-We show how the phenomenon of factorization in a quantum many body system is of collective nature. To this aim we study the quantum discord Q in the one dimensional XY model in a transverse field. We analyze the behavior of Q at both the critical point and at the non critical factorizing field. The factorization is found to be governed by an exponential scaling law for Q. We also address the thermal effects fanning out from the anomalies occurring at zero temperature. Close to the quantum phase transition, Q exhibits a finite-temperature crossover with universal scaling behavior, while the factorization phenomenon results in a non trivial pattern of correlations present at low temperature.

Motivated by its role as a central pillar of current theories of the dynamics of spin ice in and out of equilibrium, we study the single-ion dynamics of the magnetic rare-earth ions in their local environments, subject to the effective fields set up by the magnetic moments with which they interact. This effective field has a transverse component with respect to the local easy axis of the crystal electric field, which can induce quantum tunneling. We go beyond the projective spin-1/2 picture and use instead the full crystal-field Hamiltonian. We find that the Kramers versus non-Kramers nature, as well as the symmetries of the crystal-field Hamiltonian, result in different perturbative behavior at small fields ( 1 T), with transverse field effects being more pronounced in Ho 2 Ti 2 O 7 than in Dy 2 Ti 2 O 7 . Remarkably, the energy splitting range we find is consistent with time scales extracted from experiments. We also present a study of the static magnetic response, which highlights the anisotropy of the system in the form of an off-diagonal g tensor, and we investigate the effects of thermal fluctuations in the temperature regime of relevance to experiments. We show that there is a narrow but accessible window of experimental parameters where the anisotropic response can be observed.

Demand for freshwater is rising with factors, such as population growth, land use change and climate variations, rendering water availability in the future uncertain. Groundwater resources are being increasingly exploited to meet this growing demand. The aim of this study is to identify the influence of population growth induced by land use change and climate change on the future state of freshwater resources of Lamu Island in Kenya where a major port facility is under construction. The results of this study show that the "no industrial development" population scenario (assuming the port was not constructed) would be expected to reach ~50,000 people by 2050, while the projected population upon completion is expected to reach 1.25 million in the same year when the Lamu Port-South Sudan-Ethiopia Transport Corridor Program (LAPSSET) port reaches its full cargo-handling capacity. The groundwater abstraction in 2009 was 0.06 m 3 daily per capita, while the demand is expected to raise to 0.1 m 3 by 2050 according to the "LAPSSET development" projection. The modelling results show that the Shela aquifer in Lamu, which is the main source of water on the island, will not experience stress by 2065 for the "no industrial development" OPEN ACCESSWater 2015, 7 1265 population scenario, whereas for the "LAPSSET development projection" population scenario, it will occur sooner (between 2020 and 2028). The modelling results show that the Representative Concentration Pathways (RCP) climate change scenarios will have a smaller impact on the effective water volume reserves than Special Report on Emissions Scenarios (SRES) for the "no industrial development", while the impact is expected to be similar for the "LAPSSET development", suggesting that population growth exacerbated by land use change will be a more significant driving force than climate change in affecting freshwater availability.

The spin ice materials Ho2Ti2O7 and Dy2Ti2O7 are by now perhaps the best-studied classical frustrated magnets. A crucial step towards the understanding of their low temperature behaviour -both regarding their unusual dynamical properties and the possibility of observing their quantum coherent time evolution -is a quantitative understanding of the spin-flip processes which underpin the hopping of magnetic monopoles. We attack this problem in the framework of a quantum treatment of a single-ion subject to the crystal, exchange and dipolar fields from neighbouring ions. By studying the fundamental quantum mechanical mechanisms, we discover a bimodal distribution of hopping rates which depends on the local spin configuration, in broad agreement with rates extracted from experiment. Applying the same analysis to Pr2Sn2O7 and Pr2Zr2O7, we find an even more pronounced separation of timescales signalling the likelihood of coherent many-body dynamics. arXiv:1810.11469v3 [cond-mat.str-el]

Terbium gallium garnet (TGG), Tb3Ga5O12, is well known for its applications in laser optics, but also exhibits complex low-temperature magnetism that is not yet fully understood. Its lowtemperature magnetic order is determined by means of time-of-flight neutron powder diffraction. It is found to be a multiaxial antiferromagnet with magnetic Tb 3+ ions forming six sublattices of magnetic moments aligned parallel and anti-parallel to the 100 crystallographic directions of the cubic unit cell. The structure displays strong easy-axis anisotropy with respect to a two-fold axis of symmetry in the local orthorhombic environment of the Tb 3+ sites. The crystal-field splitting within the single-ion ground-state manifold is investigated by inelastic neutron scattering on powder samples. A strong temperature dependence of the quasidoublet ground-state is observed and revised parameters of the crystal-field Hamiltonian are given. The results of bulk magnetic susceptibility and magnetisation measurements are in good agreement with values based on the crystal-field model down to 20 K, where the onset of magnetic correlations is observed.

We analyze the quantum discordQ throughout the low temperature phase diagram of the quantum XY model in transverse field. We first focus on the T = 0 order–disorder quantum phase transition QPT both in the symmetric ground state and in the symmetry broken one. Beside it, we highlight how Q displays clear anomalies also at a noncritical value of the control parameter inside the ordered phase, where the ground state is completely factorized. We evidence how the phenomenon is in fact of collective nature and displays universal features. We also study Q at finite temperature. We show that, close to the QPT, Q exhibits quantum-classical crossover of the system with universal scaling behavior. We evidence a nontrivial pattern of thermal correlations resulting from the factorization phenomenon.

We analyze the quantum discord Q throughout the low-temperature phase diagram of the quantum XY model in transverse field. We first focus on the T = 0 order-disorder quantum phase transition both in the symmetric ground state and in the symmetry broken one. Besides it, we highlight how Q displays clear anomalies also at a non critical value of the control parameter inside the ordered phase, where the ground state is completely factorized. We evidence how the phenomenon is in fact of collective nature and displays universal features. We also study Q at finite temperature. We show that, close to the quantum phase transition, Q exhibits quantum-classical crossover of the system with universal scaling behavior. We evidence a non trivial pattern of thermal correlations resulting from the factorization phenomenon.

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