Vb = Vect[A4Object](first(sectors(V)) => 1) # not all charges on boundary, play around with what is there</code></pre><img src="../img/A4_sym_entanglement_spectrum.svg" alt="" width="90%"/><p>The plot shows the entanglement spectra of the various dual models in the middle of the ground state for the original Hamiltonian probing the <span>$\mathsf{Rep(A_4)}$</span>-symmetric phase, along with the ground state without symmetries. Every subtitle also mentions the memory required to store the same middle ground state tensor. This plot should be compared to (<a href="../../references/#Lootens_2024">Lootens <em>et al.</em>, 2024</a>; Figure 2).</p><p>This can be repeated with other parameter values for <span>$J_1$</span> and <span>$J_2$</span> in the Hamiltonian to probe the <span>$\mathsf{Rep(\mathbb{Z}_2 \times \mathbb{Z}_2)}$</span>-symmetric or <span>$\mathsf{Rep^\psi(A_4)}$</span> SPT phase.</p><div class="admonition is-info" id="Additional-functions-and-keyword-arguments-bc8cb1f84dc8b140"><header class="admonition-header">Additional functions and keyword arguments<a class="admonition-anchor" href="#Additional-functions-and-keyword-arguments-bc8cb1f84dc8b140" title="Permalink"></a></header><div class="admonition-body"><p>Certain commonly used functions within MPSKit require extra keyword arguments to be compatible with multifusion MPS simulations. In particular, the keyword argument <code>sector</code> (note the lowercase "s") appears in </p><ul><li><code>excitations</code> with <code>QuasiparticleAnsatz</code>: the sector is selected by adding an auxiliary space to the <em>domain</em> of each eigenvector of the transfer matrix. Since in a full contraction the domain of the eigenvector lies in the opposite side of the physical space (labeled by objects in <span>$\mathcal{D} = \mathsf{Rep(A_4)}$</span>), the charged excitations lie in the symmetry category <span>$\mathcal{C} = \mathcal{D^*_M}$</span>.</li><li><code>exact_diagonalization</code>: the <code>sector</code> keyword argument now requires an object in <span>$\mathcal{D}$</span>, since this is the fusion category which specifies the bond algebra from which the Hamiltonian is constructed. This is equivalent to adding a charged leg on the leftmost (or rightmost) virtual space of the MPS in conventional MPS cases.</li></ul></div></div><h2 id="Differences-with-the-infinite-case"><a class="docs-heading-anchor" href="#Differences-with-the-infinite-case">Differences with the infinite case</a><a id="Differences-with-the-infinite-case-1"></a><a class="docs-heading-anchor-permalink" href="#Differences-with-the-infinite-case" title="Permalink"></a></h2><p>We can repeat the above calcalations also for an infinite system. The <code>lattice</code> variable will change, as well as the MPS constructor and the algorithm:</p><pre><code class="language-julia hljs">lattice = InfiniteChain(1)
0 commit comments