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JerryChen97 / KitaevLadder

Using TeNPy to simulate Kitaev Ladders. This will be part of my PSI essay work.
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TODO: Phase Diagram #12

Open JerryChen97 opened 4 years ago

JerryChen97 commented 4 years ago

Plot the phase diagram of the Kitaev ladder

JerryChen97 commented 4 years ago

Plan A:

Considering that Jx and Jy are actually equivalent to each other, we can just fix one of them, e.g. Jx = 1. Then, we will vary Jy and Jz in some certain areas, e.g. [-2, 2] * [-2, 2].

Plan B:

Or we can just follow the convention of Kitaev to plot the phase diagram on the plane Jx+Jy+Jz=1.

@aaronszasz which one do you prefer?

aaronszasz commented 4 years ago

I like Plan A personally. You can always plot it in the style of Plan B later.

JerryChen97 commented 4 years ago

I like Plan A personally. You can always plot it in the style of Plan B later.

Cool I will start with Plan A

JerryChen97 commented 4 years ago

I like Plan A personally. You can always plot it in the style of Plan B later.

I just reconsidered this choice: since the Hamiltonian for our Kitaev ladder is scalable (Jx, Jy, and Jz are of the same dimension), actually working with the plane Jx+Jy+Jz=1 will reflect more information of the phase diagram. What do you think of this argument? @aaronszasz

aaronszasz commented 4 years ago

The problem is, I'm not really sure what Plan B actually entails. You need a two-parameter parametrization of the Jx+Jy+Jz plane, and fixing Jx = constant seems like a reasonable one. Setting it to 1 is also fine, because you can just correct the energy later to put it on the desired plane.

JerryChen97 commented 4 years ago

The problem is, I'm not really sure what Plan B actually entails. You need a two-parameter parametrization of the Jx+Jy+Jz plane, and fixing Jx = constant seems like a reasonable one. Setting it to 1 is also fine, because you can just correct the energy later to put it on the desired plane.

Hmmm indeed this is also true.

JerryChen97 commented 4 years ago

Actually now I am trying mapping the parameters onto the unit sphere so that not only it can faithfully keep all the information we want but also the implementation is very easy and convenient.