3-fold degeneracy: what is it?

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SUMMARY

The discussion centers on the concept of 3-fold degeneracy in the context of anyons and the quantum Hall Effect, specifically at a filling factor of v=1/3. Participants confirm that a 3-fold degenerate ground state indicates three distinct quantum states that share the same energy level. This phenomenon is analogous to the energy levels of the hydrogen atom, where multiple magnetic quantum numbers correspond to the same energy for a given angular momentum quantum number. The conversation also highlights the need for beginner-friendly resources on topological quantum computing (TQC).

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly degeneracy.
  • Familiarity with anyons and their role in quantum Hall systems.
  • Basic knowledge of topological quantum computing (TQC).
  • Awareness of quantum numbers and their significance in atomic physics.
NEXT STEPS
  • Research the concept of anyons in quantum mechanics.
  • Study the quantum Hall Effect, focusing on filling factors and their implications.
  • Explore topological quantum computing (TQC) resources for beginners.
  • Learn about quantum degeneracy and its applications in various physical systems.
USEFUL FOR

Students and researchers in quantum physics, particularly those interested in anyons, the quantum Hall Effect, and topological quantum computing. This discussion is beneficial for anyone seeking to deepen their understanding of quantum degeneracy and its implications in modern physics.

gioialorusso
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Hi everybody,
I apologize for my trivial question, I'm reading a paper by Freedman and Kitaev and, when describing anyons and quantum Hall Effect with v=1/3, they say that "the ground state of electron liquid on the torus is 3-fold degenerate". What is the meaning? It means that there are 3 levels with the same energy? I'm sorry, I'm italian and sometimes it's hard to understand english math words.
Is there any paper you would suggest me on TQC for beginners?
Thank you so much,
best regards,
Gioia
 
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Hi Gioia, I'm from Italy too (I think I must however answer in English). However I'm not an expert in anyons, but usually when someone speak about a n-fold degenerate ground state it means exactly what you said. It means that there are n states that have the same energy.
It's the same thing that happen, for example, in hydrogen atom when, for any given value of the quantum number L you have many values of m (between -L and L) that share the same energy.
I hope I haven't writter stupid things.

Einj
 
Thank you so much, Einj.

Gioia
 

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