From 1039fc2231bca8edf8c340875359e9cf07efd61a Mon Sep 17 00:00:00 2001 From: Jutho Haegeman Date: Thu, 3 Sep 2020 17:20:42 +0200 Subject: [PATCH] final docs additions before tagging? --- docs/src/man/tensors.md | 19 +++++++++++++------ 1 file changed, 13 insertions(+), 6 deletions(-) diff --git a/docs/src/man/tensors.md b/docs/src/man/tensors.md index 433be7b5..a5cc732e 100644 --- a/docs/src/man/tensors.md +++ b/docs/src/man/tensors.md @@ -333,16 +333,23 @@ for (c,b) in blocks(t3) println() end ``` -To construct the proper `data`, one has to know where to find each sector in the range -`1:dim(V)` of every index `i` with associated space `V`, as well as the internal structure -of the representation space when the corresponding sector `c` has `dim(c)>1`, i.e. in the -case of `FusionStyle(c) isa NonAbelian`. Currently, the only non-abelian sectors are -`Irrep[SU₂]` and `Irrep[CU₁]`, for which the internal structure is the natural one. +Hence, we recognize that the Heisenberg interaction has eigenvalue ``-1`` in the coupled +spin zero sector (`SUIrrep(0)`), and eigenvalue ``+1`` in the coupled spin 1 sector +(`SU2Irrep(1)`). Using `Irrep[U₁]` instead, we observe that both coupled charge +`U1Irrep(+1)` and `U1Irrep(-1)` have eigenvalue ``+1``. The coupled charge `U1Irrep(0)` +sector is two-dimensional, and has an eigenvalue ``+1`` and an eigenvalue ``-1``. + +To construct the proper `data` in more complicated cases, one has to know where to find +each sector in the range `1:dim(V)` of every index `i` with associated space `V`, as well +as the internal structure of the representation space when the corresponding sector `c` has +`dim(c)>1`, i.e. in the case of `FusionStyle(c) isa NonAbelian`. Currently, the only non- +abelian sectors are `Irrep[SU₂]` and `Irrep[CU₁]`, for which the internal structure is the +natural one. There are some tools available to facilate finding the proper range of sector `c` in space `V`, namely `axes(V, c)`. This also works on a `ProductSpace`, with a tuple of sectors. An example -```julia +```@repl tensors V = SU2Space(0=>3, 1=>2, 2=>1) P = V ⊗ V ⊗ V axes(P, (SU2Irrep(1), SU2Irrep(0), SU2Irrep(2)))