Calculation Of Correlation Functions Research Articles

Fermionic logarithmic negativity in the Krawtchouk chain

Abstract The entanglement of non-complementary regions is investigated in an inhomogeneous free-fermion chain through the lens of the fermionic logarithmic negativity. Focus is on the Krawtchouk chain, whose relation to the eponymous orthogonal polynomials allows for exact diagonalization and analytical calculations of certain correlation functions. For adjacent regions, the negativity scaling corresponds to that of a conformal field theory with central charge c = 1, in agreement with previous studies on bipartite entanglement in the Krawtchouk chain. For disjoint regions, we focus on the skeletal regime where each region reduces to a single site. This regime is sufficient to extract the leading behaviour at large distances. In the bulk, the negativity decays as d − 4 Δ f with Δ f = 1 / 2 , where d is the separation between the regions. This is in agreement with the homogeneous result of free Dirac fermions in one dimension. Surprisingly, when one site is close to the boundary, this exponent changes and depends on the parity of the boundary site m = 0 , 1 , 2 , … , with Δ f even = 3 / 8 and Δ f odd = 5 / 8 . The results are supported by numerics and analytical calculations.

Dual-Isometric Projected Entangled Pair States

Efficient characterization of higher dimensional many-body physical states presents significant challenges. In this Letter, we propose a new class of projected entangled pair states (PEPS) that incorporates two isometric conditions. This new class facilitates the efficient calculation of general local observables and certain two-point correlation functions, which have been previously shown to be intractable for general PEPS, or PEPS with only a single isometric constraint. Despite incorporating two isometric conditions, our class preserves the rich physical structure while enhancing the analytical capabilities. It features a large set of tunable parameters, with only a subleading correction compared to that of general PEPS. Furthermore, we analytically demonstrate that this class can encode universal quantum computation and can represent a transition from topological to trivial order. Published by the American Physical Society 2024

The infrared spectrum of the protic ionic liquid 1-methylimidazolium nitrate: An ab initio molecular dynamics simulation study

Complex features observed in the infrared (IR) spectrum of the protic ionic liquid 1-methylimidazolium nitrate, [C1im][NO3], are assigned using ab initio molecular dynamics (AIMD) simulation. AIMD is used at the same level of theory to simulate the known X-ray crystal structure of [C1im][NO3] and a cluster of ionic pairs representing the liquid phase. The calculation of several single particle and collective time correlation functions of velocity forms the basis for the AIMD simulation assignment of the infrared spectra. The AIMD simulation demonstrates that the lift of the degeneracy of the anion asymmetric stretching mode, νas(NO3), due to symmetry breaking and coupling to external modes result in multiple band splitting in the crystal spectrum in the region of the νas(NO3) mode. Owing of the intrinsic anharmonic characteristic of the AIMD simulation, the calculation accounts for the broad band in the high-frequency range of the IR spectrum caused by the cation ν(NH) stretching mode in strong cation–anion hydrogen bond. The AIMD simulation of the liquid captures spectral changes upon melting of [C1im][NO3] due to loosening of the NH···O hydrogen bond and changes in the [NO3]- interaction with other hydrogen atoms of the imidazolium ring. The AIMD simulation assigns the intermolecular stretching mode of the hydrogen bond, ν(NH…O), as the band at 183 cm−1 in the far infrared spectrum of the [C1im][NO3] crystal.

Correlation functions from tensor network influence functionals: The case of the spin-boson model.

We investigate the application of matrix product state (MPS) representations of the influence functionals (IFs) for the calculation of real-time equilibrium correlation functions in open quantum systems. Focusing specifically on the unbiased spin-boson model, we explore the use of IF-MPSs for complex time propagation, as well as IF-MPSs for constructing correlation functions in the steady state. We examine three different IF approaches: one based on the Kadanoff-Baym contour targeting correlation functions at all times, one based on a complex contour targeting the correlation function at a single time, and a steady state formulation, which avoids imaginary or complex times, while providing access to correlation functions at all times. We show that within the IF language, the steady state formulation provides a powerful approach to evaluate equilibrium correlation functions.

