The complete conformal spectrum of a sl(2∣1)sl(2|1) invariant network model and logarithmic corrections

We investigate the low temperature asymptotics and the finite size spectrum of a class of Temperley-Lieb models. As reference system we use the spin-1/2 Heisenberg chain with anisotropy parameter $\Delta$ and twisted boundary conditions. Special emphasis is placed on the study of logarithmic corrections appearing in the case of $\Delta=1/2$ in the bulk susceptibility data and in the low-energy spectrum yielding the conformal dimensions. For the $sl(2|1)$ invariant 3-state representation of the Temperley-Lieb algebra with $\Delta=1/2$ we give the complete set of scaling dimensions which show huge degeneracies.Comment: 18 pages, 5 figure

Computation of static Heisenberg-chain correlators: Control over length and temperature dependence

We communicate results on correlation functions for the spin-1/2 Heisenberg-chain in two particularly important cases: (a) for the infinite chain at arbitrary finite temperature $T$, and (b) for finite chains of arbitrary length $L$ in the ground-state. In both cases we present explicit formulas expressing the short-range correlators in a range of up to seven lattice sites in terms of a single function $\omega$ encoding the dependence of the correlators on $T$ ($L$). These formulas allow us to obtain accurate numerical values for the correlators and derived quantities like the entanglement entropy. By calculating the low $T$ (large $L$) asymptotics of $\omega$ we show that the asymptotics of the static correlation functions at any finite distance are $T^2$ ($1/L^2$) terms. We obtain exact and explicit formulas for the coefficients of the leading order terms for up to eight lattice sites.Comment: 5 pages, 3 figures, v2: text slightly shortened, typos in eqns. (16), (17) corrected, Fig. 1 replaced, v3: typo in eqn. (11) correcte

Insight into hydrochemistry: a multi-catchment comparison using Horizontal Visibility Graphs

Long time series of environmental variables are reflecting the dynamics and functioning of ecosystems. Here, we investigate data from a long-term monitoring site in Germany, the Bramke valley in the Harz mountains, where time series of ion concentrations in stream water are obtained since the 1970ies at four measurement locations from three small adjacent forested catchments. Since for (only) one of the catchments daily runoff rates are also available, we invent a method to generate time series of nutrient output from the catchments. Both concentrations and outputs show a number of remarkable long-term changes, including ones not obviously related to changes in atmospheric deposition, management or properties of the forest stands. For the analysis of the Bramke data, we investigate Horizontal Visibility Graphs (HVGs), a recently developed method to construct networks based on time series. Values (the nodes of the network) of the time series are linked to each other if there is no value higher between them. The network properties, such as the degree and distance distributions, reflect the nonlinear dynamics of the time series. For certain classes of stochastic processes and for periodic time series, analytic results can be obtained for some network properties. HVGs have the potential to discern between deterministic-chaotic and correlated-stochastic time series. We classify the Bramke series according to their stochastic nature, with a focus on inter-catchment comparison on one hand, on different nutrients for one catchment on the other, and conclude on possible reasons for the observed changes and their ecological interpretation

A homomorphism between link and XXZ modules over the periodic Temperley-Lieb algebra

We study finite loop models on a lattice wrapped around a cylinder. A section of the cylinder has N sites. We use a family of link modules over the periodic Temperley-Lieb algebra EPTL_N(\beta, \alpha) introduced by Martin and Saleur, and Graham and Lehrer. These are labeled by the numbers of sites N and of defects d, and extend the standard modules of the original Temperley-Lieb algebra. Beside the defining parameters \beta=u^2+u^{-2} with u=e^{i\lambda/2} (weight of contractible loops) and \alpha (weight of non-contractible loops), this family also depends on a twist parameter v that keeps track of how the defects wind around the cylinder. The transfer matrix T_N(\lambda, \nu) depends on the anisotropy \nu and the spectral parameter \lambda that fixes the model. (The thermodynamic limit of T_N is believed to describe a conformal field theory of central charge c=1-6\lambda^2/(\pi(\lambda-\pi)).) The family of periodic XXZ Hamiltonians is extended to depend on this new parameter v and the relationship between this family and the loop models is established. The Gram determinant for the natural bilinear form on these link modules is shown to factorize in terms of an intertwiner i_N^d between these link representations and the eigenspaces of S^z of the XXZ models. This map is shown to be an isomorphism for generic values of u and v and the critical curves in the plane of these parameters for which i_N^d fails to be an isomorphism are given.Comment: Replacement of "The Gram matrix as a connection between periodic loop models and XXZ Hamiltonians", 31 page

Quantum spin chains of Temperley-Lieb type: periodic boundary conditions, spectral multiplicities and finite temperature

We determine the spectra of a class of quantum spin chains of Temperley-Lieb type by utilizing the concept of Temperley-Lieb equivalence with the S=1/2 XXZ chain as a reference system. We consider open boundary conditions and in particular periodic boundary conditions. For both types of boundaries the identification with XXZ spectra is performed within isomorphic representations of the underlying Temperley-Lieb algebra. For open boundaries the spectra of these models differ from the spectrum of the associated XXZ chain only in the multiplicities of the eigenvalues. The periodic case is rather different. Here we show how the spectrum is obtained sector-wise from the spectra of globally twisted XXZ chains. As a spin-off, we obtain a compact formula for the degeneracy of the momentum operator eigenvalues. Our representation theoretical results allow for the study of the thermodynamics by establishing a TL-equivalence at finite temperature and finite field.Comment: 29 pages, LaTeX, two references added, redundant figures remove

