Entanglement and SU(n) symmetry in one-dimensional valence bond solid states

Here we evaluate the many-body entanglement properties of a generalized SU(n) valence bond solid state on a chain. Our results follow from a derivation of the transfer matrix of the system which, in combination with symmetry properties, allows for a new, elegant and straightforward evaluation of different entanglement measures. In particular, the geometric entanglement per block, correlation length, von Neumann and R\'enyi entropies of a block, localizable entanglement and entanglement length are obtained in a very simple way. All our results are in agreement with previous derivations for the SU(2) case.Comment: 4 pages, 2 figure

Visualizing elusive phase transitions with geometric entanglement

We show that by examining the global geometric entanglement it is possible to identify "elusive" or hard to detect quantum phase transitions. We analyze several one-dimensional quantum spin chains and demonstrate the existence of non-analyticities in the geometric entanglement, in particular across a Kosterlitz-Thouless transition and across a transition for a gapped deformed Affleck-Kennedy-Lieb-Tasaki chain. The observed non-analyticities can be understood and classified in connection to the nature of the transitions, and are in sharp contrast to the analytic behavior of all the two-body reduced density operators and their derived entanglement measures.Comment: 7 pages, 5 figures, revised version, accepted for publication in PR

First order phase transition in the anisotropic quantum orbital compass model

We investigate the anisotropic quantum orbital compass model on an infinite square lattice by means of the infinite projected entangled-pair state algorithm. For varying values of the $J_x$ and $J_z$ coupling constants of the model, we approximate the ground state and evaluate quantities such as its expected energy and local order parameters. We also compute adiabatic time evolutions of the ground state, and show that several ground states with different local properties coexist at $J_x = J_z$. All our calculations are fully consistent with a first order quantum phase transition at this point, thus corroborating previous numerical evidence. Our results also suggest that tensor network algorithms are particularly fitted to characterize first order quantum phase transitions.Comment: 4 pages, 3 figures, major revision with new result

Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model

We establish a relation between several entanglement properties in the Lipkin-Meshkov-Glick model, which is a system of mutually interacting spins embedded in a magnetic field. We provide analytical proofs that the single-copy entanglement and the global geometric entanglement of the ground state close to and at criticality behave as the entanglement entropy. These results are in deep contrast to what is found in one- dimensional spin systems where these three entanglement measures behave differently.Comment: 4 pages, 2 figures, published versio

On Higher Derivatives as Constraints in Field Theory: a Geometric Perspective

We formalize geometrically the idea that the (de Donder) Hamiltonian formulation of a higher derivative Lagrangian field theory can be constructed understanding the latter as a first derivative theory subjected to constraints.Comment: 7 page

THE ECONOMIC IMPLICATIONS of TIED AID and LOCAL CONTENT REQUIREMENTS for CLIMATE FINANCE

The Paris Agreement states that from 2020 developed countries will mobilize at least USD 100 billion per year to support climate action in developing countries. The attainment of this objective involves decisions by donor countries about the channel and destination of climate finance disbursements. This paper explores how the spending conditions associated to different disbursement options can affect the opportunities for donors to expand their exports. In particular, using a Multiregional Input-Output Model, it finds that donors have an economic incentive for choosing bilateral channels that enable to tie aid to the detriment of multilateral ones, such as the Green Climate Fund. On the other hand, local content requirements imposed by recipient countries do not substantially affect donors' exports, since they do not reduce intermediate exports, which represent a relevant share of the total exports generated by the mitigation and adaptation actions analysed. © 2020 World Scientific Publishing Company.The participation of María Victoria Román and Ibon Galarraga on this paper has been funded by CICEP (Strategic Challenges in International Climate and Energy Policy), one of three centres for social science based research on environment-friendly energy established by the Research Council of Norway in 2011 (http://www.cicep.uio.no/). Alberto Ansuategi also thanks financial support from Economy and Competitiveness Ministry of Spain (ECO2015-68023) and the Basque Government (IT-799-13)