Browse
Submit Data
Databases
API
Help

Dataset Information

0 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Variational structure of Luttinger-Ward formalism and bold diagrammatic expansion for Euclidean lattice field theory.

ABSTRACT: The Luttinger-Ward functional was proposed more than five decades ago and has been used to formally justify most practically used Green's function methods for quantum many-body systems. Nonetheless, the very existence of the Luttinger-Ward functional has been challenged by recent theoretical and numerical evidence. We provide a rigorously justified Luttinger-Ward formalism, in the context of Euclidean lattice field theory. Using the Luttinger-Ward functional, the free energy can be variationally minimized with respect to Green's functions in its domain. We then derive the widely used bold diagrammatic expansion rigorously, without relying on formal arguments such as partial resummation of bare diagrams to infinite order.

SUBMITTER: Lin L

PROVIDER: S-EPMC5877950 | biostudies-literature | 2018 Mar

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

Variational structure of Luttinger-Ward formalism and bold diagrammatic expansion for Euclidean lattice field theory.

Lin Lin L Lindsey Michael M

Proceedings of the National Academy of Sciences of the United States of America 20180220 10

The Luttinger-Ward functional was proposed more than five decades ago and has been used to formally justify most practically used Green's function methods for quantum many-body systems. Nonetheless, the very existence of the Luttinger-Ward functional has been challenged by recent theoretical and numerical evidence. We provide a rigorously justified Luttinger-Ward formalism, in the context of Euclidean lattice field theory. Using the Luttinger-Ward functional, the free energy can be variationally ...[more]

PMID: 29463752

Similar Datasets

Variational Implicit Solvation with Poisson-Boltzmann Theory.

Project description:We incorporate the Poisson-Boltzmann (PB) theory of electrostatics into our variational implicit-solvent model (VISM) for the solvation of charged molecules in an aqueous solvent. In order to numerically relax the VISM free-energy functional by our level-set method, we develop highly accurate methods for solving the dielectric PB equation and for computing the dielectric boundary force. We also apply our VISM-PB theory to analyze the solvent potentials of mean force and the effect of charges on the hydrophobic hydration for some selected molecular systems. These include some single ions, two charged particles, two charged plates, and the host-guest system Cucurbit[7]uril and Bicyclo[2.2.2]octane. Our computational results show that VISM with PB theory can capture well the sensitive response of capillary evaporation to the charge in hydrophobic confinement and the polymodal hydration behavior and can provide accurate estimates of binding affinity of the host-guest system. We finally discuss several issues for further improvement of VISM.

| S-EPMC3985794 | biostudies-other

Advances in High-Field BOLD fMRI.

Project description:This review article examines the current state of BOLD fMRI at a high magnetic field strength of 7 Tesla. The following aspects are covered: a short description of the BOLD contrast, spatial and temporal resolution, BOLD sensitivity, localization and spatial specificity, technical challenges as well as an outlook on future developments are given. It is shown that the main technical challenges of performing BOLD fMRI at high magnetic field strengths-namely development of array coils, imaging sequences and parallel imaging reconstruction-have been solved successfully. The combination of these developments has lead to the availability of high-resolution BOLD fMRI protocols that are able to cover the whole brain with a repetition time (TR) shorter than 3 s. The structural information available from these high-resolution fMRI images itself is already very detailed, which helps to co-localize structure and function. Potential future applications include whole-brain connectivity analysis on a laminar resolution and single subject examinations.

| S-EPMC5448847 | biostudies-other

Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice.

Project description:In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic-to-paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models.

| S-EPMC5056370 | biostudies-literature

Self-Consistent Field Lattice Model for Polymer Networks.

Project description:A lattice model based on polymer self-consistent field theory is developed to predict the equilibrium statistics of arbitrary polymer networks. For a given network topology, our approach uses moment propagators on a lattice to self-consistently construct the ensemble of polymer conformations and cross-link spatial probability distributions. Remarkably, the calculation can be performed "in the dark", without any prior knowledge on preferred chain conformations or cross-link positions. Numerical results from the model for a test network exhibit close agreement with molecular dynamics simulations, including when the network is strongly sheared. Our model captures nonaffine deformation, mean-field monomer interactions, cross-link fluctuations, and finite extensibility of chains, yielding predictions that differ markedly from classical rubber elasticity theory for polymer networks. By examining polymer networks with different degrees of interconnectivity, we gain insight into cross-link entropy, an important quantity in the macroscopic behavior of gels and self-healing materials as they are deformed.

| S-EPMC5746847 | biostudies-literature

Field theory for recurrent mobility.

Project description:Understanding human mobility is crucial for applications such as forecasting epidemic spreading, planning transport infrastructure and urbanism in general. While, traditionally, mobility information has been collected via surveys, the pervasive adoption of mobile technologies has brought a wealth of (real time) data. The easy access to this information opens the door to study theoretical questions so far unexplored. In this work, we show for a series of worldwide cities that commuting daily flows can be mapped into a well behaved vector field, fulfilling the divergence theorem and which is, besides, irrotational. This property allows us to define a potential for the field that can become a major instrument to determine separate mobility basins and discern contiguous urban areas. We also show that empirical fluxes and potentials can be well reproduced and analytically characterized using the so-called gravity model, while other models based on intervening opportunities have serious difficulties.

| S-EPMC6715718 | biostudies-literature

Bayesian Learning in Sparse Graphical Factor Models via Variational Mean-Field Annealing.

