Browsing by Author "González Rendel, Santiago"

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    Topological description of pure invariant states of the Weyl C-algebra
    (2025) De Nittis, Giuseppe; González Rendel, Santiago
    In this work we study the topology of certain families of states of the Weyl $C^*$-algebra with finite degrees of freedom. We focus on families of pure states characterized by symmetries and a (semi-)regularity condition, and obtain precise topological descriptions through homeomorphisms with other explicit spaces. Of special importance are the families of pure, semi-regular states invariant under either continuous (plane-wave states) or discrete (Bloch-wave states) spatial translations, and the family of states invariant under discrete, mutually commuting spatial and momentum translations (Zak-wave states), all of which we completely characterize.
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    Topology of invariant states
    (2025) González Rendel, Santiago; De Nittis, Giuseppe; Pontificia Universidad Católica de Chile. Instituto de Física
    We provide an abstract topological classification scheme for symmetry-invariant states, and discuss its application in the setting of finite degrees of freedom and no spin. We define two invariant states to be equivalent if the localized states conforming them as a superposition can be continuously deformed into each other. Using this notion, we show that the equivalence classes of the so-called gapped states classify the topological phases of topological insulators of types A and AI.