In low-dimensional systems, e.g., one-dimensional (1D) Fermi wire with proximity-induced superconductor pairings, exponential ground state degeneracy is taken as a hallmark of underlying topological phase with localized edge modes. Entanglement spectrum showing degenerate eigenvalues, and exponential decay of (electron creation operator) provide more 'confirmations' of the same. However, these criteria have been well demonstrated mostly for gapped systems.
Question: What would be some good criteria to 'recognize' topological phases in gapped number-conserving systems in low dimensions?
Some context: We explored a 1D Fermi gas with attractive interactions (Article Fermion parity gap and exponential ground state degeneracy o...
) to look for exponential degeneracy in the system, following a recipe for realizing Majorana modes in such a system (Article Topological States in a One-Dimensional Fermi Gas with Attra...
). We found the exponential degeneracy, but only in the clean system. It reduced to power-law behavior with system size in presence of local defects. This indicates that the exponential degeneracy was not robust. What could be some more concrete ways to look for robust topological phases in similar charge-conserving systems?
Dear Monalisa Singh Roy, I am a beginner self-learner of topological materials, I found this morning the following reference, that might interest you:
Preprint The layered phase of anisotropic gauge theories: A model for...
My pleasure, Dear Monalisa Singh Roy I also found the following information a month ago, that might interest you.
I was answering a question about the stabilization of magnetical phases in topological insulators. I unquote my previous answer, although is not related to invariants:
https://www.researchgate.net/post/What_is_the_role_of_2DXY-magnetism_in_the_stablization_of_topological_phase
2 physicists from MPTI and Institute for Theoretical Physics. L. Landau in Russia found recently some very interesting results concerning the physics of topological insulators and magnetic impurities *.
The researchers managed to find out how the interaction between the atoms of magnetic impurities is arranged in topological insulators. They examined the interaction of atoms with a non-zero magnetic moment when they are located near the boundary of a two-dimensional topological insulator.
I. Burmistrov together with Pavel and V. Kurilovich studied the indirect exchange interaction between manganese atoms in a two-dimensional topological insulator based on the CdTe / HgTe / CdTe quantum well. I unquote from [1,2]
- Prof. Burmistrov says, "The two atoms with magnetic moments can interact in different ways, depending on their positions: If both of them are near the edge, they behave as if they were in metal, but when both of them are situated away from the edge, they interact the way they do in a semiconductor."
- They also were able to explain the following, what makes two-dimensional topological insulators special: "In a two-dimensional topological insulator, quasiparticles move in a plane because the size-quantization energy is higher in the quantum well.
- The theoretical analysis, most importantly, resulted in the prediction of a new type of indirect exchange interaction between atoms with magnetic moments in a two-dimensional insulator.
- The interaction between pairs of magnetic atoms, one of which is near the edge and another away from it is important for further studies of the effect of magnetic atoms on the electric current along the edge of a two-dimensional topological insulator.
* https://phys.org/news/2017-07-physicists-magnetic-impurities-topological-insulators.html
https://mipt.ru/news/fiziki_izuchili_magnitnye_primesi_v_topologicheskikh_izolyatorakh