Transfer Matrices and Excitations with Matrix Product States

We investigate the relation between static correlation functions in the ground state of local quantum many-body Hamiltonians and the dispersion relations of the corresponding low energy excitations using the formalism of tensor network states. In particular, we show that the Matrix Product State Transfer Matrix (MPS-TM) - a central object in the computation of static correlation functions - provides important information about the location and magnitude of the minima of the low energy dispersion relation(s) and present supporting numerical data for one-dimensional lattice and continuum models as well as two-dimensional lattice models on a cylinder. We elaborate on the peculiar structure of the MPS-TM's eigenspectrum and give several arguments for the close relation between the structure of the low energy spectrum of the system and the form of static correlation functions. Finally, we discuss how the MPS-TM connects to the exact Quantum Transfer Matrix (QTM) of the model at zero temperature. We present a renormalization group argument for obtaining finite bond dimension approximations of MPS, which allows to reinterpret variational MPS techniques (such as the Density Matrix Renormalization Group) as an application of Wilson's Numerical Renormalization Group along the virtual (imaginary time) dimension of the system.Comment: 39 pages (+8 pages appendix), 14 figure

Symmetry Breaking and the Geometry of Reduced Density Matrices

The concept of symmetry breaking and the emergence of corresponding local order parameters constitute the pillars of modern day many body physics. The theory of quantum entanglement is currently leading to a paradigm shift in understanding quantum correlations in many body systems and in this work we show how symmetry breaking can be understood from this wavefunction centered point of view. We demonstrate that the existence of symmetry breaking is a consequence of the geometric structure of the convex set of reduced density matrices of all possible many body wavefunctions. The surfaces of those convex bodies exhibit non-analytic behavior in the form of ruled surfaces, which turn out to be the defining signatures for the emergence of symmetry breaking and of an associated order parameter. We illustrate this by plotting the convex sets arising in the context of three paradigmatic examples of many body systems exhibiting symmetry breaking: the quantum Ising model in transverse magnetic field, exhibiting a second order quantum phase transition; the classical Ising model at finite temperature in two dimensions, which orders below a critical temperature $T_c$; and a system of free bosons at finite temperature in three dimensions, exhibiting the phenomenon of Bose-Einstein condensation together with an associated order parameter $\langle\psi\rangle$. Remarkably, these convex sets look all very much alike. We believe that this wavefunction based way of looking at phase transitions demystifies the emergence of order parameters and provides a unique novel tool for studying exotic quantum phenomena.Comment: 5 pages, 3 figures, Appendix with 2 pages, 3 figure

Mapping the aerosol over Eurasia from the Zotino Tall Tower

The present study covers more than 5 yr corresponding to more than 40 000 hours of particle and gas data measured at the Siberian tall tower Zotino Tall Tower (ZOTTO) (60.8%26deg%3BN; 89.35%26deg%3BE). Extrapolated along 10-d back trajectories, the ZOTTO measurements cover large parts of the Eurasian land mass. Mapping the extrapolated ZOTTO data points to major anthropogenic source regions and Siberian fire regions, consistent with emission data for CO and vegetation fires. Middle East mid-latitude sources stand out strongly and possibly emissions from Northern China may be seen at times from ZOTTO. The maps of measured light scattering and absorption characteristics support the interpretation of different source types. Three clusters of substantially different submicrometer particle size distributions were found, the maps of which also could be related to major aerosol source regions

Large emissions from floodplain trees close the Amazon methane budget

Wetlands are the largest global source of atmospheric methane (CH4), a potent greenhouse gas. However, methane emission inventories from the Amazon floodplain, the largest natural geographic source of CH4 in the tropics, consistently underestimate the atmospheric burden of CH4 determined via remote sensing and inversion modelling, pointing to a major gap in our understanding of the contribution of these ecosystems to CH4 emissions. Here we report CH4 fluxes from the stems of 2,357 individual Amazonian floodplain trees from 13 locations across the central Amazon basin. We find that escape of soil gas through wetland trees is the dominant source of regional CH4 emissions. Methane fluxes from Amazon tree stems were up to 200 times larger than emissions reported for temperate wet forests6 and tropical peat swamp forests, representing the largest non-ebullitive wetland fluxes observed. Emissions from trees had an average stable carbon isotope value (δ13C) of −66.2 ± 6.4 per mil, consistent with a soil biogenic origin. We estimate that floodplain trees emit 15.1 ± 1.8 to 21.2 ± 2.5 teragrams of CH4 a year, in addition to the 20.5 ± 5.3 teragrams a year emitted regionally from other sources. Furthermore, we provide a ‘top-down’ regional estimate of CH4 emissions of 42.7 ± 5.6 teragrams of CH4 a year for the Amazon basin, based on regular vertical lower-troposphere CH4 profiles covering the period 2010–2013. We find close agreement between our ‘top-down’ and combined ‘bottom-up’ estimates, indicating that large CH4 emissions from trees adapted to permanent or seasonal inundation can account for the emission source that is required to close the Amazon CH4 budget. Our findings demonstrate the importance of tree stem surfaces in mediating approximately half of all wetland CH4 emissions in the Amazon floodplain, a region that represents up to one-third of the global wetland CH4 source when trees are combined with other emission sources

