build based on 1c19ff6

previews/PR213/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2024-01-03T19:32:21","documenter_version":"1.2.1"}}
+{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2024-01-03T19:36:17","documenter_version":"1.2.1"}}

previews/PR213/examples/01_LSWT_SU3_FeI2.html

@@ -156,4 +156,4 @@
 fig = Figure()
 ax = Axis(fig[1,1]; xlabel="Momentum (r.l.u.)", ylabel="Energy (meV)", xticks, xticklabelrotation=π/6)
 heatmap!(ax, 1:size(is_averaged, 1), energies, is_averaged)
-fig</code></pre><img src="01_LSWT_SU3_FeI2-5ad5f204.png" alt="Example block output"/><p>This result can be directly compared to experimental neutron scattering data from <a href="https://doi.org/10.1038/s41567-020-01110-1">Bai et al.</a></p><img src="https://raw.githubusercontent.com/SunnySuite/Sunny.jl/main/docs/src/assets/FeI2_intensity.jpg"><p>(The publication figure accidentally used a non-standard coordinate system to label the wave vectors.)</p><p>To get this agreement, the use of SU(3) coherent states is essential. In other words, we needed a theory of multi-flavored bosons. The lower band has large quadrupolar character, and arises from the strong easy-axis anisotropy of FeI₂. By setting <code>mode = :SUN</code>, the calculation captures this coupled dipole-quadrupole dynamics.</p><p>An interesting exercise is to repeat the same study, but using <code>mode = :dipole</code> instead of <code>:SUN</code>. That alternative choice would constrain the coherent state dynamics to the space of dipoles only.</p><p>The full dynamical spin structure factor (DSSF) can be retrieved as a <span>$3×3$</span> matrix with the <a href="../library.html#Sunny.dssf-Tuple{SpinWaveTheory, Any}"><code>dssf</code></a> function, for a given path of <span>$𝐪$</span>-vectors.</p><pre><code class="language-julia hljs">disp, is = dssf(swt, path);</code></pre><p>The first output <code>disp</code> is identical to that obtained from <code>dispersion</code>. The second output <code>is</code> contains a list of <span>$3×3$</span> matrix of intensities. For example, <code>is[q,n][2,3]</code> yields the <span>$(ŷ,ẑ)$</span> component of the structure factor intensity for <code>nth</code> mode at the <code>q</code>th wavevector in the <code>path</code>.</p><h2 id="What&#39;s-next?"><a class="docs-heading-anchor" href="#What&#39;s-next?">What&#39;s next?</a><a id="What&#39;s-next?-1"></a><a class="docs-heading-anchor-permalink" href="#What&#39;s-next?" title="Permalink"></a></h2><p>The multi-boson linear spin wave theory, applied above, can be understood as the quantization of a certain generalization of the Landau-Lifshitz spin dynamics. Rather than dipoles, this dynamics takes places on the space of <a href="https://arxiv.org/abs/2106.14125">SU(<em>N</em>) coherent states</a>.</p><p>The full SU(<em>N</em>) coherent state dynamics, with appropriate quantum correction factors, can be useful to model finite temperature scattering data. In particular, it captures certain anharmonic effects due to thermal fluctuations. See our <a href="04_GSD_FeI2.html#4.-Generalized-spin-dynamics-of-FeI-at-finite-*T*">generalized spin dynamics tutorial</a>.</p><p>The classical dynamics is also a good starting point to study non-equilibrium phenomena. Empirical noise and damping terms can be used to model <a href="https://arxiv.org/abs/2209.01265">coupling to a thermal bath</a>. This yields a Langevin dynamics of SU(<em>N</em>) coherent states. Our <a href="06_CP2_Skyrmions.html#6.-Dynamical-quench-into-CP-skyrmion-liquid">dynamical SU(<em>N</em>) quench</a> tutorial illustrates how a temperature quench can give rise to novel liquid phase of CP² skyrmions.