The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

The momentum bands, energy dispersions, and velocities of the charge $c$ fermions and spin-neutral two-spinon $s1$ fermions of a square-lattice quantum liquid referring to the Hubbard model on such a lattice of edge length $L$ in the one- and two-electron subspace are studied. The model involves the effective nearest-neighbor integral $t$ and on-site repulsion $U$ and can be experimentally realized in systems of correlated ultra-cold fermionic atoms on an optical lattice and thus our results are of interest for such systems. Our investigations profit from a general rotated-electron description, which is consistent with the model global $SO(3)\times SO(3)\times U(1)$ symmetry. For the model in the one- and two-electron subspace the discrete momentum values of the $c$ and $s1$ fermions are good quantum numbers so that in contrast to the original strongly-correlated electronic problem their interactions are residual. The use of our description renders an involved many-electron problem into a quantum liquid with some similarities with a Fermi liquid.Comment: 61 pages, 1 figure, published in Nuclear Physics

System complexity and policy integration challenges: The Brazilian Energy- Water-Food Nexus

The Energy-Water-Food Nexus is one of the most complex sustainability challenges faced by the world. This is particularly true in Brazil, where insufficiently understood interactions within the Nexus are contributing to large-scale deforestation and land-use change, water and energy scarcity, and increased vulnerability to climate change. The reason is a combination of global environmental change and global economic change, putting unprecedented pressures on the Brazilian environment and ecosystems. In this paper, we identify and discuss the main Nexus challenges faced by Brazil across sectors (e.g. energy, agriculture, water) and scales (e.g. federal, state, municipal). We use four case studies to explore all nodes of the Nexus. For each, we analyse data from economic and biophysical modelling sources in combination with an overview of the legislative and policy landscape, in order to identify governance shortcomings in the context of growing challenges. We analyse the complex interdependence of developments at the global and local (Brazilian) levels, highlighting the impact of global environmental and economic change on Brazil and, conversely, that of developments in Brazil for other countries and the world. We conclude that there is a need to adjust the scientific approach to these challenges as an enabling condition for stronger science-policy bridges for sustainability policy-making. © 2019 The Author(s

Spinon and η -spinon correlation functions of the Hubbard chain

We calculate real-space static correlation functions of spin and charge degrees of freedom of the one-dimensional Hubbard model that are described by operators related to singly occupied sites with spin up or spin down (spinons) and unoccupied or doubly occupied sites ( η -spinons). The spatial decay of their correlation functions is determined using density matrix renormalization group results. The nature and spatial extent of the correlations between two sites on the Hubbard chain is studied using the eigenstates and eigenvalues of the two-site reduced density matrix. The results show that the spinon-spinon correlation functions decay algebraically and the η -spinon correlation functions decay exponentially, both in the half- filling and metallic phases. The results provide evidence that these degrees of freedom are organized in boundstates in the interacting system.Portuguese FCT both in the frame- work of the Strategic Project PEST-C/FIS/UI607/2011 and under SFRH/BSAB/1177 /201