Ground state phase diagram of the half-filled bilayer Hubbard model

Employing a combination of functional renormalization group calculations and projective determinantal quantum Monte Carlo simulations, we examine the Hubbard model on the square lattice bilayer at half filling. From this combined analysis, we obtain a comprehensive account on the ground state phase diagram with respect to the extent of the system's metallic and (antiferromagnetically ordered) Mott-insulating as well as band-insulating regions. By means of an unbiased functional renormalization group approach, we exhibit the antiferromagnetic Mott-insulating state as the relevant instability of the free metallic state, induced by any weak finite onsite repulsion. Upon performing a careful analysis of the quantum Monte Carlo data, we resolve the difficulty of identifying this antiferromagnetic ground state for finite interlayer hopping in the weak-coupling regime, where nonmonotonous finite-size corrections are shown to relate to the two-sheeted Fermi surface structure of the metallic phase. On the other hand, quantum Monte Carlo simulations are well suited to identify the transition between the Mott-insulating phase and the band insulator in the intermediate-to-strong coupling regime. Here, we compare our numerical findings to indications for the transition region obtained from the functional renormalization group procedure.Comment: 12 pages, 15 figure

Poor farmers - poor yields: socio-economic, soil fertility and crop management indicators affecting climbing bean productivity in northern Rwanda

Climbing bean is the key staple legume crop in the highlands of East and Central Africa. We assessed the impact of interactions between soil fertility characteristics, crop management and socio-economic factors, such as household resource endowment and gender of the farmer, on climbing bean productivity and yield responses to basal P fertiliser in northern Rwanda. Through a combination of detailed characterisations of 12 farms and on-farm demonstration trials at 110 sites, we evaluated variability in grain yields and responses to fertiliser. Grain yields varied between 0.14 and 6.9 t ha−1 with an overall average of 1.69 t ha−1. Household resource endowment and gender of the farmer was strongly associated with climbing bean yield, even though these were partly confounded with Sector. Poorer households and women farmers achieved lower yields than wealthier households and male farmers. Household resource endowment and gender were likely to act as proxies for a range of agronomic and crop management factors that determine crop productivity, such as soil fertility, current and past access to organic manure and mineral fertiliser, access to sufficient quality staking material, ability to conduct crop management operation on time, but we found evidence for only some of these relationships. Poorer households and female farmers grew beans on soils with poorer soil fertility. Moreover, poorer households had a lower density of stakes, while stake density was strongly correlated with yield. Diammonium phosphate (DAP) fertiliser application led to a substantial increase in the average grain yield (0.66 t ha−1), but a large variability in responses implied that its use would be economically worthwhile for roughly half of the farmers. For the sake of targeting agricultural innovations to those households that are most likely to adopt, the Ubudehe household typology – a Rwandan government system of wealth categorisation – could be a useful and easily available tool to structure rural households within regions of Rwanda that are relatively uniform in agro-ecology

Environmental impacts of Scottish faba bean-based beer in an integrated beer and animal feed value chain

Beer is one of themost popular drinks globally and productionmethods clearly need to becomemore sustainable. The brewing of legume grains could contribute to improved sustainability through encouraging the diversification of cropped systems and by providing more nutritious local co-products as animal feed. The aim of this studywas to assess the potential environmental effect of partially substituting malted barley with grain legumes as an option to mitigate the environmental impact of beer. A Life Cycle Assessment (LCA) was performed to compare a novel Scottish beer produced with malted barley and UK-grown faba beans with a traditional malted barley beer. Weconsidered beer production as part of amulti-functional beer and animal feed value chain, where coproducts are used as a high-protein UK-grown animal feed. The environmental performances of the different beers were highly dependent on the system boundaries adopted. The simple attributional LCA indicated that a barley-bean beer could offer environmental savingswhen alcohol yields are optimised, with environmental burdens that were significantly smaller than those of the barley beer across 6 categories. When boundarieswere expanded to include both feed substitution and agricultural rotations, the barley-bean beer with current alcohol yields outperformed the barley beer across 8 impact categories, with a 15 %-17 % smaller climate change burden, mainly due to higher feed substitution achieved froma larger volumeof brewing co-productswith higher protein concentrations. Therefore, brewers should consider the use of legumes in their brewing recipes to lower their environmental footprint, increasing the availability of more nutritious beer co-products as a local source of animal feed, and diversifying cropping systems while adding novelty to their product range. Different boundaries settings and scenarios should be assessed in a beer LCA, and entire cropping rotations should be integrated to capture a more accurate picture of the agricultural stage.(c) 2022 Published by Elsevier Ltd on behalf of Institution of Chemical Engineers

Grain legume yields are as stable as other spring crops in long-term experiments across northern Europe

Grain legumes produce high-quality protein for food and feed, and potentially contribute to sustainable cropping systems, but they are grown on only 1.5% of European arable land. Low temporal yield stability is one of the reasons held responsible for the low proportion of grain legumes, without sufficient quantitative evidence. The objective of this study was to compare the yield stability of grain legumes with other crop species in a northern European context and accounting for the effects of scale in the analysis and the data. To avoid aggregation biases in the yield data, we used data from long-term field experiments. The experiments included grain legumes (lupin, field pea, and faba bean), other broad-leaved crops, spring, and winter cereals. Experiments were conducted in the UK, Sweden, and Germany. To compare yield stability between grain legumes and other crops, we used a scale-adjusted yield stability indicator that accounts for the yield differences between crops following Taylor's Power Law. Here, we show that temporal yield instability of grain legumes (30%) was higher than that of autumn-sown cereals (19%), but lower than that of other spring-sown broad-leaved crops (35%), and only slightly greater than spring-sown cereals (27%). With the scale-adjusted yield stability indicator, we estimated 21% higher yield stability for grain legumes compared to a standard stability measure. These novel findings demonstrate that grain legume yields are as reliable as those of other spring-sown crops in major production systems of northern Europe, which could influence the current negative perception on grain legume cultivation. Initiatives are still needed to improve the crops agronomy to provide higher and more stable yields in future.Peer reviewe

Grain Yield Stability of Cereal-Legume Intercrops Is Greater Than Sole Crops in More Productive Conditions

The intercropping of two or more crop species on the same piece of land at a given time has been hypothesized to enhance crop yield stability. To address this hypothesis, we assessed the grain yield stability of various barley-pea and wheat-faba bean mixtures grown in seven experimental field trials (locations) across Europe during two years with contrasting weather (2017 and 2018). Three different yield stability measures were used, all based on the expected yield variability of the mixture components grown as sole crops, and the corresponding observed yield variability of the same components grown in 50:50 mixtures in a replacement design. Stability indices were calculated as ratios between the expected and observed variabilities, with values > 1 indicating greater stability of the intercrops. Mean grain yields tended to be higher in intercrops than sole crops. However, in contrast to our hypothesis, the observed (intercrop) yield stability was similar or lower than the expected (sole crop) stability in most locations except one. Furthermore, yield stability significantly increased with increasing mean yields when assessed across differentially productive locations. The results are relevant for the designing of intercropping systems as a means to increase yield stability and the resilience of cropping systems.This research was funded by the DIVERSify project, a grant from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 727284. MR was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—420661662. A.J.K. and A.C.N. are also supported by the strategic research programme funded by the Scottish Government’s Rural and Environment Science and Analytical Services Division.Peer reviewe