The quantum steeplechase

Abstract

Quantum Steeplechase is the study of a Luttinger liquid (LL) in one dimension in the presence of a finite number of barriers and wells clustered around an origin. The powerful non-chiral bosonization technique (NCBT) is introduced to write down closed formulas for the two-point functions in the sense of the random phase approximation (RPA). Unlike g-ology based methods that are tied to the translationally invariant, free particle basis, the NCBT explicitly makes use of the translationally non-invariant single particle wavefunctions. The present method that provides the most singular part of the asymptotically exact Green function in a closed form, is in contrast to competing methods that require a combination of renormalization group and/or numerical methods in addition to the bosonization techniques. arXiv:1608.05826v5 [cond-mat.str-el]

Transport properties of a Luttinger liquid with a cluster of impurities

“…For an asymmetric double delta system, V (x) = V 1 δ(x + a) + V 2 δ(x − a), the anomalous exponents can be calculated using NCBT. The form of the exponents are the same as given in Appendix A but the expression of the reflection amplitude is now different and is given by (here ξ 0 = 2k F a) [8].…”

Conductance of inhomogeneous Luttinger liquids with a finite bandwidth

“…The transcendental equation given by the equation (12) and expression of the exponent η(τ ) given by equation (13) remains the same upon inclusion of backward scattering interactions between fermions. The difference comes in the expression of the holon velocity v h (note that g = v F /v h ), which is now modified to include the effect of backward scattering.…”

“…As temperature is further increased the strength of interactions has to be decreased for a more favorable comparison. The central equation of finite bandwidth conductance of Matveev et al valid for weak interactions as given by equation (14) can actually be obtained by considering the weak interaction limit of the transcendental equation (12) obtained using NCBT which is valid for any strength of interactions. Setting y = k B T D0 , equation (12) reads as follows.…”

“…It has been observed from the earlier plots that with an increase in temperature, conductance typically decreases for attractive interactions and increases for repulsive interactions. This is because the exponent η in equation (12) is typically positive for repulsive cases and negative for attractive cases. But in absence of interactions (g =1), the exponent η vanishes and the conductance becomes independent of temperature and is given by…”

“…[2,10,11] Transport and other physical properties of quantum systems can be studied if one is in possession of closed analytical expressions of the Green functions of such systems. To this end, a recently developed technique called non-chiral bosonization is employed here that yields the most singular part of the asymptotic Green functions of strongly inhomogeneous Luttinger liquids with arbitrary strengths of impurities as well as that of interactions [12]. The same method also yields the Green functions of a one * gsetlur@iitg.ernet.in step fermionic ladder system comprising two Luttinger liquids placed parallel to each other with a finite probability of hopping of electrons between a pair of opposing points [13].…”