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{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2024-12-12T02:03:20","documenter_version":"1.8.0"}}
{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2024-12-13T19:29:53","documenter_version":"1.8.0"}}
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Springer Science &amp; Business Media.</code></pre></li><li class="footnote" id="footnote-kitaev"><a class="tag is-link" href="#citeref-kitaev">kitaev</a><pre><code class="nohighlight hljs"> Kitaev, A. (2006). Anyons in an exactly solved model and beyond.
Annals of Physics, 321(1), 2-111.</code></pre></li><li class="footnote" id="footnote-beer"><a class="tag is-link" href="#citeref-beer">beer</a><pre><code class="nohighlight hljs"> From categories to anyons: a travelogue
Kerstin Beer, Dmytro Bondarenko, Alexander Hahn, Maria Kalabakov, Nicole Knust, Laura Niermann, Tobias J. Osborne, Christin Schridde, Stefan Seckmeyer, Deniz E. Stiegemann, and Ramona Wolf
[https://arxiv.org/abs/1811.06670](https://arxiv.org/abs/1811.06670)</code></pre></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../tutorial/">« Tutorial</a><a class="docs-footer-nextpage" href="../spaces/">Vector spaces »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Thursday 12 December 2024 02:03">Thursday 12 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
[https://arxiv.org/abs/1811.06670](https://arxiv.org/abs/1811.06670)</code></pre></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../tutorial/">« Tutorial</a><a class="docs-footer-nextpage" href="../spaces/">Vector spaces »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Friday 13 December 2024 19:29">Friday 13 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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FusionTree{Irrep[SU₂]}((1/2, 1/2, 1/2, 1/2, 1/2), 1/2, (true, false, false, true, false), (1, 1/2, 0))
FusionTree{Irrep[SU₂]}((1/2, 1/2, 1/2, 1/2, 1/2), 1/2, (true, false, false, true, false), (0, 1/2, 1))
FusionTree{Irrep[SU₂]}((1/2, 1/2, 1/2, 1/2, 1/2), 1/2, (true, false, false, true, false), (1, 1/2, 1))
FusionTree{Irrep[SU₂]}((1/2, 1/2, 1/2, 1/2, 1/2), 1/2, (true, false, false, true, false), (1, 3/2, 1))</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; iter = fusiontrees(ntuple(n-&gt;s, 16))</code><code class="nohighlight hljs ansi" style="display:block;">TensorKit.FusionTreeIterator{SU2Irrep, 16, NTuple{16, Tuple{SU2Irrep}}}(((Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),)), Irrep[SU₂](0), (false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false))</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; sum(n-&gt;1, iter)</code><code class="nohighlight hljs ansi" style="display:block;">1430</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; length(iter)</code><code class="nohighlight hljs ansi" style="display:block;">1430</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; @elapsed sum(n-&gt;1, iter)</code><code class="nohighlight hljs ansi" style="display:block;">0.06184278</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; @elapsed length(iter)</code><code class="nohighlight hljs ansi" style="display:block;">4.6897e-5</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; s2 = s ⊠ s</code><code class="nohighlight hljs ansi" style="display:block;">Irrep[SU₂ × SU₂](1/2, 1/2)</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; collect(fusiontrees((s2,s2,s2,s2)))</code><code class="nohighlight hljs ansi" style="display:block;">4-element Vector{FusionTree{ProductSector{Tuple{SU2Irrep, SU2Irrep}}, 4, 2, 3}}:
FusionTree{Irrep[SU₂]}((1/2, 1/2, 1/2, 1/2, 1/2), 1/2, (true, false, false, true, false), (1, 3/2, 1))</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; iter = fusiontrees(ntuple(n-&gt;s, 16))</code><code class="nohighlight hljs ansi" style="display:block;">TensorKit.FusionTreeIterator{SU2Irrep, 16, NTuple{16, Tuple{SU2Irrep}}}(((Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),), (Irrep[SU₂](1/2),)), Irrep[SU₂](0), (false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false))</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; sum(n-&gt;1, iter)</code><code class="nohighlight hljs ansi" style="display:block;">1430</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; length(iter)</code><code class="nohighlight hljs ansi" style="display:block;">1430</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; @elapsed sum(n-&gt;1, iter)</code><code class="nohighlight hljs ansi" style="display:block;">0.052836663</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; @elapsed length(iter)</code><code class="nohighlight hljs ansi" style="display:block;">4.1907e-5</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; s2 = s ⊠ s</code><code class="nohighlight hljs ansi" style="display:block;">Irrep[SU₂ × SU₂](1/2, 1/2)</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; collect(fusiontrees((s2,s2,s2,s2)))</code><code class="nohighlight hljs ansi" style="display:block;">4-element Vector{FusionTree{ProductSector{Tuple{SU2Irrep, SU2Irrep}}, 4, 2, 3}}:
FusionTree{Irrep[SU₂ × SU₂]}(((1/2, 1/2), (1/2, 1/2), (1/2, 1/2), (1/2, 1/2)), (0, 0), (false, false, false, false), ((0, 0), (1/2, 1/2)))
FusionTree{Irrep[SU₂ × SU₂]}(((1/2, 1/2), (1/2, 1/2), (1/2, 1/2), (1/2, 1/2)), (0, 0), (false, false, false, false), ((1, 0), (1/2, 1/2)))
FusionTree{Irrep[SU₂ × SU₂]}(((1/2, 1/2), (1/2, 1/2), (1/2, 1/2), (1/2, 1/2)), (0, 0), (false, false, false, false), ((0, 1), (1/2, 1/2)))
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0.618034 0.786151
0.786151 -0.618034</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; Fτ&#39;*Fτ</code><code class="nohighlight hljs ansi" style="display:block;">2×2 Matrix{Float64}:
1.0 0.0
0.0 1.0</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; polar(x) = rationalize.((abs(x), angle(x)/(2pi)))</code><code class="nohighlight hljs ansi" style="display:block;">polar (generic function with 1 method)</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; Rsymbol(τ,τ,𝟙) |&gt; polar</code><code class="nohighlight hljs ansi" style="display:block;">(1//1, 2//5)</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; Rsymbol(τ,τ,τ) |&gt; polar</code><code class="nohighlight hljs ansi" style="display:block;">(1//1, -3//10)</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; twist(τ) |&gt; polar</code><code class="nohighlight hljs ansi" style="display:block;">(1//1, -2//5)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../spaces/">« Vector spaces</a><a class="docs-footer-nextpage" href="../tensors/">Tensors and the <code>TensorMap</code> type »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Thursday 12 December 2024 02:03">Thursday 12 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
0.0 1.0</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; polar(x) = rationalize.((abs(x), angle(x)/(2pi)))</code><code class="nohighlight hljs ansi" style="display:block;">polar (generic function with 1 method)</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; Rsymbol(τ,τ,𝟙) |&gt; polar</code><code class="nohighlight hljs ansi" style="display:block;">(1//1, 2//5)</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; Rsymbol(τ,τ,τ) |&gt; polar</code><code class="nohighlight hljs ansi" style="display:block;">(1//1, -3//10)</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; twist(τ) |&gt; polar</code><code class="nohighlight hljs ansi" style="display:block;">(1//1, -2//5)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../spaces/">« Vector spaces</a><a class="docs-footer-nextpage" href="../tensors/">Tensors and the <code>TensorMap</code> type »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Friday 13 December 2024 19:29">Friday 13 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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