Add option to use full-infinite (4x4) environment in CTMRG

[Yue-Zhengyuan]

In the supplemental material of arXiv 1402.2859, it is stated that using half-infinite (2 x 4) environment to find projectors in CTMRG is "less accurate":

A computationally cheaper variant of this (but less accurate) is to compute the QR decomposition shown in Fig. 1(b) only based on the upper left corner (made of 4 tensors), and lower left corner (made of 4 tensors), instead of the upper and lower half of the 4 × 4 network.

Although #73 claims that full-infinite (4 x 4) environment can be less stable for differentiation, in full update (involving only the forward pass) it can still be a useful option. I suggest the following changes:

• Add an attribute half_infinite::Bool to struct CTMRG;
• The 4x4 environments can be obtained by further contracting QQ with two more enlarged corners in the function ctmrg_projectors in src/algorithms/ctmrg.jl. Alternatively, you can also write a lot of overloaded fullinfinite_environment functions, but I'm not sure this approach is better for future maintenance...

[lkdvos]

Hi Yue,
This is definitely a good idea. We had some pre-planning on how we would like to achieve something like this, utilizing the projector_alg defined here. The idea would be that we define a separate "full" from the "half" struct, on which we can then specialize.

[Yue-Zhengyuan]

Thanks! I’ll try to implement the “full” version recently and make a PR. I notice that the construction of half-infinite environments has been almost completely rewritten since v.0.2.2, and my previous code does not fit the new format any more; maybe it is better to let @pbrehmer continue the work?

[pbrehmer]

Thank you for the idea. I will try to add full-infinite environment projectors in the coming days. I should be able to get the PR done by the end of this week (hopefully) :)

[pbrehmer]

This is now merged into master with #99. Feel free to try this out @Yue-Zhengyuan!