Questions tagged [berry-pancharatnam-phase]
The phase difference acquired over the course of a closed loop which results from the geometrical properties of the parameter space of the Hamiltonian.
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Berry phases in closed timelike curves
Does anyone know what the physical significance of a Berry phase induced by parallel transport around a closed timelike curve would be? There is a preprint from 1994 describing that parallel transport ...
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How to verify the compatibility condition for Berry's connection?
I am reading Mikio Nakahara's Geometry, Topology and Physics. In Chapter 10, he defines the Berry's connection one-form on the $U(1)$ bundle as
$$
\mathcal{A}=\left\langle\mathbf{R}\right|d\left|\...
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Derivation of Berry Phase
I'm learning about Berry phase for a presentation and am working through Berry's original paper.
I can't quite make the connection between equation 4
$$
\dot{\gamma}(t) = i \langle n(\vec{R}) |\...
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Is the Berry phase at a degeneracy trivial or non-trivial?
This question is about the original paper on Berry phases by M. Berry (1984). There, the Berry phase $\phi_{B}$ is defined as
$$
\phi_{B}= \oint_\mathcal{C}\underbrace{ \left\langle n(\mathbf{R}) \...
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Divergence of the Berry connection
Given the Berry connection
\begin{equation}
\boldsymbol{\mathcal{A}}(\mathbf{R}) = i \langle u(\mathbf{R}) | \nabla_\mathbf{R} | u(\mathbf{R}) \rangle,
\end{equation}
the Berry curvature can be ...
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Can the derivative of a gauge-invariant quantity be gauge-dependent?
I am wondering whether it is possible for derivatives of a gauge-invariant quantity to be gauge-dependent. Certainly, the converse is true; taking the curl of a gauge-dependent quantity (the vector ...
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Gauge constraint in the definition of the $\mathbb{Z}_2$ invariant
Cross-posted at MMSE.
In Fu and Kane's paper from 2006, the authors define the $\mathbb{Z}_2$ invariant for time-reversal invariant topological insulators as an obstruction to Stoke's theorem,
$$
\...
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Does the total Zak phase always sum to zero?
In 2D, the sum of the Chern numbers over all bands is zero. However, this result relies on the ability to define a Berry curvature, which is only possible in $d \geq 2$ dimensions. In 1D it is ...
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Can you evaluate the Berry phase integral? [closed]
This is my first post. Can anyone simplify the integral in eq(8.16) in the picture. How the integral is evaluated ? How the sign function came to the scenarion? The pic taken from the book "...
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Deriving the non-abelian Berry connection
I'm slightly confused about a manipulation in Section 1.5.4 of Tong's notes on the Quantum Hall Effect.
This concerns the derivation of the non-abelian Berry phase.
Setup:
We have an $N$-dimensional ...
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Non-abelian Berry connection : clashing time-ordering conventions, and component-wise form
Let $\mathcal{M}$ be a $k$-dimensional parameter space associated to a quantum system with an $N$-dimensional ground state. As usual, we assume the system is subject to some adiabatic tuning of ...
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Gauge freedom issues when numerically calculating overlap of states
Calculations of quantities of the form:
$$\langle\psi(k)|\partial_k|\psi(k) \rangle \ ,$$
require a smooth choice of the wave function $|\psi(k)\rangle$ over the whole BZ. This is not a problem. ...
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Strange manipulation of Hamiltonian operator and gradient
I'm reading M. V. Berry's Quantal Phase Factors Accompanying Adiabatic Changes and came across an unfamiliar identity in eq. (8), namely $\langle m | \nabla _Rn \rangle = \frac{\langle m | \nabla_R \...
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How can I calculate this equation if we know that there is non zero Berry-phase between the valence and conduction band
The geometric phase can be interpreted as a Berry curvature in the momentum space. My guess is $(q^2+\text{Berry-phase}/\text{lattice constant}^2)/\text{direct gap}$.
$$\langle\psi_{n',\mathbf{k}+\...
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Calculating the Berry potential: Questions
[Reference: Modern Quantum Mechanics, J.J. Sakurai, Chapter 5]
The Berry potential is defined by,
$$ \mathbf{A}_{n} (\mathbf{R}) \ = \ i \langle n | \mathbf{\nabla}_{\mathbf{R}}|n\rangle$$
Here, $\...
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