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

Synoptic-scale controls on the δ18O in precipitation across Beringia

Oxygen isotope records of precipitation (δ18Oprecip) from Beringia are thought to reflect synoptic-scale circulation changes associated with the Aleutian Low. To delineate the spatial pattern of δ18Oprecip associated with the two dominant modes of Aleutian Low circulation, we combine modern δ18Oprecip and deuterium excess data with climate reanalysis and back-trajectory modelling. Aleutian Low strength and position are revealed to systematically affect regional moisture source and δ18Oprecip; whereby a strengthened Aleutian Low causes lower (higher) δ18Oprecip in western (eastern) Beringia. We compare a new 100-year-long δ18O record from the Aleutian Islands with the North Pacific Index, the primary indicator of Aleutian Low strength, and find a significant positive relationship (r = 0.43, p < 0.02, n = 28) that tracks late 20th century change. This study demonstrates synoptic-scale circulation controls on our isotope record, and provides a coherent framework for interpreting existing and emerging paleo-isotope data from the region

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

Western Pacific atmospheric nutrient deposition fluxes, their impact on surface ocean productivity

The atmospheric deposition of both macronutrients and micronutrients plays an important role in driving primary productivity, particularly in the low-latitude ocean. We report aerosol major ion measurements for five ship-based sampling campaigns in the western Pacific from similar to 25 degrees N to 20 degrees S and compare the results with those from Atlantic meridional transects (similar to 50 degrees N to 50 degrees S) with aerosols collected and analyzed in the same laboratory, allowing full incomparability. We discuss sources of the main nutrient species (nitrogen (N), phosphorus (P), and iron (Fe)) in the aerosols and their stoichiometry. Striking north-south gradients are evident over both basins with the Northern Hemisphere more impacted by terrestrial dust sources and anthropogenic emissions and the North Atlantic apparently more impacted than the North Pacific. We estimate the atmospheric supply rates of these nutrients and the potential impact of the atmospheric deposition on the tropical western Pacific. Our results suggest that the atmospheric deposition is P deficient relative to the needs of the resident phytoplankton. These findings suggest that atmospheric supply of N, Fe, and P increases primary productivity utilizing some of the residual excess phosphorus (P*) in the surface waters to compensate for aerosol P deficiency. Regional primary productivity is further enhanced via the stimulation of nitrogen fixation fuelled by the residual atmospheric iron and P*. Our stoichiometric calculations reveal that a P* of 0.1 mu mol L-1 can offset the P deficiency in atmospheric supply for many months. This study suggests that atmospheric deposition may sustain similar to 10% of primary production in both the western tropical Pacific