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../index.html">« Overview</a><a class="docs-footer-nextpage" href="02_LSWT_CoRh2O4.html">2. Spin wave simulations of CoRh₂O₄ »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Wednesday 3 January 2024 19:32">Wednesday 3 January 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+fig</code></pre><img src="01_LSWT_SU3_FeI2-5ad5f204.png" alt="Example block output"/><p>This result can be directly compared to experimental neutron scattering data from <a href="https://doi.org/10.1038/s41567-020-01110-1">Bai et al.</a></p><img src="https://raw.githubusercontent.com/SunnySuite/Sunny.jl/main/docs/src/assets/FeI2_intensity.jpg"><p>(The publication figure accidentally used a non-standard coordinate system to label the wave vectors.)</p><p>To get this agreement, the use of SU(3) coherent states is essential. In other words, we needed a theory of multi-flavored bosons. The lower band has large quadrupolar character, and arises from the strong easy-axis anisotropy of FeI₂. By setting <code>mode = :SUN</code>, the calculation captures this coupled dipole-quadrupole dynamics.</p><p>An interesting exercise is to repeat the same study, but using <code>mode = :dipole</code> instead of <code>:SUN</code>. That alternative choice would constrain the coherent state dynamics to the space of dipoles only.</p><p>The full dynamical spin structure factor (DSSF) can be retrieved as a <span>$3×3$</span> matrix with the <a href="../library.html#Sunny.dssf-Tuple{SpinWaveTheory, Any}"><code>dssf</code></a> function, for a given path of <span>$𝐪$</span>-vectors.</p><pre><code class="language-julia hljs">disp, is = dssf(swt, path);</code></pre><p>The first output <code>disp</code> is identical to that obtained from <code>dispersion</code>. The second output <code>is</code> contains a list of <span>$3×3$</span> matrix of intensities. For example, <code>is[q,n][2,3]</code> yields the <span>$(ŷ,ẑ)$</span> component of the structure factor intensity for <code>nth</code> mode at the <code>q</code>th wavevector in the <code>path</code>.</p><h2 id="What&#39;s-next?"><a class="docs-heading-anchor" href="#What&#39;s-next?">What&#39;s next?</a><a id="What&#39;s-next?-1"></a><a class="docs-heading-anchor-permalink" href="#What&#39;s-next?" title="Permalink"></a></h2><p>The multi-boson linear spin wave theory, applied above, can be understood as the quantization of a certain generalization of the Landau-Lifshitz spin dynamics. Rather than dipoles, this dynamics takes places on the space of <a href="https://arxiv.org/abs/2106.14125">SU(<em>N</em>) coherent states</a>.</p><p>The full SU(<em>N</em>) coherent state dynamics, with appropriate quantum correction factors, can be useful to model finite temperature scattering data. In particular, it captures certain anharmonic effects due to thermal fluctuations. See our <a href="04_GSD_FeI2.html#4.-Generalized-spin-dynamics-of-FeI-at-finite-*T*">generalized spin dynamics tutorial</a>.</p><p>The classical dynamics is also a good starting point to study non-equilibrium phenomena. Empirical noise and damping terms can be used to model <a href="https://arxiv.org/abs/2209.01265">coupling to a thermal bath</a>. This yields a Langevin dynamics of SU(<em>N</em>) coherent states. Our <a href="06_CP2_Skyrmions.html#6.-Dynamical-quench-into-CP-skyrmion-liquid">dynamical SU(<em>N</em>) quench</a> tutorial illustrates how a temperature quench can give rise to novel liquid phase of CP² skyrmions.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../index.html">« Overview</a><a class="docs-footer-nextpage" href="02_LSWT_CoRh2O4.html">2. Spin wave simulations of CoRh₂O₄ »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Wednesday 3 January 2024 19:36">Wednesday 3 January 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR213/examples/02_LSWT_CoRh2O4.html

