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{"documenter":{"julia_version":"1.12.4","generation_timestamp":"2026-01-26T11:07:50","documenter_version":"1.16.1"}}
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{"documenter":{"julia_version":"1.12.4","generation_timestamp":"2026-01-26T12:24:45","documenter_version":"1.16.1"}}

previews/PR321/changelog/index.html

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previews/PR321/examples/2d_ising_partition_function/index.html

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@show (e - e_exact) / e_exact;</code></pre><pre><code class="nohighlight hljs">(-(log(λ)) / beta - f_exact) / f_exact = -8.807417386354037e-16 + 1.736415096112634e-16im
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(abs(m) - abs(m_exact)) / abs(m_exact) = -3.420952570843561e-16
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(e - e_exact) / e_exact = -0.02373206809908996 - 7.653023727290916e-17im
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</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../j1j2_su/">« Three-site simple update for the <span>$J_1$</span>-<span>$J_2$</span> model</a><a class="docs-footer-nextpage" href="../3d_ising_partition_function/">The 3D classical 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="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 1.16.1 on <span class="colophon-date" title="Monday 26 January 2026 11:07">Monday 26 January 2026</span>. Using Julia version 1.12.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../j1j2_su/">« Three-site simple update for the <span>$J_1$</span>-<span>$J_2$</span> model</a><a class="docs-footer-nextpage" href="../3d_ising_partition_function/">The 3D classical 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="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 1.16.1 on <span class="colophon-date" title="Monday 26 January 2026 12:24">Monday 26 January 2026</span>. Using Julia version 1.12.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR321/examples/3d_ising_partition_function/index.html

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m_ref = 0.667162
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@show abs(m - m_ref)</code></pre><pre><code class="nohighlight hljs">0.00011315585491944447</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../2d_ising_partition_function/">« The 2D classical Ising model using CTMRG</a><a class="docs-footer-nextpage" href="../boundary_mps/">Boundary MPS contractions of 2D networks »</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 1.16.1 on <span class="colophon-date" title="Monday 26 January 2026 11:07">Monday 26 January 2026</span>. Using Julia version 1.12.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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@show abs(m - m_ref)</code></pre><pre><code class="nohighlight hljs">0.00011315585491944447</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../2d_ising_partition_function/">« The 2D classical Ising model using CTMRG</a><a class="docs-footer-nextpage" href="../boundary_mps/">Boundary MPS contractions of 2D networks »</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 1.16.1 on <span class="colophon-date" title="Monday 26 January 2026 12:24">Monday 26 January 2026</span>. Using Julia version 1.12.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR321/examples/bose_hubbard/index.html

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E = -0.273255733455233
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</code></pre><p>We can compare our PEPS result to the energy obtained using a cylinder-MPS calculation using a cylinder circumference of <span>$L_y = 7$</span> and a bond dimension of 446, which yields <span>$E = -0.273284888$</span>:</p><pre><code class="language-julia hljs">E_ref = -0.273284888
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@show (E - E_ref) / E_ref;</code></pre><pre><code class="nohighlight hljs">(E - E_ref) / E_ref = -0.00010668187685147442
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</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../heisenberg/">« Optimizing the 2D Heisenberg model</a><a class="docs-footer-nextpage" href="../xxz/">Néel order in the <span>$U(1)$</span>-symmetric XXZ 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="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 1.16.1 on <span class="colophon-date" title="Monday 26 January 2026 11:07">Monday 26 January 2026</span>. Using Julia version 1.12.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../heisenberg/">« Optimizing the 2D Heisenberg model</a><a class="docs-footer-nextpage" href="../xxz/">Néel order in the <span>$U(1)$</span>-symmetric XXZ 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="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 1.16.1 on <span class="colophon-date" title="Monday 26 January 2026 12:24">Monday 26 January 2026</span>. Using Julia version 1.12.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR321/examples/boundary_mps/index.html

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┌ Warning: VUMPS cancel 200: obj = +9.094977761227e+01 -6.006566625488e+00im err = 3.5527156917e-01 time = 50.63 sec
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└ @ MPSKit ~/.julia/packages/MPSKit/hiGZg/src/algorithms/groundstate/vumps.jl:76
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norm_pepo = 91.14790667014051
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</code></pre><p>These objects and routines can be used to optimize PEPS fixed points of 3D partition functions, see for example <a href="../../references/#vanderstraeten_residual_2018">Vanderstraeten et al.</a></p><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../3d_ising_partition_function/">« The 3D classical Ising model</a><a class="docs-footer-nextpage" href="../../lib/lib/">Library »</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 1.16.1 on <span class="colophon-date" title="Monday 26 January 2026 11:07">Monday 26 January 2026</span>. Using Julia version 1.12.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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</code></pre><p>These objects and routines can be used to optimize PEPS fixed points of 3D partition functions, see for example <a href="../../references/#vanderstraeten_residual_2018">Vanderstraeten et al.</a></p><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../3d_ising_partition_function/">« The 3D classical Ising model</a><a class="docs-footer-nextpage" href="../../lib/lib/">Library »</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 1.16.1 on <span class="colophon-date" title="Monday 26 January 2026 12:24">Monday 26 January 2026</span>. Using Julia version 1.12.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR321/examples/fermi_hubbard/index.html

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E = -2.0711744883679684
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</code></pre><p>Finally, let&#39;s compare the obtained energy against a reference energy from a QMC study by <a href="../../references/#qin_benchmark_2016">Qin et al.</a>. With the parameters specified above, they obtain an energy of <span>$E_\text{ref} \approx 4 \times -0.5244140625 = -2.09765625$</span> (the factor 4 comes from the <span>$2 \times 2$</span> unit cell that we use here). Thus, we find:</p><pre><code class="language-julia hljs">E_ref = -2.09765625
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@show (E - E_ref) / E_ref;</code></pre><pre><code class="nohighlight hljs">(E - E_ref) / E_ref = -0.012624452472625886
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</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../xxz/">« Néel order in the <span>$U(1)$</span>-symmetric XXZ model</a><a class="docs-footer-nextpage" href="../heisenberg_su/">Simple update for the Heisenberg 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="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 1.16.1 on <span class="colophon-date" title="Monday 26 January 2026 11:07">Monday 26 January 2026</span>. Using Julia version 1.12.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../xxz/">« Néel order in the <span>$U(1)$</span>-symmetric XXZ model</a><a class="docs-footer-nextpage" href="../heisenberg_su/">Simple update for the Heisenberg 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="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 1.16.1 on <span class="colophon-date" title="Monday 26 January 2026 12:24">Monday 26 January 2026</span>. Using Julia version 1.12.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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