Hidden Behind the Wall: West German State Building and the Emergence of the Iron Curtain

It is widely accepted that the inter-German border was constructed by East German authorities to halt the emigration to the west, which had damaged the East German economy and undermined the East German state agencies' power. This article argues that this is an inaccurate understanding, which mistakenly treats perceptions and insights gained from studying the Berlin Wall as representative of the mostly rural border between East and West Germany. It emphasizes crucial transformations of frontier society during the 1950s, highlighting the important role of western as well as eastern policy in shaping them

Lateglacial and Holocene climate and environmental change in the northeastern Mediterranean region: Diatom evidence from Lake Dojran (Republic of Macedonia/Greece)

The juncture between the west-east and north-south contrasting Holocene climatic domains across the Mediterranean is complex and poorly understood. Diatom analysis of Lake Dojran (Republic of Macedonia/Greece) provides a new insight into lake levels and trophic status during the Lateglacial and Holocene periods in the northeastern Mediterranean. Following a very shallow or even desiccated state at the core base at ca. 12,500 cal yr BP, indicated by sedimentological and hydro-acoustic data, diatoms indicate lake infilling, from a shallow state with abundant benthos to a plankton-dominated relatively high lake level and eutrophic state thereafter. Diatom-inferred shallowing between ca. 12,400 - 12,000 cal yr BP and a very low lake level and eutrophic, oligosaline state between ca. 12,000 - 11,500 cal yr BP provide strong evidence for Younger Dryas aridity. The earliest Holocene (ca. 11,500 - 10,700 cal yr BP) was characterised by a high lake level, followed by a lake-level reduction and increased trophic level between ca. 10,700-8,500 cal yr BP. The lake was relatively deep and exhibited peak Holocene trophic level between ca. 8,500-3,000 cal yr BP, becoming shallow thereafter. The diatom data provide more robust evidence and strengthen previous lake-level interpretation based on sedimentological and geochemical data during the earliest, mid and late Holocene, and also clarify previous uncertainty in interpretation of Lateglacial and early-Holocene lake-level change. Our results are also important in disentangling regional climate effects from local catchment dynamics during the Holocene, and to this end we exploit extant regional palynological evidence for vegetation change in the highlands and lowlands. The importance of seasonality in driving Holocene climate change is assessed by reference to the summer and winter latitudinal temperature gradient (LTG) model of Davis and Brewer (2009). We suggest that increased precipitation drove the high lake level during the earliest Holocene. The early- Holocene low lake level and relatively high trophic state may result climatically from high seasonality of precipitation and locally from limited, nutrient-rich catchment runoff. We argue that the mid- Holocene relatively deep and eutrophic state was driven mainly by local vegetation succession and associated changes in catchment processes, rather than showing a close relationship to climate change. The late-Holocene shallow state may have been influenced by a temperature-induced increase in evaporative concentration, but was coupled with clear evidence for intensified human impact. This study improves understanding of Lateglacial and Holocene climate change in the northeastern Mediterranean, suggests the important role of the LTG on moisture availability during the Holocene, and clarifies the influence of catchment processes on palaeohydrology

Local correlations in the 1D Bose gas from a scaling limit of the XXZ chain

We consider the K-body local correlations in the (repulsive) 1D Bose gas for general K, both at finite size and in the thermodynamic limit. Concerning the latter we develop a multiple integral formula which applies for arbitrary states of the system with a smooth distribution of Bethe roots, including the ground state and finite temperature Gibbs-states. In the cases K<=4 we perform the explicit factorization of the multiple integral. In the case of K=3 we obtain the recent result of Kormos et.al., whereas our formula for K=4 is new. Numerical results are presented as well.Comment: 23 pages, 2 figures, v2: minor modifications and references adde

From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics

We derive exact formulas for the expectation value of local observables in a one-dimensional gas of bosons with point-wise repulsive interactions (Lieb-Liniger model). Starting from a recently conjectured expression for the expectation value of vertex operators in the sinh-Gordon field theory, we derive explicit analytic expressions for the one-point K-body correlation functions \u27e8(\u3a8\u2020)K(\u3a8)K\u27e9 in the Lieb-Liniger gas, for arbitrary integer K. These are valid for all excited states in the thermodynamic limit, including thermal states, generalized Gibbs ensembles and non-equilibrium steady states arising in transport settings. Our formulas display several physically interesting applications: most prominently, they allow us to compute the full counting statistics for the particle-number fluctuations in a short interval. Furthermore, combining our findings with the recently introduced generalized hydrodynamics, we are able to study multi-point correlation functions at the Eulerian scale in non-homogeneous settings. Our results complement previous studies in the literature and provide a full solution to the problem of computing one-point functions in the Lieb Liniger model