arXiv subjects

Javier Rodríguez-Laguna

Publications and source records attributed to Javier Rodríguez-Laguna.

At least 19 recordsLinked to original sources

arXiv2026

The hyperlink representation of entanglement and the inclusion-exclusion principle

The entanglement entropy (EE) of any bipartition of a pure state can be approximately expressed as a sum of entanglement links (ELs). In this work, we introduce their exact extension, i.e. the entanglement hyperlinks (EHLs), a type of generalized mutual informations defined through the inclusion-exclusion principle, each of which captures contributions to the multipartite entanglement that are not reducible to lower-order terms. We show that any EHL crossing a factorized partition must vanish, and that the EHLs between any set of blocks can be expressed as a sum of all the EHLs that join all of them. This last result allows us to provide an exact representation of the EE of any block of a pure state, from the sum of the EHLs which cross its boundary. In order to illustrate their rich structure, we discuss some explicit numerical examples using ground states of local Hamiltonians. The EHLs thus provide a remarkable tool to characterize multipartite entanglement in quantum information theory and quantum many-body physics.

quant-ph↗

arXiv2026

Emergent correlations in the selected link-times along optimal paths

In the context of first-passage percolation (FPP), we investigate the statistical properties of the selected link-times (SLTs) -the random link times comprising the optimal paths (or geodesics) connecting two given points. We focus on weakly disordered square lattices, whose geodesics are known to fall under the Kardar-Parisi-Zhang (KPZ) universality class. Our analysis reveals universal power-law decays with the end-to-end distance for both the average and standard deviation of the SLTs, along with an intricate pattern of long-range correlations, whose scaling exponents are directly linked to KPZ universality. Crucially, the SLT distributions for diagonal and axial paths exhibit significant differences, which we trace back to the distinct directed and undirected nature, respectively, of the underlying geodesics. Moreover, we demonstrate that the SLT distribution violates the conditions of the central limit theorem. Instead, SLT sums follow the Tracy-Widom distribution characteristic of the KPZ class, which we associate with evidence for the emergence of high-order long-range correlations in the ensemble.

cond-mat.stat-mech↗

arXiv2025

Entanglement Halos

We introduce the concept of entanglement halos, a set of strongly entangled distant sites within the ground state of a quantum many-body system. Such halos emerge in star-like systems with exponentially decaying couplings, as we show using both free-fermions and the spin-1/2 antiferromagnetic Heisenberg model. Depending on the central connectivity, entanglement halos may exhibit trivial and non trivial symmetry-protected topological features. Our findings highlight how geometry and connectivity can generate complex entanglement structures with rich physical content, which can be experimentally accessible via state-of-the-art technologies.

cond-mat.str-el↗

arXiv2023

Universal fluctuations of global geometrical measurements in planar clusters

We characterize universal features of the sample-to-sample fluctuations of global geometrical observables, such as the area, width, length, and center-of-mass position, in random growing planar clusters. Our examples are taken from simulations of both continuous and discrete models of kinetically rough interfaces, including several universality classes, such as Kardar-Parisi-Zhang. We mostly focus on the scaling behavior with time of the sample-to-sample deviation for those global magnitudes, but we have also characterized their histograms and correlations.

cond-mat.stat-mech↗

arXiv2023

Shape effects in the fluctuations of random isochrones on a square lattice

We consider the isochrone curves in first-passage percolation on a 2D square lattice, i.e. the boundary of the set of points which can be reached in less than a given time from a certain origin. The occurrence of an instantaneous average shape is described in terms of its Fourier components, highlighting a crossover between a diamond and a circular geometry as the noise level is increased. Generally, these isochrones can be understood as fluctuating interfaces with an inhomogeneous local width which reveals the underlying lattice structure. We show that once these inhomogeneities have been taken into account, the fluctuations fall into the Kardar-Parisi-Zhang (KPZ) universality class with very good accuracy, where they reproduce the Family-Vicsek Ansatz with the expected exponents and the Tracy-Widom histogram for the local radial fluctuations.

cond-mat.stat-mech↗

arXiv2023

Long term behavior of the stirred vacuum on a Dirac chain: geometry blur and the random Slater ensemble