@@ -60,4 +60,4 @@
 fig = Figure()
 ax = Axis(fig[1,1]; xlabel="Q (Å⁻¹)", ylabel="ω (meV)")
 heatmap!(ax, radii, energies, output, colormap=:gnuplot2)
-fig</code></pre><img src="02_LSWT_CoRh2O4-19eaaa6f.png" alt="Example block output"/><p>This result can be compared to experimental neutron scattering data from Fig. 5 of <a href="https://doi.org/10.1103/PhysRevB.96.064413">Ge et al.</a></p><img width="95%" src="https://raw.githubusercontent.com/SunnySuite/Sunny.jl/main/docs/src/assets/CoRh2O4_intensity.jpg"></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="01_LSWT_SU3_FeI2.html">« 1. Multi-flavor spin wave simulations of FeI₂ (Showcase)</a><a class="docs-footer-nextpage" href="03_LLD_CoRh2O4.html">3. Landau-Lifshitz dynamics of CoRh₂O₄ at finite <em>T</em> »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Wednesday 3 January 2024 19:32">Wednesday 3 January 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+fig</code></pre><img src="02_LSWT_CoRh2O4-19eaaa6f.png" alt="Example block output"/><p>This result can be compared to experimental neutron scattering data from Fig. 5 of <a href="https://doi.org/10.1103/PhysRevB.96.064413">Ge et al.</a></p><img width="95%" src="https://raw.githubusercontent.com/SunnySuite/Sunny.jl/main/docs/src/assets/CoRh2O4_intensity.jpg"></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="01_LSWT_SU3_FeI2.html">« 1. Multi-flavor spin wave simulations of FeI₂ (Showcase)</a><a class="docs-footer-nextpage" href="03_LLD_CoRh2O4.html">3. Landau-Lifshitz dynamics of CoRh₂O₄ at finite <em>T</em> »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Wednesday 3 January 2024 19:36">Wednesday 3 January 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR213/examples/03_LLD_CoRh2O4.html

@@ -85,4 +85,4 @@
         aspect = 1.4,
     ),
     colorrange = (0, 20.0)
-)</code></pre><img src="03_LLD_CoRh2O4-2e9c8c64.png" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="02_LSWT_CoRh2O4.html">« 2. Spin wave simulations of CoRh₂O₄</a><a class="docs-footer-nextpage" href="04_GSD_FeI2.html">4. Generalized spin dynamics of FeI₂ at finite <em>T</em> »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Wednesday 3 January 2024 19:32">Wednesday 3 January 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+)</code></pre><img src="03_LLD_CoRh2O4-2e9c8c64.png" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="02_LSWT_CoRh2O4.html">« 2. Spin wave simulations of CoRh₂O₄</a><a class="docs-footer-nextpage" href="04_GSD_FeI2.html">4. Generalized spin dynamics of FeI₂ at finite <em>T</em> »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Wednesday 3 January 2024 19:36">Wednesday 3 January 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR213/examples/04_GSD_FeI2.html

@@ -171,4 +171,4 @@
     )
 )
 Colorbar(hm.figure[1,2], hm.plot)
-hm</code></pre><img src="04_GSD_FeI2-f95a8d5a.png" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="03_LLD_CoRh2O4.html">« 3. Landau-Lifshitz dynamics of CoRh₂O₄ at finite <em>T</em></a><a class="docs-footer-nextpage" href="05_MC_Ising.html">5. Monte Carlo sampling of the Ising model »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Wednesday 3 January 2024 19:32">Wednesday 3 January 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+hm</code></pre><img src="04_GSD_FeI2-f95a8d5a.png" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="03_LLD_CoRh2O4.html">« 3. Landau-Lifshitz dynamics of CoRh₂O₄ at finite <em>T</em></a><a class="docs-footer-nextpage" href="05_MC_Ising.html">5. Monte Carlo sampling of the Ising model »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Wednesday 3 January 2024 19:36">Wednesday 3 January 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>