Thermodyamic bounds on Drude weights in terms of almost-conserved quantities

We consider one-dimensional translationally invariant quantum spin (or fermionic) lattices and prove a Mazur-type inequality bounding the time-averaged thermodynamic limit of a finite-temperature expectation of a spatio-temporal autocorrelation function of a local observable in terms of quasi-local conservation laws with open boundary conditions. Namely, the commutator between the Hamiltonian and the conservation law of a finite chain may result in boundary terms only. No reference to techniques used in Suzuki's proof of Mazur bound is made (which strictly applies only to finite-size systems with exact conservation laws), but Lieb-Robinson bounds and exponential clustering theorems of quasi-local C^* quantum spin algebras are invoked instead. Our result has an important application in the transport theory of quantum spin chains, in particular it provides rigorous non-trivial examples of positive finite-temperature spin Drude weight in the anisotropic Heisenberg XXZ spin 1/2 chain [Phys. Rev. Lett. 106, 217206 (2011)].Comment: version as accepted by Communications in Mathematical Physics (22 pages with 2 pdf-figures

Folate Deficiency, Hyperhomocysteinemia, Low Urinary Creatinine, and Hypomethylation of Leukocyte DNA Are Risk Factors for Arsenic-Induced Skin Lesions

Background Arsenic methylation relies on folate-dependent one-carbon metabolism and facilitates urinary As elimination. Clinical manifestations of As toxicity vary considerably among individuals and populations, and poor methylation capacity is thought to confer greater susceptibility. Objective After determining that folate deficiency, hyperhomocysteinemia, and low urinary creatinine are associated with reduced As methylation, and that As exposure is associated with increased genomic methylation of leukocyte DNA, we asked whether these factors are associated with As-induced skin lesion risk among Bangladeshi adults. Methods We conducted a nested case–control study of 274 cases who developed lesions 2 years after recruitment, and 274 controls matched to cases for sex, age, and water As. Results The odds ratios and 95% confidence intervals (CIs) for development of skin lesions for participants who had low folate (\u3c 9 nmol/L), hyperhomocysteinemia (men, \u3e 11.4 μmol/L; women, \u3e 10.4 μmol/L), or hypomethylated leukocyte DNA at recruitment (\u3c median) were 1.8 (95% CI, 1.1–2.9), 1.7 (95% CI, 1.1–2.6), and 1.8 (95% CI, 1.2–2.8), respectively. Compared with the subjects in the first quartile, those in the third and fourth quartiles for urinary creatinine had a 0.4-fold decrease in the odds of skin lesions (p \u3c 0.01). Conclusions These results suggest that folate deficiency, hyperhomocysteinemia, and low urinary creatinine, each associated with decreased As methylation, are risk factors for As-induced skin lesions. The increased DNA methylation associated with As exposure previously observed, and confirmed among controls in this study, may be an adaptive change because hypomethylation of leukocyte DNA is associated with increased risk for skin lesions

Folate, Homocysteine, and Arsenic Metabolism in Arsenic-Exposed Individuals in Bangladesh

Chronic exposure to arsenic is occurring throughout South and East Asia due to groundwater contamination of well water. Variability in susceptibility to arsenic toxicity may be related to nutritional status. Arsenic is methylated to monomethylarsonic acid (MMA) and dimethylarsinic acid (DMA) via one-carbon metabolism, a biochemical pathway that is dependent on folate. The majority of one-carbon metabolism methylation reactions are devoted to biosynthesis of creatine, the precursor of creatinine. Our objectives of this cross-sectional study were to characterize the relationships among folate, cobalamin, homocysteine, and arsenic metabolism in Bangladeshi adults. Water arsenic, urinary arsenic, urinary creatinine, plasma folate, cobalamin, and homocysteine were assessed in 1,650 adults; urinary arsenic metabolites were analyzed for a subset of 300 individuals. The percentage of DMA in urine was positively associated with plasma folate (r = 0.14, p = 0.02) and negatively associated with total homocysteine (tHcys; r = −0.14, p = 0.01). Conversely, percent MMA was negatively associated with folate (r = −0.12, p = 0.04) and positively associated with tHcys (r = 0.21, p = 0.0002); percent inorganic arsenic (InAs) was negatively associated with folate (r = −0.12, p = 0.03). Urinary creatinine was positively correlated with percent DMA (r = 0.40 for males, p < 0.0001; 0.25 for females, p = 0.001), and with percent InAs (r = −0.45 for males, p < 0.0001; −0.20 for females, p = 0.01). Collectively, these data suggest that folate, tHcys, and other factors involved in one-carbon metabolism influence arsenic methylation. This may be particularly relevant in Bangladesh, where the prevalence of hyperhomocysteinemia is extremely high

From the quantum transfer matrix to the quench action: the Loschmidt echo in XXZ Heisenberg spin chains

