All Questions
27
questions
3
votes
1
answer
166
views
Is there a Majorana representation for toric code
Kitaev's toric code is known to be the Z2 gauge field theory, which suggests that there might exists a Majorana representation for the toric code, e.g., Majorana + Z2 gauge field. Hence, I wonder if ...
- 81
3
votes
0
answers
75
views
Infinite stacking of integer quantum Hall systems
Let us consider a (3+1)-dimensional system $\mathcal{H}$ constructed by stacking (2+1)-dimensional integer quantum Hall systems $\mathcal{H}_\text{Hall}$, e.g., $E_8$ bosonic systems (or $\sigma_H=1$ ...
- 813
3
votes
1
answer
242
views
Topological phase and Chern number
the relation between topological phase and Chern numbers is unclear to me.
For Haldane model if the Chern numbers of its two bands go from (+1,-1) to (0,0), we say that it goes from topological phase ...
- 41
0
votes
0
answers
68
views
Absence of topology in semi-dirac materials
Good morning everybody, I am facing a problem when calculating the topological invariant in a semi-dirac system, whose Hamiltonian is:
$$
H=k_x^2\sigma_x+k_y\sigma_y
$$
My question is that this ...
4
votes
2
answers
267
views
Why are topological materials/phases "exotic"?
From what I understand, when a system has topological order, any local perturbation doesn't change the phases and thus its properties. This would suggest that it should be really easy to find ...
- 423
1
vote
1
answer
84
views
Why number of left-moving and right-moving edge states on a finite lattice system is equal?
I read an arguments about number of left-movers and right-mover in finite system in paper titled as
Antichiral Edge States in a Modified Haldane Nanoribbon. In second paragraph of introduction, it ...
- 337
1
vote
1
answer
256
views
How to describe SSH chain with odd number of sites?
Usually when we discuss SSH(Su-Schrieffer–Heeger) chain, we discuss a chain with 2N atoms, with v the intra-cell coupling and w the inter-cell coupling. When N is infinite, the system becomes bulk, ...
- 442
0
votes
2
answers
332
views
What does "continuous transformation" mean with regard to the Hamiltonian of a system?
When dealing with topological phases of matter (topological insulators, quantum hall effect, etc...) one says that the system remains in the same phase as long as any continuous transformation of the ...
- 423
5
votes
1
answer
473
views
About Chern insulator
I know when we talk about Insulator, U(1)charge symmetry naturally exists.
But in this article:Quantum phase transitions of topological insulators without gap closing, the author claims that:
"...
- 61
1
vote
1
answer
82
views
Why topologically non-trivial materials are robust againist any external perturbations or defects?
Topologically non-trivial materials are insensitive to perturbations or defects. How can I prove it mathematically?
I thought of making the first-order perturbation term zero.
$$\left< \psi \right|...
- 1,348
4
votes
1
answer
200
views
Bosonic SPT phases with time reversal and a $Z_2$ symmetry
Consider a bosonic system with time reversal symmetry $\mathcal{T}$ and a unitary on-site $\mathbb{Z}_2$ symmetry. Suppose the symmetry is realized in a special way such that $$\mathcal{T}^2= (-1)^B$$ ...
- 407
1
vote
1
answer
232
views
Alternatives for calculating topological invariants in topological materials
My questing is regarding the different alternatives for calculating topological invariants in topological materials protected by symmetry, specially time-reversal invariant topological insulators, ...
3
votes
1
answer
146
views
Experimental confirmation of Majorana modes in Kitaev chain
I'm confused about majorana modes at the edge of Kitaev chain, what do we seek in experiment? When we first define this one we write the creation and annihilation operators as:
$$a^{+}=\frac{1}{2}(\...
- 341
6
votes
1
answer
236
views
Topological materials and fractionalized excitations
I've been told several times that topological materials (such topological insulators) must have "fractionalized" excitations. Equivalently, if a material does not have fractionalized excitations, it ...
- 225
1
vote
0
answers
29
views
Linking phase of flux lines and excitation energy of monopole
I am reading this paper and on the left-hand side of pp.10 it states the following relation between linking phase and excitation energy of monopole:
Now the $\theta = \pi$ term in the bulk implies ...
- 351