We characterize the long-term state of the 1D Dirac vacuum stirred by an impenetrable object, modeled as the ground state of a finite free-fermionic chain dynamically perturbed by a moving classical obstacle which suppresses the local hopping amplitudes. We find two different regimes, depending on the velocity of the obstacle. For a slow motion, the effective Floquet Hamiltonian presents features which are typical of the Gaussian orthogonal ensemble, and the occupation of the Floquet modes becomes roughly homogeneous. Moreover, the long term entanglement entropy of a contiguous block follows a Gaussian analogue of Page's law, i.e. a volumetric behavior. Indeed, the statistical properties of the reduced density matrices correspond to those of a random Slater determinant, which can be described using the Jacobi ensemble from random matrix theory. On the other hand, if the obstacle moves fast enough, the effective Floquet Hamiltonian presents a Poissonian behavior. The nature of the transition is clarified by the entanglement links, which determine the effective geometry underlying the entanglement structure, showing that the one-dimensionality of the physical Hamiltonian dissolves into a random adjacency matrix as we slow down the obstacle motion.

quant-ph↗

arXiv2023

Entanglement links and the quasiparticle picture

The time evolution of a quantum state with short-range correlations after a quench to a one-dimensional critical Hamiltonian can be understood using the quasi-particle picture, which states that local entanglement spreads as if it was carried by quasi-particles which separate at a fixed speed. We extend the quasi-particle picture using the recently introduced link representation of entanglement, allowing us to apply it to initial states presenting long-range correlations. The entanglement links are current correlators, and therefore follow a wave equation on the appropriate configurational space which allows us to predict the time evolution of the entanglement entropies. Our results are checked numerically for free fermionic chains with different initial entanglement patterns.

quant-ph↗

arXiv2023

Depletion in fermionic chains with inhomogeneous hoppings

The ground state of a free-fermionic chain with inhomogeneous hoppings at half-filling can be mapped into the Dirac vacuum on a static curved space-time, which presents exactly homogeneous occupations due to particle-hole symmetry. Yet, far from half-filling we observe density modulations and depletion effects. The system can be described by a 1D Schrödinger equation on a different static space-time, with an effective potential which accounts for the depleted regions. We provide a semiclassical expression for the single-particle modes and the density profiles associated to different hopping patterns and filling fractions. Moreover, we show that the depletion effects can be compensated for all filling fractions by adding a chemical potential proportional to the hoppings. Interestingly, we can obtain exactly the same density profiles on a homogeneous chain if we introduce a chemical potential which is inverse to the hopping intensities, even though the ground state is different from the original one.

quant-ph↗

arXiv2023

Ergotropy and entanglement in critical spin chains

A subsystem of an entangled ground state 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 ground state, 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 1D critical states.

quant-ph↗

arXiv2022

Segregation in spatially structured cities

Half of the world population resides in cities and urban segregation is becoming a global issue. One of the best known attempts to understand it is the Schelling model, which considers two types of agents that relocate whenever a transfer rule depending on the neighbor distribution is verified. The main aim of the present study is to broaden our understanding of segregated neighborhoods in the city, i.e. ghettos, extending the Schelling model to consider economic aspects and their spatial distribution. To this end we have considered a monetary gap between the two social groups and five types of urban structures, defined by the house pricing city map. The results show that ghetto sizes tend to follow a power law distribution in all the considered cases. For each city framework the interplay between economical aspects and the geometrical features determine the location where ghettos reach their maximum size. The system first steps shape greatly the city's final appearance. Moreover, the segregated population ratios depends largely on the monetary gap and not on the city type, implying that ghettos are able to adapt to different urban frameworks.

physics.soc-ph↗

arXiv2022

Exotic correlation spread in free-fermionic states with initial patterns

We describe a relation between the light-cone velocities after a quantum quench and the internal structure of the initial state, in the particular case of free fermions on a chain at half filling. The considered states include short-range valence bond solids, i.e., dimerized states, and long-range states such as the rainbow. In all the considered cases the correlations spread into one or a few well-defined light cones, each of them presenting an effective velocity which can be read from the form factor. Interestingly, we find that the observed velocities range from zero to the Fermi velocity and may not always be obtained from the dispersion relation for valid momenta.

quant-ph↗

arXiv2021

Effects of confinement and vaccination on an epidemic outburst: a statistical mechanics approach

This work describes a simple agent model for the spread of an epidemic outburst, with special emphasis on mobility and geographical considerations, which we characterize via statistical mechanics and numerical simulations. As the mobility is decreased, a percolation phase transition is found separating a free-propagation phase in which the outburst spreads without finding spatial barriers and a localized phase in which the outburst dies off. Interestingly, the number of infected agents is subject to maximal fluctuations at the transition point, building upon the unpredictability of the evolution of an epidemic outburst. Our model also lends itself to testing vaccination schedules. Indeed, it has been suggested that if a vaccine is available but scarce it is convenient to carefully select the vaccination program to maximize the chances of halting the outburst. We discuss and evaluate several schemes, with special interest on how the percolation transition point can be shifted, allowing for higher mobility without epidemiological impact.