We consider the computation of the Loschmidt echo after quantum quenches in the interacting XXZ Heisenberg spin chain both for real and imaginary times. We study two-site product initial states, focusing in particular on the N\ue9el and tilted N\ue9el states. We apply the Quantum Transfer Matrix (QTM) approach to derive generalized TBA equations, which follow from the fusion hierarchy of the appropriate QTM's. Our formulas are valid for arbitrary imaginary time and for real times at least up to a time t0, after which the integral equations have to be modified. In some regimes, t0 is seen to be either very large or infinite, allowing to explore in detail the post-quench dynamics of the system. As an important part of our work, we show that for the N\ue9el state our imaginary time results can be recovered by means of the quench action approach, unveiling a direct connection with the quantum transfer matrix formalism. In particular, we show that in the zero-time limit, the study of our TBA equations allows for a simple alternative derivation of the recently obtained Bethe ansatz distribution functions for the N\ue9el, tilted N\ue9el and tilted ferromagnet states

Low-temperature transport in out-of-equilibrium XXZ chains

We study the low-temperature transport properties of out-of-equilibrium XXZ spin-1/2 chains. We consider the protocol where two semi-infinite chains are prepared in two thermal states at small but different temperatures and suddenly joined together. We focus on the qualitative and quantitative features of the profiles of local observables, which at large times t and distances x from the junction become functions of the ratio \u3b6=x/t. By means of the generalized hydrodynamic equations, we analyse the rich phenomenology arising by considering different regimes of the phase diagram. In the gapped phases, variations of the profiles are found to be exponentially small in the temperatures but described by non-trivial functions of \u3b6. We provide analytical formulae for the latter, which give accurate results also for small but finite temperatures. In the gapless regime, we show how the three-step conformal predictions for the profiles of energy density and energy current are naturally recovered from the hydrodynamic equations. Moreover, we also recover the recent non-linear Luttinger liquid predictions for low-temperature transport: universal peaks of width \u394\u3b6 1dT emerge at the edges of the light cone in the profiles of generic observables. Such peaks are described by the same function of \u3b6 for all local observables

R\ue9nyi entropies of generic thermodynamic macrostates in integrable systems

We study the behaviour of R\ue9nyi entropies in a generic thermodynamic macrostate of an integrable model. In the standard quench action approach to quench dynamics, the R\ue9nyi entropies may be derived from the overlaps of the initial state with Bethe eigenstates. These overlaps fix the driving term in the thermodynamic Bethe ansatz (TBA) formalism. We show that this driving term can be also reconstructed starting from the macrostate's particle densities. We then compute explicitly the stationary R\ue9nyi entropies after the quench from the dimer and the tilted N\ue9el state in XXZ spin chains. For the former state we employ the overlap TBA approach, while for the latter we reconstruct the driving terms from the macrostate. We discuss in full detail the limits that can be analytically handled and we use numerical simulations to check our results against the large time limit of the entanglement entropies

Entanglement Hamiltonians in 1D free lattice models after a global quantum quench

We study the temporal evolution of the entanglement Hamiltonian of an interval after a global quantum quench in free lattice models in one spatial dimension. In a harmonic chain we explore a quench of the frequency parameter. In a chain of free fermions at half filling we consider the evolution of the ground state of a fully dimerised chain through the homogeneous Hamiltonian. We focus on critical evolution Hamiltonians. The temporal evolutions of the gaps in the entanglement spectrum are analysed. The entanglement Hamiltonians in these models are characterised by matrices that provide also contours for the entanglement entropies. The temporal evolution of these contours for the entanglement entropy is studied, also by employing existing conformal field theory results for the semi-infinite line and the quasi-particle picture for the global quench

Associations of Plasma Selenium with Arsenic and Genomic Methylation of Leukocyte DNA in Bangladesh

Background Global hypomethylation of DNA is thought to constitute an early event in some cancers and occurs in response to arsenic (As) exposure and/or selenium (Se) deficiency in both in vitro and animal models. In addition, antagonism between As and Se, whereby each reduces toxicity of the other, has been well documented in animal models. Se status may therefore modify the health effects of As in As-exposed populations. Objective The primary objectives of our study were to test the hypothesis that Se deficiency is associated with genomic hypomethylation of lymphocyte DNA and to determine whether Se levels are associated with blood As (bAs) and urinary As (uAs) concentrations in adults exposed to As-contaminated groundwater in Bangladesh. A secondary objective was to explore the relationships between plasma Se and As metabolites. Design We assessed plasma Se concentrations, As metabolite profiles in blood and urine, and genomic methylation of leukocyte DNA in a cross-sectional study of 287 adults. Results After adjustment for potential confounders, we observed an inverse association between Se (micrograms per liter) and genomic DNA methylation (disintegrations per minute per 1-μg/L increase in Se): β = 345.6; 95% confidence interval (CI), 59–632. Se concentrations were inversely associated with total As concentrations (micrograms per liter) in blood (β = −0.04; 95% CI, −0.08 to −0.01) and urine (β = −20.1; 95% CI, −29.3 to −10.9). Se levels were negatively associated with the percentage of monomethylarsinic acid (β = −0.59; 95% CI, −1.04 to −0.13) and positively associated with the percentage of dimethylarsinic acid (β = 0.53; 95% CI, 0.04 to 1.01) in blood. Conclusions Our results suggest that Se is inversely associated with genomic DNA methylation. The underlying mechanisms and implications of this observation are unclear and warrant further investigation. In addition, Se may influence bAs and uAs concentrations, as well as relative proportions of As metabolites in blood