Nitrate stable isotopes and major ions in snow and ice samples from four Svalbard sites

Increasing reactive nitrogen (N-r) deposition in the Arctic may adversely impact N-limited ecosystems. To investigate atmospheric transport of N-r to Svalbard, Norwegian Arctic, snow and firn samples were collected from glaciers and analysed to define spatial and temporal variations (1 10 years) in major ion concentrations and the stable isotope composition (delta N-15 and delta O-18) of nitrate (NO3-) across the archipelago. The delta N-15(NO3-) and delta O-18(NO3-) averaged -4 parts per thousand and 67 parts per thousand in seasonal snow (2010-11) and -9 parts per thousand and 74 parts per thousand in firn accumulated over the decade 2001-2011. East-west zonal gradients were observed across the archipelago for some major ions (non-sea salt sulphate and magnesium) and also for delta N-15(NO3-) and delta O-18(NO3-) in snow, which suggests a different origin for air masses arriving in different sectors of Svalbard. We propose that snowfall associated with long-distance air mass transport over the Arctic Ocean inherits relatively low delta N-15(NO3-) due to in-transport N isotope fractionation. In contrast, faster air mass transport from the north-west Atlantic or northern Europe results in snowfall with higher delta N-15(NO3-) because in-transport fractionation of N is then time-limited

Temporal changes in the epidemiology, management, and outcome from acute respiratory distress syndrome in European intensive care units: a comparison of two large cohorts

Background: Mortality rates for patients with ARDS remain high. We assessed temporal changes in the epidemiology and management of ARDS patients requiring invasive mechanical ventilation in European ICUs. We also investigated the association between ventilatory settings and outcome in these patients. Methods: This was a post hoc analysis of two cohorts of adult ICU patients admitted between May 1–15, 2002 (SOAP study, n = 3147), and May 8–18, 2012 (ICON audit, n = 4601 admitted to ICUs in the same 24 countries as the SOAP study). ARDS was defined retrospectively using the Berlin definitions. Values of tidal volume, PEEP, plateau pressure, and FiO2 corresponding to the most abnormal value of arterial PO2 were recorded prospectively every 24 h. In both studies, patients were followed for outcome until death, hospital discharge or for 60 days. Results: The frequency of ARDS requiring mechanical ventilation during the ICU stay was similar in SOAP and ICON (327[10.4%] vs. 494[10.7%], p = 0.793). The diagnosis of ARDS was established at a median of 3 (IQ: 1–7) days after admission in SOAP and 2 (1–6) days in ICON. Within 24 h of diagnosis, ARDS was mild in 244 (29.7%), moderate in 388 (47.3%), and severe in 189 (23.0%) patients. In patients with ARDS, tidal volumes were lower in the later (ICON) than in the earlier (SOAP) cohort. Plateau and driving pressures were also lower in ICON than in SOAP. ICU (134[41.1%] vs 179[36.9%]) and hospital (151[46.2%] vs 212[44.4%]) mortality rates in patients with ARDS were similar in SOAP and ICON. High plateau pressure (> 29 cmH2O) and driving pressure (> 14 cmH2O) on the first day of mechanical ventilation but not tidal volume (> 8 ml/kg predicted body weight [PBW]) were independently associated with a higher risk of in-hospital death. Conclusion: The frequency of and outcome from ARDS remained relatively stable between 2002 and 2012. Plateau pressure > 29 cmH2O and driving pressure > 14 cmH2O on the first day of mechanical ventilation but not tidal volume > 8 ml/kg PBW were independently associated with a higher risk of death. These data highlight the continued burden of ARDS and provide hypothesis-generating data for the design of future studies

Holocene sea ice variability driven by wind and polynya efficiency in the Ross Sea

The causes of the recent increase in Antarctic sea ice extent, characterised by large regional contrasts and decadal variations, remain unclear. In the Ross Sea, where such a sea ice increase is reported, 50% of the sea ice is produced within wind-sustained latent-heat polynyas. Combining information from marine diatom records and sea salt sodium and water isotope ice core records, we here document contrasting patterns in sea ice variations between coastal and open sea areas in Western Ross Sea over the current interglacial period. Since about 3600 years before present, an increase in the efficiency of regional latent-heat polynyas resulted in more coastal sea ice, while sea ice extent decreased overall. These past changes coincide with remarkable optima or minima in the abundances of penguins, silverfish and seal remains, confirming the high sensitivity of marine ecosystems to environmental and especially coastal sea ice conditions