强非均匀Luttinger液体的统一场玻色化技术
Unified Field Bosonization Technique for strongly inhomogenous Luttinger Liquids
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- National Institute of Technology Tiruchirappalli（国立技术学院特鲁奇拉帕利）
- Assam Engineering College（阿萨姆工程学院）
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中文总结 AI 辅助
本文提出统一场玻色化技术（UFBT），直接处理含静态杂质的强非均匀Luttinger液体，无需重正化或微扰，给出任意N点关联函数闭式解，并证明指数与杂质强度无关，为输运和振荡研究奠基。
中文摘要 AI 辅助
我们引入了统一场玻色化技术（UFBT），这是一种针对含有静态杂质的强非均匀一维Luttinger液体（LLs）的直接玻色化框架。UFBT通过玻色子相位场的对称组合纳入杂质散射，并为广泛的静态杂质势（包括δ势垒、有限势垒和有限势阱）提供了任意N点关联函数的闭式表达式。该形式体系既不需要重正化群分析，也不需要微扰展开，从而在玻色化层面上提供了对非均匀系统的解析描述。该技术通过恢复已知极限情况、与相互作用强度的一阶微扰展开结果一致以及与Schwinger-Dyson方程的一致性得到验证。一个关键结果是，关联函数的指数保持与杂质强度无关，而杂质依赖性则通过关联函数的空间结构和振幅来体现。所得的关联函数为强非均匀Luttinger液体中输运、Friedel振荡以及局域和动态态密度的解析研究奠定了基础。
英文摘要
We introduce the Unified Field Bosonization Technique (UFBT), a direct bosonization framework for strongly inhomogeneous one-dimensional Luttinger liquids (LLs) containing static impurities. UFBT incorporates impurity scattering through a symmetrized combination of bosonic phase fields and yields closed-form expressions for arbitrary N-point correlation functions for a broad class of static impurity potentials, including delta barriers, finite barriers and finite wells. The formalism requires neither renormalization-group analysis nor perturbative expansions, providing an analytical description of the inhomogeneous system at the bosonized level. The resulting correlation functions capture the leading singular contributions relevant to the present analysis. The technique is validated by recovering known limiting cases, showing agreement with the first-order perturbative expansion in the interaction strength, and demonstrating consistency with the Schwinger-Dyson equations. A key result is that the correlation function exponents remain independent of the impurity strength, while the impurity dependence is captured by the spatial structure and amplitudes of the correlation functions. The resulting correlation functions establish a foundation for analytical studies of transport, Friedel oscillations, and the local and dynamical density of states in strongly inhomogeneous Luttinger liquids.
