Silvia N. Santalla

In the context of first-passage percolation, 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 the 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.

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 information 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. 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.

We introduce the concept of , a set of strongly entangled distant sites within the ground state of a quantum many-body system. Such halos emerge in starlike 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 nontrivial 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.

Until very recently, the asymptotic occurrence of intrinsic anomalous scaling has been expected to require concomitant effects for kinetically rough interfaces, like quenched disorder or morphological instabilities. However, counterexamples have been recently reported for simpler situations dominated by time-dependent noise, as in the discrete growth system associated with an Ising model proposed by Dashti-Naserabadi et al (2019 Phys. Rev. E 100, 060101(R)), who assessed the equilibrium behaviour of the model. Here, we revisit this system to characterise its time-dependent behaviour in two and three dimensions (one- and two-dimensional interfaces, respectively). While the 3D case seems dominated by a fast evolution beyond critical dynamics, in the 2D case, numerical simulations of an associated time-dependent Ginzburg–Landau equation retrieve the same static (roughness) exponents and the same intrinsic anomalous scaling ansatz as in the equilibrium case throughout the complete time evolution. However, the dynamic exponent is seen to cross over between two different values, none of which enables identification with previously known universality classes of kinetic roughening. Moreover, simulations for larger system sizes suggest a breakdown of scaling behaviour at the largest scales, suggesting that the previously reported scaling behaviour may be effective and restricted to relatively small systems.

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.

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 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.

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 quasiparticle picture, which states that local entanglement spreads as if it was carried by quasiparticles which separate at a fixed speed. We extend the quasiparticle 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.

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.

A 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.

We discuss the expressive power of the quantum restricted Boltzmann machine Ansatz in order to represent faithfully the operation process of a quantum spin-glass system undergoing an adiabatic quantum computation process. We address both the representability and the trainability problems associated to the restricted Boltzmann machine Ansatz when we try to describe the ground state of a quantum Ising spin-glass in a transverse field. In our approach, we obtain the ground state of the system using exact diagonalization and find the optimal restricted Boltzman machine. Our preliminary results show that due to the complex spin-glass landscape, for some topologies of the restricted Bolztmann machine, the parameters of the representation are hard to be found.