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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Examples · PEPSKit.jl</title><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../"><img class="docs-light-only" src="../assets/logo.svg" alt="PEPSKit.jl logo"/><img class="docs-dark-only" src="../assets/logo-dark.svg" alt="PEPSKit.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../">PEPSKit.jl</a></span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../man/intro/">Manual</a></li><li class="is-active"><a class="tocitem" href>Examples</a></li><li><a class="tocitem" href="../lib/lib/">Library</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Examples</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Examples</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/QuantumKitHub/PEPSKit.jl/blob/master/docs/src/examples/index.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><p>For now, refer to the <a href="https://github.com/QuantumKitHub/PEPSKit.jl/tree/master/examples">examples folder</a> on GitHub.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../man/intro/">« Manual</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Tuesday 9 July 2024 13:28">Tuesday 9 July 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Examples · PEPSKit.jl</title><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../"><img class="docs-light-only" src="../assets/logo.svg" alt="PEPSKit.jl logo"/><img class="docs-dark-only" src="../assets/logo-dark.svg" alt="PEPSKit.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../">PEPSKit.jl</a></span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../man/intro/">Manual</a></li><li class="is-active"><a class="tocitem" href>Examples</a></li><li><a class="tocitem" href="../lib/lib/">Library</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Examples</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Examples</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/QuantumKitHub/PEPSKit.jl/blob/master/docs/src/examples/index.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><p>For now, refer to the <a href="https://github.com/QuantumKitHub/PEPSKit.jl/tree/master/examples">examples folder</a> on GitHub.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../man/intro/">« Manual</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 10 July 2024 10:14">Wednesday 10 July 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · PEPSKit.jl</title><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href><img class="docs-light-only" src="assets/logo.svg" alt="PEPSKit.jl logo"/><img class="docs-dark-only" src="assets/logo-dark.svg" alt="PEPSKit.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href>PEPSKit.jl</a></span></div><form class="docs-search" action="search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a><ul class="internal"><li><a class="tocitem" href="#Installation"><span>Installation</span></a></li><li><a class="tocitem" href="#Quickstart"><span>Quickstart</span></a></li></ul></li><li><a class="tocitem" href="man/intro/">Manual</a></li><li><a class="tocitem" href="examples/">Examples</a></li><li><a class="tocitem" href="lib/lib/">Library</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/QuantumKitHub/PEPSKit.jl/blob/master/docs/src/index.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="PEPSKit.jl"><a class="docs-heading-anchor" href="#PEPSKit.jl">PEPSKit.jl</a><a id="PEPSKit.jl-1"></a><a class="docs-heading-anchor-permalink" href="#PEPSKit.jl" title="Permalink"></a></h1><p><strong>Tools for working with projected entangled-pair states</strong></p><p>It contracts, it optimizes, it may break.</p><h2 id="Installation"><a class="docs-heading-anchor" href="#Installation">Installation</a><a id="Installation-1"></a><a class="docs-heading-anchor-permalink" href="#Installation" title="Permalink"></a></h2><p>The package can be installed through the Julia general registry, via the package manager:</p><pre><code class="language-julia-repl hljs">pkg&gt; add PEPSKit</code></pre><h2 id="Quickstart"><a class="docs-heading-anchor" href="#Quickstart">Quickstart</a><a id="Quickstart-1"></a><a class="docs-heading-anchor-permalink" href="#Quickstart" title="Permalink"></a></h2><p>After following the installation process, it should now be possible to load the packages and start simulating. For example, in order to obtain the groundstate of the 2D Heisenberg model, we can use the following code:</p><pre><code class="language-julia hljs">using TensorKit, PEPSKit, KrylovKit, OptimKit

# constructing the Hamiltonian:
Jx, Jy, Jz = (-1, 1, -1) # sublattice rotation to obtain single-site unit cell
physical_space = ComplexSpace(2)
T = ComplexF64
σx = TensorMap(T[0 1; 1 0], physical_space, physical_space)
σy = TensorMap(T[0 im; -im 0], physical_space, physical_space)
σz = TensorMap(T[1 0; 0 -1], physical_space, physical_space)
H = (Jx * σx ⊗ σx) + (Jy * σy ⊗ σy) + (Jz * σz ⊗ σz)
Heisenberg_hamiltonian = NLocalOperator{NearestNeighbor}(H / 4)
H = square_lattice_heisenberg(; Jx=-1, Jy=1, Jz=-1) # sublattice rotation to obtain single-site unit cell

# configuring the parameters
D = 2
chi = 20
ctm_alg = CTMRG(; trscheme = truncdim(chi), tol=1e-20, miniter=4, maxiter=100, verbosity=1)
ctm_alg = CTMRG(; tol=1e-10, miniter=4, maxiter=100, verbosity=1, trscheme=truncdim(chi))
opt_alg = PEPSOptimize(;
boundary_alg=ctm_alg,
optimizer=LBFGS(4; maxiter=100, gradtol=1e-4, verbosity=2),
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# ground state search
state = InfinitePEPS(2, D)
ctm = leading_boundary(CTMRGEnv(state; Venv=ComplexSpace(chi)), state, ctm_alg)
result = fixedpoint(state, Heisenberg_hamiltonian, opt_alg, ctm)
result = fixedpoint(state, H, opt_alg, ctm)

@show result.E # -0.6625...</code></pre></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="man/intro/">Manual »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Tuesday 9 July 2024 13:28">Tuesday 9 July 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
@show result.E # -0.6625...</code></pre></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="man/intro/">Manual »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 10 July 2024 10:14">Wednesday 10 July 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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