Entanglement guided search for parent Hamiltonians

We introduce a method for the search of parent Hamiltonians of input wave-functions based on the structure of their reduced density matrix. The two key elements of our recipe are an ansatz on the relation between reduced density matrix and parent Hamiltonian that is exact at the field theory level, and a minimization procedure on the space of relative entropies, which is particularly convenient due to its convexity. As examples, we show how our method correctly reconstructs the parent Hamiltonian correspondent to several non-trivial ground state wave functions, including conformal and symmetry-protected-topological phases, and quantum critical points of two-dimensional antiferromagnets described by strongly coupled field theories. Our results show the entanglement structure of ground state wave-functions considerably simplifies the search for parent Hamiltonians.Comment: 5 pages, 5 figures, supplementary materia

Measuring von Neumann entanglement entropies without wave functions

We present a method to measure the von Neumann entanglement entropy of ground states of quantum many-body systems which does not require access to the system wave function. The technique is based on a direct thermodynamic study of entanglement Hamiltonians, whose functional form is available from field theoretical insights. The method is applicable to classical simulations such as quantum Monte Carlo methods, and to experiments that allow for thermodynamic measurements such as the density of states, accessible via quantum quenches. We benchmark our technique on critical quantum spin chains, and apply it to several two-dimensional quantum magnets, where we are able to unambiguously determine the onset of area law in the entanglement entropy, the number of Goldstone bosons, and to check a recent conjecture on geometric entanglement contribution at critical points described by strongly coupled field theories

The hydrogeological role of an aquitard in preventing drinkable water well contamination: a case study.

Groundwater pollution has become a worrisome phenomenon, mainly for aquifers underlying industrialized areas. In order to evaluate the risk of pollution, a model of the aquifer is needed. Herewith, we describe a quasi-tridimensional model, which we applied to a multilayered aquifer where a phreatic aquifer was coupled to a confined one by means of an aquitard. This hydrogeological scheme is often met in practice and, therefore, models a number of situations. Moreover, aquitards play and important role in the management of natural resources of this kind. The model we adopted contains some approximations: the flow within the aquifers is assumed to be horizontal, whereas leakage is assumed vertical. The effect of some wells drilled in these aquifers is also taken into account. In order to evaluate the leakage fluxes that correspond to different exploitation conditions, we numerically solve a system of quasilinear and time-dependent partial differential equations. This model has been calibrated by the hydrogeological data from a water supply station of the Milan Water Works, where water is polluted by some halocarbons. Our simulations account for several experimental facts, both from the hydrogeological and hydrogeochemical viewpoints. Maxima of computed downward leakage rates are found to correspond with measured pollutant concentration maxima. Other results show how the aquitard can help in minimizing the contamination of drinkable water

Trimer states with ℤ₃ topological order in Rydberg atom arrays.

Trimers are defined as two adjacent edges on a graph. We study the quantum states obtained as equal-weight superpositions of all trimer coverings of a lattice, with the constraint of having a trimer on each vertex: the so-called trimer resonating-valence-bond (tRVB) states. Exploiting their tensor network representation, we show that these states can host $\mathbb{Z}_3$ topological order or can be gapless liquids with $\mathrm{U}(1) \times \mathrm{U}(1)$ local symmetry. We prove that this continuous symmetry emerges whenever the lattice can be tripartite such that each trimer covers all the three sublattices. In the gapped case, we demonstrate the stability of topological order against dilution of maximal trimer coverings, which is relevant for realistic models where the density of trimers can fluctuate. Furthermore, we clarify the connection between gapped tRVB states and $\mathbb{Z}_3$ lattice gauge theories by smoothly connecting the former to the $\mathbb{Z}_3$ toric code, and discuss the non-local excitations on top of tRVB states. Finally, we analyze via exact diagonalization the zero-temperature phase diagram of a diluted trimer model on the square lattice and demonstrate that the ground state exhibits topological properties in a narrow region in parameter space. We show that a similar model can be implemented in Rydberg atom arrays exploiting the blockade effect. We investigate dynamical preparation schemes in this setup and provide a viable route for probing experimentally $\mathbb{Z}_3$ quantum spin liquids

