Quantum Impurity in Luttinger Liquid: Universal Conductance with Entanglement Renormalization

We study numerically the universal conductance of Luttinger liquids wire with a single impurity via the Muti-scale Entanglement Renormalization Ansatz (MERA). The scale invariant MERA provides an efficient way to extract scaling operators and scaling dimensions for both the bulk and the boundary conformal field theories. By utilizing the key relationship between the conductance tensor and ground-state correlation function, the universal conductance can be evaluated within the framework of the boundary MERA. We construct the boundary MERA to compute the correlation functions and scaling dimensions for the Kane-Fisher fixed points by modeling the single impurity as a junction (weak link) of two interacting wires. We show that the universal behavior of the junction can be easily identified within the MERA and argue that the boundary MERA framework has tremendous potential to classify the fixed points in general multi-wire junctions.Comment: 14 pages, 18 figure

XRCC1, but not APE1 and hOGG1 gene polymorphisms is a risk factor for pterygium.

PurposeEpidemiological evidence suggests that UV irradiation plays an important role in pterygium pathogenesis. UV irradiation can produce a wide range of DNA damage. The base excision repair (BER) pathway is considered the most important pathway involved in the repair of radiation-induced DNA damage. Based on previous studies, single-nucleotide polymorphisms (SNPs) in 8-oxoguanine glycosylase-1 (OGG1), X-ray repair cross-complementing-1 (XRCC1), and AP-endonuclease-1 (APE1) genes in the BER pathway have been found to affect the individual sensitivity to radiation exposure and induction of DNA damage. Therefore, we hypothesize that the genetic polymorphisms of these repair genes increase the risk of pterygium.MethodsXRCC1, APE1, and hOGG1 polymorphisms were studied using fluorescence-labeled Taq Man probes on 83 pterygial specimens and 206 normal controls.ResultsThere was a significant difference between the case and control groups in the XRCC1 genotype (p=0.038) but not in hOGG1 (p=0.383) and APE1 (p=0.898). The odds ratio of the XRCC1 A/G polymorphism was 2.592 (95% CI=1.225-5.484, p=0.013) and the G/G polymorphism was 1.212 (95% CI=0.914-1.607), compared to the A/A wild-type genotype. Moreover, individuals who carried at least one C-allele (A/G and G/G) had a 1.710 fold increased risk of developing pterygium compared to those who carried the A/A wild type genotype (OR=1.710; 95% CI: 1.015-2.882, p=0.044). The hOGG1 and APE1 polymorphisms did not have an increased odds ratio compared with the wild type.ConclusionsXRCC1 (Arg399 Glu) is correlated with pterygium and might become a potential marker for the prediction of pterygium susceptibility