Refactor _step_hotrg(3d)_x(y)

[Yue-Zhengyuan]

This PR refactors the functions _step_hotrg(3d)_x(y) by moving the part to find the projectors out of them, so they can be reused by impurity HOTRG (motivated by #105).

[Yue-Zhengyuan]

@VictorVanthilt I now tend to believe that the macOS test failure (again on the accuracy of Ising scaling dimension) is caused by Julia 1.12. Maybe you can follow other QuantumKitHub packages to set up test with the LTS version (currently it is 1.10.10) of Julia?

[VictorVanthilt]

We had issues like this before, where mac os was actually the only one not failing. There is some difference in between apple silicon and intel/amd chips when it comes to floating point arithmetic. Previously it was showing up because we were dividing really small (on the order of machine precision) numbers.

I will add testing with LTS to the test suite to check if it is indeed a julia 1.12 issue.

[Yue-Zhengyuan]

Before that let's refrain from merging master into this branch.

[VictorVanthilt]

#108

[Adwait-Naravane]

I think this _get_hotrg_projector() function needs to be generalised at some point to allow for different algorithms to construct projectors like in the anisotropic case, using QR decompositions to construct oblique projectors (like in appendix A of the Boundary TRG paper).

[VictorVanthilt]

Can you merge the TNRKit master branch into this one, then I can merge this.

[Yue-Zhengyuan]

Considering @Adwait-Naravane's comment, should we rename BTRG to BwTRG to avoid ambiguity? (Bond-weighted vs boundary)

[VictorVanthilt]

The Boundary TRG paper was first (2019) at calling their method BTRG, the Bond-weighted TRG paper also calls their method BTRG but only did so in 2020.

So @dartsushi, what do you think?
I suggest that if we implement the Boundary Tensor Renormalization Group:

• We use BWTRG for what is now called BTRG in TRNKit.
• We call Boundary Tensor Renormalization Group BoundaryTRG

For now keeping BTRG as is okay for me.

[dartsushi]

I believe people refer to Bond-weighted TRG as BTRG more often nowadays. I would like to call this the other as BoundaryTRG and keep BTRG as it is

[VictorVanthilt]

Okay thanks!