Positional Challenges and Advantages of a PhD Student Researching the PhD

It is fairly uncommon for a PhD student to conduct a study that looks at PhD education, and this paper discusses the challenges and advantages of my experience as a PhD student in conducting a PhD research about the PhD. This PhD research project was not an action research or self-reflective of my own educational journey. In this paper, I identify the challenges concerning my position as both a PhD student and a researcher exploring the educational processes of the PhD, and illustrate the ways I adopted to overcome these challenges. I also point out that having addressed these challenges; there are advantages due to the concurrent position of being a PhD student and a researcher that contributed to the development of new knowledge in the field of PhD education

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