The one step fermionic ladder

Abstract

The one step fermionic ladder refers to two parallel Luttinger Liquids (poles of the ladder) placed such that there is a finite probability of electrons hopping between the two poles at a pair of opposing points along each of the poles. The many-body Green function for such a system is calculated in presence of forward scattering interactions using the powerful non-chiral bosonization technique (NCBT). This technique is based on a non-standard harmonic analysis of the rapidly varying parts of the density fields appropriate for the study of strongly inhomogeneous ladder systems. The closed analytical expression for the correlation function obtained from NCBT is nothing but the series involving the RPA (Random Phase Approximation) diagrams in powers of the forward scattering coupling strength resummed to include only the most singular terms with the source of inhomogeneities treated exactly. Finally the correlation functions are used to study physical phenomena such as Friedel oscillations and the conductance of such systems with the potential difference applied across various ends.Comment: 13 pages,9 figures, 4 tables. arXiv admin note: text overlap with arXiv:1608.0582

Nonchiral Bosonization of Strongly Inhomogeneous Luttinger Liquids

“…It is also to be noted that there are some additional global quantities that are needed to be incorporated into the C-numbers in equation ( 5) to make sure the upspin field anti-commutes with the down spin field, the left leg of the ladder anti-commutes with the right leg (in case of a one step fermionic ladder) and so on. They are described in an earlier work [14].…”

“…This approach, which goes by the name "Non-chiral bosonization technique", is based on a nonstandard harmonic analysis of the rapidly varying parts of the density fields. It has been successfully applied to yield the most singular part of the Green functions of different categories of systems like a cluster of impurities around an origin [9], one step ladder [14], one and two slowly moving impurities [15], etc. Any novel technique needs validation.…”

Nonchiral bosonization of strongly inhomogeneous Luttinger liquids

“…Необходимо подчеркнуть, что добавление в соотношение (5) схемы некиральной бозонизации дополнительного члена, содержащего ρ s (−y, σ, t), не нарушает ни одного из приведенных выше правил коммутации из-за наличия множителя 2πi, при этом интеграл от плотности является просто натуральным числом. Следует также отметить, что имеются некоторые дополнительные глобальные величины, которые необходимо включить в множители C в выражении (5), чтобы убедиться, что поле со спином вверх антикоммутирует с полем со спином вниз, левая нога лестницы антикоммутирует с правой ногой (в случае одноступенчатой фермионной лестницы) и т. д. Это описано в нашей работе [14].…”

“…Этот подход, получивший название некиральная бозонизация, основан на нестандартном гармоническом анализе быстро меняющихся частей полей плотности. Он успешно применялся для расчета наиболее сингулярной части функций Грина таких систем, как кластер примесей в окрестности начала координат [9], потенциал типа лестницы с одной ступенькой [14], одна и две медленно движущиеся примеси [15] и т. д.…”

Ponderous impurities in a Luttinger liquid

“…In this work, the Green functions of a Luttinger liquid in the presence of a slowly moving heavy particle (or a pair of them) is calculated using a combination of perturbative approaches and the non-chiral bosonization method [22,23]. Using the Green function, the force acting on the heavy particle is calculated in terms of its terminal velocity, both in the linear and non-linear regime.…”