cond-mat.stat-mech↗

arXiv2021

Random walkers on a deformable medium

We consider random walkers that deform the medium as they move, enabling a faster motion in regions which have been recently visited. This induces an effective attraction between walkers mediated by the medium, which can be regarded as a space metric, giving rise to a statistical mechanics toy model either for gravity, motion through deformable matter or adaptable geometry. In the strong-deformability regime, we find that diffusion is initially described by the porous medium equation, thus yielding subdiffusive behavior of an initially localized cloud of particles. Indeed, while the average width of a single cloud will sustain a $σ\sim t^{1/2}$ growth, the combined width of the whole ensemble will grow like $σ\sim t^{1/3}$ in a certain time regime. This difference can be accounted for by the strong correlations between the particles, which we explore indirectly through the fluctuations of the center of mass of the cloud and the expected value of the experienced density, defined as the average density measured by the particles themselves.

cond-mat.stat-mech↗

arXiv2021

Entanglement in non-critical inhomogeneous quantum chains

We study an inhomogeneous critical Ising chain in a transverse field whose couplings decay exponentially from the center. In the strong inhomogeneity limit we apply Fisher's renormalization group to show that the ground state is formed by concentric singlets similar to those of the rainbow state of the XX model. In the weak inhomogeneity limit we map the model to a massless Majorana fermion living in a hyperbolic spacetime, where, using CFT techniques, we derive the entanglement entropy that is violated linearly. We also study an inhomogeneous non-critical Ising model that for weak inhomogeneity is mapped to a massive Majorana fermion, while for strong inhomogeneity regime it exhibits trivial and non-trivial topological phases and a separation between regions with high and low entanglement. We also present the entanglement Hamiltonian of the model.

cond-mat.str-el↗

arXiv2021

Bulk-edge correspondence in the Haldane phase of the bilinear-biquadratic spin-1 Hamiltonian

The Haldane phase is the prototype of symmetry protected topological (SPT) phases of spin chain systems. It can be protected by several symmetries having in common the degeneracy of the entanglement spectrum. Here we explore in depth this degeneracy for the spin-1 AKLT and bilinear-biquadratic Hamiltonians and show the emergence of a bulk-edge correspondence that relates the low energy properties of the entanglement Hamiltonian of a periodic chain and that of the physical Hamiltonian of an open chain. We find that the entanglement spectrum can be described in terms of two spins-1/2 behaving as the effective spins at the end of the open chain. In the case of non-contiguous partitions, we find that the entanglement Hamiltonian is given by the spin-1/2 Heisenberg Hamiltonian, which suggests a relationship between SPT phases and conformal field theory. We finally investigate the string order parameter and the relation with the bulk-edge correspondence.

quant-ph↗

arXiv2021

A Schelling model with a variable treshold in a closed city segregation model. Analysis of the universality classes

Residential segregation is analyzed via the Schelling model, in which two types of agents attempt to optimize their situation according to certain preferences and tolerance levels. Several variants of this work are focused on urban or social aspects. Whereas these models consider fixed values for wealth or tolerance, here we consider how sudden changes in the tolerance level affect the urban structure in the closed city model. In this framework, when tolerance decreases continuously, the change rate is a key parameter for the final state reached by the system. On the other hand, sudden drops in tolerance tend to group agents into clusters whose boundary can be characterized using tools from kinetic roughening. This frontier can be categorized into the Edward-Wilkinson (EW) universality class. Likewise, the understanding of these processes and how society adapts to tolerance variations are of the utmost importance in a world where migratory movements and pro-segregational attitudes are commonplace.

physics.soc-ph↗

arXiv2021

Emergent geometry from entanglement structure

We attempt to reveal the geometry, emerged from the entanglement structure of any general $N$-party pure quantum many-body state by representing entanglement entropies corresponding to all $2^N $ bipartitions of the state by means of a generalized adjacency matrix. We show this representation is often exact and may lead to a geometry very different than suggested by the Hamiltonian. Moreover, in all the cases, it yields a natural entanglement contour, similar to previous proposals. The formalism is extended for conformal invariant systems, and a more insightful interpretation of entanglement is presented as a flow among different parts of the system.

quant-ph↗

arXiv2021

Avalanches in an extended Schelling model: an explanation of urban gentrification

In this work we characterize sudden increases in the land price of certain urban areas, a phenomenon causing gentrification, via an extended Schelling model. An initial price rise forces some of the disadvantaged inhabitants out of the area, creating vacancies which other groups find economically attractive. Intolerance issues forces further displacements, possibly giving rise to an avalanche. We consider how gradual changes in the economic environment affect the urban architecture through such avalanche processes, when agents may enter or leave the city freely. The avalanches are characterized by power-law histograms, as it is usually the case in self-organized critical phenomena.

physics.soc-ph↗