Persona: Rodríguez Laguna, Javier
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Rodríguez Laguna
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Javier
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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, JavierThe 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.Publicación Ergotropy and entanglement in critical spin chains(American Physical Society, 2023-02-08) Mula, Begoña; Fernández, Julio J.; Santalla, Silvia N.; Alvarellos Bermejo, José Enrique; García Aldea, David; Rodríguez Laguna, Javier; Fernández Sánchez, Eva MaríaA subsystem of an entangled ground state (GS) is in a mixed state. Thus, if we isolate this subsystem from its surroundings, we may be able to extract work applying unitary transformations, up to a maximal amount which is called ergotropy. Once this work has been extracted, the subsystem will still contain some bound energy above its local GS, which can provide valuable information about the entanglement structure. We show that the bound energy for half a free fermionic chain decays as the square of the entanglement entropy divided by the chain length, thus approaching zero for large system sizes, and we conjecture that this relation holds for all one-dimensional critical states.Publicación Semblanzas de científicas y científicos españoles: Juan Ignacio Cirac Sasturain(Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias, 2018-01-01) Fernández González, Carlos; Rodríguez Laguna, JavierPublicación 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, JavierThe 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.Publicación Semblanzas de los Premios Nobel 2016 en Física(Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias, 2016-01-01) Rodríguez Laguna, JavierPublicación Recensiones: Cine en ciencias: El enigma Agustina(Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias, 2019-01-01) Fernández, Eva María; Rodríguez Laguna, JavierPublicación A New Thermodynamic Model to Approximate Properties of Subcritical Liquids(MDPI, 2023-06-29) Sánchez Orgaz, Susana; González Fernández, M. Celina; Varela Díez, Fernando; Rodríguez Laguna, JavierIn order to obtain the thermodynamic properties of compressed liquids, it is usual to consider them as incompressible systems, since liquids and solids are well represented by this thermodynamic model. Within this model, there are two usual hypotheses that can be derived in two different submodels: the strictly incompressible (SI) model, which supposes a constant specific volume 𝑣=𝑣0, and a more general model, called temperature-dependent incompressible (TDI) model, which relates a specific volume to temperature, 𝑣=𝑣(𝑇). But, usually, this difference ends here in the thermal equation of state, and only the SI model was developed for caloric and entropic equations. The aim of this work is to provide a complete formulation for the TDI model and show where it can be advantageously used rather than the SI model. The study concludes that the proposed model outperforms the traditional model in the study of subcritical liquid. One conceivable utilization of this model is its integration into certain thermodynamic calculation software packages (e.g., EES), which integrate the more elementary SI model into its code for certain incompressible substances.Publicación Casimir forces on deformed fermionic chains(American Physical Society, 2021-01-20) Mula, Begoña; Santalla, Silvia N.; Rodríguez Laguna, JavierWe characterize the Casimir forces for the Dirac vacuum on free-fermionic chains with smoothly varying hopping amplitudes, which correspond to ( 1 + 1 )-dimensional [( 1 + 1 )D] curved spacetimes with a static metric in the continuum limit. The first-order energy potential for an obstacle on that lattice corresponds to the Newtonian potential associated with the metric, while the finite-size corrections are described by a curved extension of the conformal field theory predictions, including a suitable boundary term. We show that for weak deformations of the Minkowski metric, Casimir forces measured by a local observer at the boundary are universal. We provide numerical evidence for our results on a variety of (1+1)D deformations: Minkowski, Rindler, anti–de Sitter (the so-called rainbow system), and sinusoidal metrics. Moreover, we show that interactions do not preclude our conclusions, exemplifying this with the deformed Heisenberg chain.Publicación Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems(IOPScience, 2018-04) Tonni, Erik; Sierra, Germán; Rodríguez Laguna, JavierInhomogeneous 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.Publicación Entanglement as geometry and flow(American Physical Society, 2020-05-20) Singha Roy, Sudipto; Santalla, Silvia N.; Sierra, Germán; Rodríguez Laguna, JavierWe 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.