Persona:
Rodríguez Laguna, Javier

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0000-0003-2218-7980
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Rodríguez Laguna
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Javier
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2018 - 201922020 - 20212
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Autor: Sierra, Germán × Fecha de inicio: 2018 ×

Resultados de la búsqueda

Mostrando 1 - 4 de 4
  • Miniatura
    Publicación
    Piercing the rainbow state: Entanglement on an inhomogeneous spin chain with a defect
    (American Physical Society, 2021-05-15) Sáenz de Buruaga, Nadir Samos; Santalla, Silvia N.; Sierra, Germán; Rodríguez Laguna, Javier
    The rainbow state denotes a set of valence bond states organized concentrically around the center of a spin 1/2 chain. It is the ground state of an inhomogeneous XX Hamiltonian and presents a maximal violation of the area law of entanglement entropy. Here, we add a tunable exchange coupling constant at the center, γ , and show that it induces entanglement transitions of the ground state. At very strong inhomogeneity, the rainbow state survives for 0≤γ≤1 , while outside that region the ground state is a product of dimers. In the weak inhomogeneity regime, the entanglement entropy satisfies a volume law, derived from CFT in curved space-time, with an effective central charge that depends on the inhomogeneity parameter and γ . In all regimes we have found that the entanglement properties are invariant under the transformation γ ⟷ 1 − γ , whose fixed point γ = 1 / 2 corresponds to the usual rainbow model. Finally, we study the robustness of nontrivial topological phases in the presence of the defect.
  • Miniatura
    Publicación
    Entanglement as geometry and flow
    (American Physical Society, 2020-05-20) Singha Roy, Sudipto; Santalla, Silvia N.; Sierra, Germán; Rodríguez Laguna, Javier
    We explore the connection between the area law for entanglement and geometry by representing the entanglement entropies corresponding to all 2 N bipartitions of an N -party pure quantum system by means of a (generalized) adjacency matrix. In the cases where the representation is exact, the elements of that matrix coincide with the mutual information between pairs of sites. In others, it provides a very good approximation, and in all the cases it yields a natural entanglement contour which is similar to previous proposals. Moreover, for one-dimensional conformal invariant systems, the generalized adjacency matrix is given by the two-point correlator of an entanglement current operator. We conjecture how this entanglement current may give rise to a metric entirely built from entanglement.
  • Miniatura
    Publicación
    Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems
    (IOPScience, 2018-04) Tonni, Erik; Sierra, Germán; Rodríguez Laguna, Javier
    Inhomogeneous quantum critical systems in one spatial dimension have been studied by using conformal field theory in static curved backgrounds. Two interesting examples are the free fermion gas in the harmonic trap and the inhomogeneous XX spin chain called rainbow chain. For conformal field theories defined on static curved spacetimes characterised by a metric which is Weyl equivalent to the flat metric, with the Weyl factor depending only on the spatial coordinate, we study the entanglement hamiltonian and the entanglement spectrum of an interval adjacent to the boundary of a segment where the same boundary condition is imposed at the endpoints. A contour function for the entanglement entropies corresponding to this configuration is also considered, being closely related to the entanglement hamiltonian. The analytic expressions obtained by considering the curved spacetime which characterises the rainbow model have been checked against numerical data for the rainbow chain, finding an excellent agreement.
  • Miniatura
    Publicación
    Unusual area-law violation in random inhomogeneous systems
    (IOPScience, 2019-02-26) Alba, Vincenzo; Santalla, Silvia N.; Ruggiero, Paola; Calabrese, Pasquale; Sierra, Germán; Rodríguez Laguna, Javier
    The discovery of novel entanglement patterns in quantum manybody systems is a prominent research direction in contemporary physics. Here we provide the example of a spin chain with random and inhomogeneous couplings that in the ground state exhibits a very unusual area-law violation. In the clean limit, i.e. without disorder, the model is the rainbow chain and has volume law entanglement. We show that, in the presence of disorder, the entanglement entropy exhibits a power-law growth with the subsystem size, with an exponent 1/2. By employing the strong disorder renormalization group (SDRG) framework, we show that this exponent is related to the survival probability of certain random walks. The ground state of the model exhibits extended regions of short-range singlets (that we term ‘bubble’ regions) as well as rare long range singlet (‘rainbow’ regions). Crucially, while the probability of extended rainbow regions decays exponentially with their size, that of the bubble regions is power law. We provide strong numerical evidence for the correctness of SDRG results by exploiting the free-fermion solution of the model. Finally, we investigate the role of interactions by considering the random inhomogeneous XXZ spin chain. Within the SDRG framework and in the strong inhomogeneous limit, we show that the above area-law violation takes place only at the free-fermion point of phase diagram. This point divides two extended regions, which exhibit volume-law and area-law entanglement, respectively.