Resource complexity of Symmetry Protected Topological phases

Fuente: arXiv
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Autores principales: Catalano, Alberto Giuseppe, Kožić, Sven Benjamin, Torre, Gianpaolo, Ciaramelletti, Carola, Paganelli, Simone, Franchini, Fabio, Giampaolo, Salvatore Marco
Formato: Preprint
Publicado: 2025
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author Catalano, Alberto Giuseppe
Kožić, Sven Benjamin
Torre, Gianpaolo
Ciaramelletti, Carola
Paganelli, Simone
Franchini, Fabio
Giampaolo, Salvatore Marco
author_facet Catalano, Alberto Giuseppe
Kožić, Sven Benjamin
Torre, Gianpaolo
Ciaramelletti, Carola
Paganelli, Simone
Franchini, Fabio
Giampaolo, Salvatore Marco
contents We pursue the identification of quantum resources carried by topological order, by evaluating quantum magic, quantified through the rank-$2$ Stabilizer Rényi entropy $\mathcal{M}_2$, in one-dimensional systems hosting symmetry-protected topological phases (SPTP). Focusing on models with an exact duality between an SPTP and a trivial one, namely the dimerized XX and the Cluster-Ising chains, we show that dual points exhibit identical amounts of magic, even thought they belong to distinct topological sectors. A subextensive asymmetry arises only under open boundary conditions, where edge effects break the duality, but this correction is non-topological and depends on microscopic parameters. These results stand in contrast to the case of topological frustration, where delocalized excitations enhance the magic logarithmically with system size. They also complement recent analyses in the literature, showing that the total magic is largely insensitive to the presence of topological order, hence suggesting that topological order is not necessarily a genuine computational resource.
format Preprint
id arxiv_https___arxiv_org_abs_2509_08053
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Resource complexity of Symmetry Protected Topological phases
Catalano, Alberto Giuseppe
Kožić, Sven Benjamin
Torre, Gianpaolo
Ciaramelletti, Carola
Paganelli, Simone
Franchini, Fabio
Giampaolo, Salvatore Marco
Quantum Physics
Strongly Correlated Electrons
High Energy Physics - Theory
We pursue the identification of quantum resources carried by topological order, by evaluating quantum magic, quantified through the rank-$2$ Stabilizer Rényi entropy $\mathcal{M}_2$, in one-dimensional systems hosting symmetry-protected topological phases (SPTP). Focusing on models with an exact duality between an SPTP and a trivial one, namely the dimerized XX and the Cluster-Ising chains, we show that dual points exhibit identical amounts of magic, even thought they belong to distinct topological sectors. A subextensive asymmetry arises only under open boundary conditions, where edge effects break the duality, but this correction is non-topological and depends on microscopic parameters. These results stand in contrast to the case of topological frustration, where delocalized excitations enhance the magic logarithmically with system size. They also complement recent analyses in the literature, showing that the total magic is largely insensitive to the presence of topological order, hence suggesting that topological order is not necessarily a genuine computational resource.
title Resource complexity of Symmetry Protected Topological phases
topic Quantum Physics
Strongly Correlated Electrons
High Energy Physics - Theory
url https://arxiv.org/abs/2509.08053