Project description:We describe a class of sparse latent factor models, called graphical factor models (GFMs), and relevant sparse learning algorithms for posterior mode estimation. Linear, Gaussian GFMs have sparse, orthogonal factor loadings matrices, that, in addition to sparsity of the implied covariance matrices, also induce conditional independence structures via zeros in the implied precision matrices. We describe the models and their use for robust estimation of sparse latent factor structure and data/signal reconstruction. We develop computational algorithms for model exploration and posterior mode search, addressing the hard combinatorial optimization involved in the search over a huge space of potential sparse configurations. A mean-field variational technique coupled with annealing is developed to successively generate "artificial" posterior distributions that, at the limiting temperature in the annealing schedule, define required posterior modes in the GFM parameter space. Several detailed empirical studies and comparisons to related approaches are discussed, including analyses of handwritten digit image and cancer gene expression data.

| S-EPMC2947451 | biostudies-literature

Elevating density functional theory to chemical accuracy for water simulations through a density-corrected many-body formalism.

Project description:Density functional theory (DFT) has been extensively used to model the properties of water. Albeit maintaining a good balance between accuracy and efficiency, no density functional has so far achieved the degree of accuracy necessary to correctly predict the properties of water across the entire phase diagram. Here, we present density-corrected SCAN (DC-SCAN) calculations for water which, minimizing density-driven errors, elevate the accuracy of the SCAN functional to that of "gold standard" coupled-cluster theory. Building upon the accuracy of DC-SCAN within a many-body formalism, we introduce a data-driven many-body potential energy function, MB-SCAN(DC), that quantitatively reproduces coupled cluster reference values for interaction, binding, and individual many-body energies of water clusters. Importantly, molecular dynamics simulations carried out with MB-SCAN(DC) also reproduce the properties of liquid water, which thus demonstrates that MB-SCAN(DC) is effectively the first DFT-based model that correctly describes water from the gas to the liquid phase.

| S-EPMC8569147 | biostudies-literature

A linear lattice model for polyglutamine in CAG-expansion diseases.

Project description:Huntington's disease and several other neurological diseases are caused by expanded polyglutamine [poly(Gln)] tracts in different proteins. Mechanisms for expanded (>36 Gln residues) poly(Gln) toxicity include the formation of aggregates that recruit and sequester essential cellular proteins [Preisinger, E., Jordan, B. M., Kazantsev, A. & Housman, D. (1999) Phil. Trans. R. Soc. London B 354, 1029-1034; Chen, S., Berthelier, V., Yang, W. & Wetzel, R. (2001) J. Mol. Biol. 311, 173-182] and functional alterations, such as improper interactions with other proteins [Cummings, C. J. & Zoghbi, H. Y. (2000) Hum. Mol. Genet. 9, 909-916]. Expansion above the "pathologic threshold" ( approximately 36 Gln) has been proposed to induce a conformational transition in poly(Gln) tracts, which has been suggested as a target for therapeutic intervention. Here we show that structural analyses of soluble huntingtin exon 1 fusion proteins with 16 to 46 glutamine residues reveal extended structures with random coil characteristics and no evidence for a global conformational change above 36 glutamines. An antibody (MW1) Fab fragment, which recognizes full-length huntingtin in mouse brain sections, binds specifically to exon 1 constructs containing normal and expanded poly(Gln) tracts, with affinity and stoichiometry that increase with poly(Gln) length. These data support a "linear lattice" model for poly(Gln), in which expanded poly(Gln) tracts have an increased number of ligand-binding sites as compared with normal poly(Gln). The linear lattice model provides a rationale for pathogenicity of expanded poly(Gln) tracts and a structural framework for drug design.

| S-EPMC129321 | biostudies-literature

Transient Electronic Depletion and Lattice Expansion Induced Ultrafast Bandedge Plasmons.

Project description:Strong optical excitation of plasmonic nanostructures may induce simultaneous interband and intraband electronic transitions. However, interaction mechanisms between interband, intraband, and plasmon-band processes have not been thoroughly understood. In particular, optical-heating-induced lattice expansion, which definitely leads to shift of the Fermi level, has not been taken into account in plasmonic studies. Here, it is shown that plasmonic bandedge shift is responsible for the optical modulation on the boundary between plasmonic electron oscillation and interband transitions via investigations on gold nanofilms and nanoparticles. Strong optical excitation induces transient depletion of the conduction band just below the Fermi level through intraband transitions, while the subsequent lattice heating induces transient thermal expansion and hence lowers the Fermi level. Both effects reduce the threshold for interband transitions and therefore push the plasmonic bandedge to the red. These discoveries introduce a first correlation between plasmonic response and optical excitation induced thermal expansion of lattices. The revealed Fermi-level adjustment mechanism allows alignment of electronic levels at the metal-semiconductor interfaces, which applies to all conductive materials and renders reliable physics for the design of plasmonic or optoelectronic devices.

| S-EPMC6974950 | biostudies-literature

Topological transitions for lattice bosons in a magnetic field.

Project description:The Hall response provides an important characterization of strongly correlated phases of matter. We study the Hall conductivity of interacting bosons on a lattice subjected to a magnetic field. We show that for any density or interaction strength, the Hall conductivity is characterized by an integer. We find that the phase diagram is intersected by topological transitions between different values of this integer. These transitions lead to surprising effects, including sign reversal of the Hall conductivity and extensive regions in the phase diagram where it acquires a negative sign, which implies that flux flow is reversed in these regions--vortices there flow upstream. Our findings have immediate applications to a wide range of phenomena in condensed matter physics, which are effectively described in terms of lattice bosons.

| S-EPMC3250117 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data