Renyi Entropies of Interacting Fermions from Determinantal Quantum Monte Carlo Simulations

Entanglement measures such as the entanglement entropy have become an indispensable tool to identify the fundamental character of ground states of interacting quantum many-body systems. For systems of interacting spin or bosonic degrees of freedom much recent progress has been made not only in the analytical description of their respective entanglement entropies but also in their numerical classification. Systems of interacting fermionic degrees of freedom however have proved to be more difficult to control, in particular with regard to the numerical understanding of their entanglement properties. Here we report a generalization of the replica technique for the calculation of Renyi entropies to the framework of determinantal Quantum Monte Carlo simulations -- the numerical method of choice for unbiased, large-scale simulations of interacting fermionic systems. We demonstrate the strength of this approach over a recent alternative proposal based on a decomposition in free fermion Green's functions by studying the entanglement entropy of one-dimensional Hubbard systems both at zero and finite temperatures.Comment: 11 pages, 10 figure

Ongoing transients in carbonate compensation

Uptake of anthropogenic CO2 is acidifying the oceans. Over the next 2000 years, this will modify the dissolution and preservation of sedimentary carbonate. By coupling new formulas for the positions of the calcite saturation horizon, zsat, the compensation depth, zcc, and the snowline, zsnow, to a biogeochemical model of the oceanic carbonate system, we evaluate how these horizons will change with ongoing ocean acidification. Our model is an extended Havardton-Bear-type box model, which includes novel kinetic descriptions for carbonate dissolution above, between, and below these critical depths. In the preindustrial ocean, zsat and zcc are at 3939 and 4750 m, respectively. When forced with the IS92a CO2 emission scenario, the model forecasts (1) that zsat will rise rapidly (“runaway” conditions) so that all deep water becomes undersaturated, (2) that zcc will also rise and over 1000 years will pass before it will be stabilized by the dissolution of previously deposited CaCO3, and (3) that zsnow will respond slowly to acidification, rising by ∼1150 m during a 2000 year timeframe. A further simplified model that equates the compensation and saturation depths produces quantitatively different results. Finally, additional feedbacks due to acidification on calcification and increased atmospheric CO2 on organic matter productivity strongly affect the positions of the compensation horizons and their dynamics.

Multidisciplinary research in the space sciences

Research activities were carried out in the following areas during this reporting period: (1) astrophysics; (2) climate and atmospheric modeling; and (3) climate applications of earth observations & geological studies. An ultra-low-noise 115 GHz receiver based upon a superconducting tunnel diode mixer has been designed and constructed. The first laboratory tests have yielded spectacular results: a single-sideband noise temperature of 75 K considerably more sensitive than any other receiver at this frequency. The receiver will replace that currently in use on the Columbia-GISS CO Sky Survey telescope. The 1.2 meter millimeter-wave telescope at Columbia University has been used to complete two large-scale surveys of molecular matter in the part of the inner galaxy which is visible from the Northern hemisphere (the first galactic quadrant); one of the distant galaxy and one of the solar neighborhood. The research conducted during the past year in the climate and atmospheric modeling programs has been focused on the development of appropriate atmospheric and upper ocean models, and preliminary applications of these models. Principal models are a one-dimensional radiative-convective model, a three-dimensional global climate model, and an upper ocean model. During the past year this project has focused on development of 2-channel satellite analysis methods and radiative transfer studies in support of multichannel analysis techniques

North Atlantic Deep Water Formation

Various studies concerning differing aspects of the North Atlantic are presented. The three major topics under which the works are classified include: (1) oceanography; (2) paleoclimate; and (3) ocean, ice and climate modeling

The effect of wind and currents on gas exchange in an estuarine system

The objectives were to develop a non-volatile tracer to use in gas exchange experiments in laterally unconfined systems and to study applications of deliberate tracers in limnology and oceanography. Progress was made on both fronts but work on the development of the non-volatile tracer proved to be more difficult and labor intensive that anticipated so no field experiments using non-volatile tracers was performed as yet. In the search for a suitable non-volatile tracer for an ocean scale gas exchange experiment a tracer was discovered which does not have the required sensitivity for a large scale experiment, but is very easy to analyze and will be well suited for smaller experiments such as gas exchange determinations on rivers and streams. Sulfur hexafluoride, SF6, was used successfully as a volatile tracer along with tritium as a non-volatile tracer to study gas exchange rates from a primary stream. This is the first gas exchange experiment in which gas exchange rates were determined on a head water stream where significant groundwater input occurs along the reach. In conjunction with SF6, Radon-222 measurements were performed on the groundwater and in the stream. The feasibility of using a combination of SF6 and radon is being studied to determine groundwater inputs and gas exchange of rates in streams with significant groundwater input without using a non-volatile tracer

Will Our Ride into the Greenhouse Future be a Smooth One?

The climate record kept in ice and in sediment reveals that since the invention of agriculture some 8000 yr ago, climate has remained remarkably stable. By contrast, during the preceding 100,000 yr, climate underwent frequent, very large, and often extremely abrupt shifts. Furthermore, these shifts occurred in lockstep across the globe. They seem to be telling us that Earth's climate system has several distinct and quite different modes of operation and that it can jump from one of these modes to another in a matter of a decade or two. So far, we know of only one element of the climate system which has multiple modes of operation: the oceans' thermohaline circulation. Numerous model simulations reveal that this circulation is quite sensitive to the freshwater budget in the high-latitude regions where deep waters form. Perhaps the mode shifts revealed in the climate record were initiated in the sea. This discovery complicates predictions of the consequences of the ongoing buildup of greenhouse gases in the atmosphere. If the major climate changes of glacial time came as the result of mode shifts, can we be certain that the warming will proceed smoothly? Or is it possible that about 100 years from now, when our descendants struggle to feed the 15 or so billion Earth inhabitants, climate will jump to a less hospitable state. It is difficult to comprehend the misery that would follow on the heels of such an event

Predictability of catastrophic events: material rupture, earthquakes, turbulence, financial crashes and human birth

We propose that catastrophic events are "outliers" with statistically different properties than the rest of the population and result from mechanisms involving amplifying critical cascades. Applications and the potential for prediction are discussed in relation to the rupture of composite materials, great earthquakes, turbulence and abrupt changes of weather regimes, financial crashes and human parturition (birth).Comment: Latex document of 22 pages including 6 ps figures, in press in PNA

Atmospheric, climatic and environmental research

Work performed on the three tasks during the report period is summarized. The climate and atmospheric modeling studies included work on climate model development and applications, paleoclimate studies, climate change applications, and SAGE II. Climate applications of Earth and planetary observations included studies on cloud climatology and planetary studies. Studies on the chemistry of the Earth and the environment are briefly described. Publications based on the above research are listed; two of these papers are included in the appendices