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
2kF Friedel oscillations and the
4kF 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.
Abstract Friedel and Wigner oscillations are well known phenomena occurring in quantum systems. Specifically, in a system composed by N confined fermions, the former are characterized by the presence of N / 2 peaks in the density distributions, whereas the last by N peaks. Here, we consider N = 2 fermions harmonically confined in one-dimensional quantum dots. It is known that the transition from the Friedel to the Wigner oscillations is induced by the increment of interaction between the fermions. The increment of temperature, on the other hand, acts on eliminating the oscillations. In this context, by employing a time-dependent density-functional theory formalism, we here obtain the emergence of Wigner oscillations in a model which simulates a real time cooling process.
We study a model in 1+2 dimensions composed of a spherical Fermi surface of N_f N f flavors of fermions coupled to a massless scalar. We present a framework to non-perturbatively calculate general fermion n n -point functions of this theory in the limit N_f\rightarrow0 N f → 0 followed by k_F\rightarrow\infty k F → ∞ where k_F k F sets both the size and curvature of the Fermi surface. Using this framework we calculate the zero-temperature fermion density-density correlation function in real space and find an exponential decay of Friedel oscillations.