匀一维量子系统中杂质诱导和相互作用驱动的密度关联提供了一个解析可控的框架。
英文摘要
We present an analytical study of impurity-induced density correlations in interacting one-dimensional Luttinger liquids using the Unified Field Bosonization Technique (UFBT). Unlike conventional approaches that treat impurities perturbatively, UFBT incorporates localized impurities exactly at the free-fermion level while treating interactions non-perturbatively. Closed analytical expressions for fermionic Green functions and density-density correlation functions are obtained for strongly inhomogeneous systems, enabling a unified description of the impurity-induced $2k_F$ Friedel oscillations and the $4k_F$ Wigner-crystal like correlations. The corresponding scaling behaviour is derived analytically, revealing a crossover in the dominant long-distance correlations at $g=1/3$: Friedel correlations dominate for $g>1/3$, whereas Wigner-crystal like correlations become dominant for $g<1/3$, corresponding to the regime of sufficiently strong repulsive interactions. A reflection-coupled harmonic analysis is developed to account for the left-right mixing induced by impurity backscattering and to consistently reproduce the resulting density correlations. The spinless limit is also obtained as a direct reduction of the spinful formulation. These results provide an analytically controlled framework for describing impurity-induced and interaction-driven density correlations in strongly inhomogeneous one-dimensional quantum systems.
