28,838 research outputs found
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
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