Unified Field Bosonization Technique for strongly inhomogenous Luttinger Liquids
Abstract
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.
Related
- Impurity-induced Friedel oscillations and Wigner crystallization in Luttinger liquids via Unified Field Bosonization Technique
- Single-Particle Spectroscopy and Cross-Barrier Dynamics in Inhomogeneous Luttinger Liquids via Unified Field Bosonization Technique
- Non-Perturbative Resolution of Luttinger's Theorem Violations in Strongly Correlated Systems
- Renormalization group analysis for bosonization coefficients in half-odd-integer Kitaev spin chains
- Effective Field Theory of Noncritical M-theory from Bosonization
BibTeX
@misc{soundarya2026unified,
title = {{Unified Field Bosonization Technique for strongly inhomogenous Luttinger Liquids}},
author = {Soundarya P and Venkata Suryanarayana M and Joy Prakash Das},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21973},
eprint = {2609.21973},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21973},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Unified Field Bosonization Technique for strongly inhomogenous Luttinger Liquids
AU - Soundarya P
AU - Venkata Suryanarayana M
AU - Joy Prakash Das
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.21973
UR - https://arxiv.org/abs/2609.21973
AB - 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.
ER -