HQT's Home Page

I started my doctoral study on the fractional quantum Hall (FQH) effect at about the same time the modern understanding of conformal Hilbert space started to materialize. A key idea of this approach is that quasihole excitations of a certain FQH phase serves as the fundamental degrees of freedom (DOF) describing all of its physics. "Fundamental DOF" is meant that within the low-energy manifold the quasiholes are the smallest indivisible (quasi)particle - to resolve it in more details requires going to higher energies. While this is the same starting point as most field theories, our aim is not to write down an effective theory by plain "guess work", but to establish a direct connection between the microscopic picture of interactions within the many-body system to the behavior of these emergent DOF.

My current interest lies in theoretical and experimental aspects of non-Abelian anyons, in particular Majorana fermions and Fibonacci anyons. Of course, I am most comfortable talking about them in the context of FQH effect, but I also try to learn about their manifestation on platforms like spin chains or topological superconductor. Some theoretical questions include how non-Abelian anyon emerges from electron density waves in a two-dimensional electron gas (2DEG), the algebraic relationship between Abelian and non-Abelian CHS, and formulation of a non-Abelian spin-statistics relation. Interesting and important experimental aspects include understanding and exploiting anyon dynamics to design a stable non-Abelian braiding scheme. Recent conversations with a colleague also got me interested in thermalization properties of anyon systems, but that will be the topic for another time.

I write most of the numerical routines used in my research. There are also other people's codes that I have rewritten after the initial project with it was done. My general goal is to organize the routines in a modular way that makes sense to me. In my PhD years I have written two libraries for FQH research (one in Python and one in Julia) that have been enjoyed by several people. Working with microscopic models also means I get to make use of visualization tools to make abstract concepts seem more tangible, such as the plot of two degenerate states of four Moore-Read anyons seen in the figure on the left. All my codes are available publicly on my Github repositories. Should you want to learn to use them, please contact me directly as I am horrible at keeping documentaries.