All Questions
Tagged with berry-pancharatnam-phase curvature
18
questions
1
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0
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87
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What is natural about the Berry connection?
So I asked a similar question here and even though I still believe it's a valid question, the formulation may have been a bit too complicated to pique people's interest, so let me try to break it up ...
- 2,123
1
vote
0
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62
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Concise formulation of Berry phase as holonomy of "natural" connection
I've been trying to understand the Berry phase (abelian/non-abelian) as the holonomy of some "natural connection". I almost have all the pieces together, but there are a few parts that are a ...
- 2,123
1
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0
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65
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How does the fiber bundle perspective on geometric phase lead to a certain connection one-form?
I'm trying to understand why the relevant connection one-form when calculating geometric phase in quantum systems is
$$\mathcal{A}_\psi(X):=i \text{Im}\langle \psi | X\rangle.$$
Set-up: I'll set the ...
- 123
2
votes
0
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168
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How can i calculate the Berry Curvature for the Dirac points in Haldane graphene?
I want to calculate the berry curvature at the Dirac points in graphene with complex next nearest hopping (haldane model) in order to show that it is non-zero at the dirac points and use it to compute ...
3
votes
3
answers
672
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‘Proof’ that non-Abelian Berry phase vanishes identically
For a degenerate system with Hamiltonian $H =H(\mathbf{R})$ and eigenstates $\left|n(\mathbf{R})\right\rangle$ the non-Abelian Berry connection is
$$A^{(mn)}_i=\mathrm{i}\left\langle m|\partial_in\...
- 2,157
0
votes
2
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738
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Berry Curvature
Can I ask two questions about the Berry curvature? The formula for the berry curvature is written below.
$$\Omega_n (k) = -Im \langle \bigtriangledown_k u_{nk} | \times | \bigtriangledown_k u_{nk} \...
- 173
1
vote
1
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234
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Curl of Berry connection
If $|n\rangle=|n( \textbf{R}(t) ) \rangle $ satisfies the equation $$H(\textbf{R}(t))|n(\textbf{R}(t)) \rangle = E_{n}(\textbf{R}(t))|n(\textbf{R}(t))\rangle$$ then the berry phase $\gamma_{n}(t)$ ...
- 13
0
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0
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177
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Berry curvature vanishes in TRS system
In spin 1/2 system with TR symmetry , the Berry curvature must vanish. Because Berry curvature is odd. How to prove it?
\begin{equation}
\langle\partial_{-k_x}u^{I}(-k)|\partial_{-k_y}u^{I}(-k)\rangle-...
- 1
8
votes
2
answers
607
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Numerical Berry curvature for bosons
I am trying to numerically compute the Berry Curvature for a generic quadratic Bosonic Hamiltonian of the form $$H = \sum_{ij} A_{ij} b_{i}^\dagger b_j + \frac{1}{2} \sum_{ij}\left( B_{ij} b_i b_j + \...
user138458
1
vote
1
answer
93
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What is the logic connection between these two statements?
What is the connection between these two statements:
the berry curvature change sign under time-reversal operation
If the system has the time-reversal symmetry, then berry curvature is odd in k.
...
- 6,095
3
votes
1
answer
4k
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Numerical Calculation of Berry Curvature
I am trying to calculate some berry curvature (BC) in a 2D lattice and I have some things I am getting lost with.
In the 2D lattice, we set up the eigenvalue problem $H|u_1\rangle = \epsilon_i|u_i\...
- 1,788
3
votes
2
answers
1k
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Derivation of the Berry Curvature and Bloch Magnetic Moment in Graphene
(I found a workable solution, skip to the "Solution" part to see it) I am attempting to derive equations 2 and 6 from Xiao et al. paper "Valley contrasting physics in graphene" (...
- 63
1
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1
answer
467
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Is it possible understand Berry curvature as Gaussian curvature in some limit?
I would like to understand the Berry curvature and the Chern number from mathematical geometry-topology.
I understand that in electronic QHE, there is a map from $k^2$ to a vector space where the ...
- 13
2
votes
1
answer
514
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Berry phase covariant derivative
I have been studying some simple examples of the covariant derivative for 2D surfaces and the way that it is constructed is by taking the usual derivative in the 3D Euclidean space at a point $p$ on ...
- 105
1
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0
answers
394
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Why gauge-invariant Berry curvature commutator looks like torsion?
The Berry Curvature is defined as (for invariant gauge transformations)
$$F_{ij} = [\partial_i, A_j] - [\partial_j,A_i] + [A_i,A_j]$$
The gauge covariance satisfies the transformation
$$A_i \...
- 606
6
votes
1
answer
1k
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Berry Curvature and Curvature Tensor
When the curvature tensor (from Einstein's theory) has a non-zero torsion, it is said to be an antisymmetric tensor in the last two indices composed of the connections of the field. Alternatively, the ...
- 606
8
votes
1
answer
2k
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Derivation of expression for Berry curvature
Many texts quote the expression for the Berry curvature for a two-level system, with Hamiltonian $\mathbf{h}(\mathbf{k})=(h_x,h_y,h_z)$ in terms of $\mathbf{k}=(k_x,k_y)$, as something like
\begin{...
- 419
7
votes
1
answer
2k
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Detail of deriving Berry Curvature From Berry Connection
The Berry curvature of the $n^{\mathrm{th}}$ eigenstate of Hamiltonian $H$ for the vector of external parameters $\vec{R}$ can be derived in part by writing the following two lines:
$$
B^n(\vec{R}) \...
- 101