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bsc-quantic / Tenet.jl

Composable Tensor Network library in Julia
https://bsc-quantic.github.io/Tenet.jl/
Apache License 2.0
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Implement `Infinite` boundary conditions for `MatrixProduct` and `ProjectedEntangledPair` #77

Closed jofrevalles closed 11 months ago

jofrevalles commented 11 months ago

Summary

MatrixProduct and ProjectedEntangledPair currently have Open and Periodic boundary conditions. We could enhance these structs by adding the Infinite boundary condition, in which a cell-like structure is repeated infinitely many times.

mofeing commented 11 months ago

Is infinite a boundary condition? Aren't there infinite open and infinite closed boundary conditions?

jofrevalles commented 11 months ago

Is infinite a boundary condition? Aren't there infinite open and infinite closed boundary conditions?

You are correct that 'infinite' is not traditionally a boundary condition, but rather a property of the system size. When I refer to Infinite boundary conditions, I am referring to the case where our tensor network is taken to represent an infinitely repeating structure, like an infinite chain or lattice. This is used commonly in physics systems where there is translational symmetry.

In iMPS and iPEPS the concept of traditional boundary conditions, such as Open or Periodic, does not directly apply because of the infinite nature of these systems. However, they inherently possess a sort of periodicity due to the translational symmetry of the infinite system. So, while Infinite might not be a boundary condition in the classical sense, I think it holds a specific and significant meaning in the case of Tensor Networks. Also, I have seen a lot of TN libraries use this notation of Open, Periodic or Infinite boundary conditions.

mofeing commented 11 months ago

Okay. Thanks for the explanation!

Then yes, it makes sense to me that Infinite <: Boundary.