In second quantization one the Particle hole trasnformation is defined as ˆCˆψAˆC−1=∑BU∗†A,Bˆψ†BˆCˆψ†AˆC−1=∑BˆψBU∗B,AˆCiˆC−1=+i
Source: Topological phases: Classification of topological insulators and superconductors of non-interacting fermions, and beyond Equation 17
Sunday, 25 June 2017
quantum mechanics - Particle hole symmetry in 2nd quantization
And if in a 2nd quantized Fermionic Hamiltonian (ˆH) Particle Hole symmetry is present then ˆCˆHˆC−1=ˆH
I want to see what this equation means in single particle basis. In single particle basis I can write the 2nd quantized Hamiltonian (ˆH) as ˆH=∑A,Bˆψ†AHA,BˆψB
Here the matrix H is the Hamiltonian in single particle basis. Now, with the transformation rules on should get UH∗U†=−H
In the single-particle basis. But what I am getting using the transformation rules is U∗HU∗†=−H
Now I have started to think whether the transformation rules given here are right or not. I wanted to know if the transformation rule or my calculation is wrong.
Subscribe to:
Post Comments (Atom)
Understanding Stagnation point in pitot fluid
What is stagnation point in fluid mechanics. At the open end of the pitot tube the velocity of the fluid becomes zero.But that should result...
-
I have an hydrogenic atom, knowing that its ground-state wavefunction has the standard form ψ=Ae−βrwith $A = \frac{\bet...
-
At room temperature, play-dough is solid(ish). But if you make a thin strip it cannot just stand up on it's own, so is it still solid? O...
-
Sometimes I am born in silence, Other times, no. I am unseen, But I make my presence known. In time, I fade without a trace. I harm no one, ...
-
I want to know what happens to the space a black hole crosses over as our galaxy travels through space.
-
I'm sitting in a room next to some totally unopened cans of carbonated soft drinks (if it matters — the two affected cans are Coke Zero...
-
Small vessels generally lean into a turn, whereas big vessels lean out. Why do ships lean to the outside, but boats lean to the inside of a ...
-
What exactly are the spikes, or peaks and valleys, caused by in pictures such as these Wikipedia states that "From the point of view of...
No comments:
Post a Comment