Modelling categorical covariates in Bayesian disease mapping by partition structures

We consider the problem of mapping the risk from a disease using a series of regional counts of observed and expected cases, and information on potential risk factors. To analyse this problem from a Bayesian viewpoint we propose a methodology, which extends a spatial partition model by including categorical covariate information. Such an extension allows to detect clusters in the residual variation, reflecting further, possibly unobserved, covariates. The methodology is implemented by means of reversible jump Markov chain Monte Carlo sampling. An application is presented, in order to illustrate and compare our proposed extensions with a purely spatial partition model. Here we analyse a well-known dataset on lip cancer incidence in Scotland

Financial contagion through space-time point processes

We propose to study the dynamics of financial contagion by means of a class of point process models employed in the modeling of seismic contagion. The proposal extends network models, recently introduced to model financial contagion, in a space-time point process perspective. The extension helps to improve the assessment of credit risk of an institution, taking into account contagion spillover effects

Bioerosion by microbial euendoliths in benthic foraminifera from heavy metal-polluted coastal environments of Portovesme (South-Western Sardinia, Italy)

A monitoring survey of the coastal area facing the industrial area of Portoscuso-Portovesme (south-western Sardinia, Italy) revealed intense bioerosional processes. Benthic foraminifera collected at the same depth (about 2 m)but at different distances from the pollution source show extensive microbial infestation, anomalous Mg/Ca molar ratios and high levels of heavy metals in the shell associated with a decrease in foraminifera richness, population density and biodiversity with the presence of morphologically abnormal specimens. We found that carbonate dissolution induced by euendoliths is selective, depending on the Mg content and morpho-structural types of foraminiferal taxa. This study provides evidences for a connection between heavy metal dispersion, decrease in pH of the sea-water and bioerosional processes on foraminifera

Evidence of breakdown of the spin symmetry in diluted 2D electron gases

Recent claims of an experimental demonstration of spontaneous spin polarisation in dilute electron gases \cite{young99} revived long standing theoretical discussions \cite{ceper99,bloch}. In two dimensions, the stabilisation of a ferromagnetic fluid might be hindered by the occurrence of the metal-insulator transition at low densities \cite{abra79}. To circumvent localisation in the two-dimensional electron gas (2DEG) we investigated the low populated second electron subband, where the disorder potential is mainly screened by the high density of the first subband. This letter reports on the breakdown of the spin symmetry in a 2DEG, revealed by the abrupt enhancement of the exchange and correlation terms of the Coulomb interaction, as determined from the energies of the collective charge and spin excitations. Inelastic light scattering experiments and calculations within the time-dependent local spin-density approximation give strong evidence for the existence of a ferromagnetic ground state in the diluted regime.Comment: 4 pages, 4 figures, Revte

Entanglement Hamiltonians of lattice models via the Bisognano-Wichmann theorem

The modular (or entanglement) Hamiltonian correspondent to the half-space bipartition of a quantum state uniquely characterizes its entanglement properties. However, in the context of lattice models, its explicit form is analytically known only for the two spin chains and certain free theories in one dimension. In this work, we provide a thorough investigation of entanglement Hamiltonians in lattice models obtained via the Bisognano-Wichmann theorem, which provides an explicit functional form for the entanglement Hamiltonian itself in quantum field theory. Our study encompasses a variety of one- and two-dimensional models, supporting diverse quantum phases and critical points, and, most importantly, scanning several universality classes, including Ising, Potts, and Luttinger liquids. We carry out extensive numerical simulations based on the density matrix renormalization group method, exact diagonalization, and quantum Monte Carlo. In particular, we compare the exact entanglement properties and correlation functions to those obtained applying the Bisognano-Wichmann theorem on the lattice. We carry out this comparison on both the eigenvalues and eigenvectors of the entanglement Hamiltonian, and expectation values of correlation functions and order parameters. Our results evidence that as long as the low-energy description of the lattice model is well captured by a Lorentz-invariant quantum field theory, the Bisognano-Wichmann theorem provides a qualitatively and quantitatively accurate description of the lattice entanglement Hamiltonian. The resulting framework paves the way to direct studies of entanglement properties utilizing well-established statistical mechanics methods and experiments