Scalar spectral functions from the spectral functional renormalization group

We compute spectral functions in a scalar ϕ4-theory in three spacetime dimensions via the spectral functional renormalization group. This approach allows for the direct, manifestly Lorentz covariant computation of correlation functions in Minkowski spacetime, including a physical on-shell renormalization. We present numerical results for the spectral functions of the two- and four-point correlation functions for different values of the coupling parameter. These results agree very well with those obtained from another functional real-time approach, the spectral Dyson-Schwinger equation. Published by the American Physical Society 2024

Bootstrap of the defect 1/2 BPS Wilson lines in N=4 Chern-Simons-matter theories

We compute correlation functions of local operator insertions on the 1/2 Bogomol’nyi-Prasad-Sommerfield Wilson lines of N=4 Chern-Simons-matter theories in three dimensions. We study the algebra preserved by the defect conformal field theory supported on the line, identify the superdisplacement multiplet, and discuss some of its weak-coupling realizations. By employing a superspace description, we present the four-point functions of the superdisplacement and show how they are determined by functions of cross ratios. Within an analytic bootstrap approach, we derive these functions at leading and next-to-leading order at strong coupling, obtaining a result in agreement with appropriate orbifolds of the ABJM case considered in Bianchi [Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT1, ]. Published by the American Physical Society 2024

Roles of boundary and equation-of-motion terms in cosmological correlation functions

We revisit the properties of total time-derivative terms as well as terms proportional to the free equation of motion (EOM) in a Schwinger-Keldysh formalism. They are relevant to the correct calculation of correlation functions of curvature perturbations in the context of inflationary Universe. We show that these two contributions to the action play different roles in the operator or the path-integral formalism, but they give the same correlation functions as each other. As a concrete example, we confirm that the Maldacena's consistency relations for the three-point correlation function in the slow-roll inflationary scenario driven by a minimally coupled canonical scalar field hold in both the operator and path-integral formalisms. We also give some comments on loop calculations.

Binning method for artifact-free time-tag based correlation function calculations.

Correlation functions are nowadays routinely computed using time-tagged photon information instead of a hardware autocorrelator. The algorithm developed by Laurence et al. [Opt. Lett.31, 829 (2006)10.1364/OL.31.000829] is a powerful example. Despite its ease of implementation and fast computation process, it presents a prevalent noisy feature at the short time-lag range when computed on commonly used logarithmically spaced bins. We identified that arbitral logarithmic spacing produces the mismatch between the edges of generated bins and acquisition frequency, resulting in an aliasing artifact at the short time-lag range of the correlation function. We introduce a binning method that considers the acquisition frequency during the bin generation. It effectively eliminates the artifact and improves the accuracy of the autocorrelation. Applying the binning method herein can be particularly crucial when one extracts photophysical processes from fluorescence correlation spectroscopy or the diffusion coefficient of nanoparticles from dynamic light scattering at the time range below 10-5 s lag time.

Correlation functions of boundary and defect conformal field theories

Applying the holographic method, we investigate correlation functions of boundary and defect conformal field theories. To describe boundary conformal field theory, we consider an end of the world brane in an asymptotic AdS space, which behaves as a boundary in the dual conformal field theory. In this holographic setup, we calculate correlation functions involving the reflection effect at the boundary. We show that, when the end of the world brane has no degrees of freedom, the holographic calculation reproduces the correlation functions known in the boundary conformal field theory. When the boundary has nontrivial boundary entropy, we calculate one- and two-point functions nontrivially relying on the boundary entropy. We further study correlation functions of defect conformal field theory after introducing a p brane. We directly derive a bulk-to-defect two-point function without introducing an image operator and determine the coefficient of the two-point function exactly in the holographic setup. Published by the American Physical Society 2024

No time to derive: unraveling total time derivatives in in-in perturbation theory

The in-in formalism provides a way to systematically organize the calculation of primordial correlation functions. Although its theoretical foundations are now firmly settled, the treatment of total time derivative interactions, incorrectly trivialized as “boundary terms”, has been the subject of intense discussions and conceptual mistakes. In this work, we demystify the use of total time derivatives — as well as terms proportional to the linear equations of motion — and show that they can lead to artificially large contributions cancelling at different orders of the in-in operator formalism. We discuss the treatment of total time derivative interactions in the Lagrangian path integral formulation of the in-in perturbation theory, and we showcase the importance of interaction terms proportional to linear equations of motion. We then provide a new route to the calculation of primordial correlation functions, which avoids the generation of total time derivatives, by working directly at the level of the full Hamiltonian in terms of phase-space variables. Instead of integrating by parts, we perform canonical transformations to simplify interactions. We explain how to retrieve correlation functions of the initial phase-space variables from the knowledge of the ones after canonical transformations. As an important first application, we find the explicit sizes of Hamiltonian cubic interactions in single-field inflation with canonical kinetic terms and for any background evolution, straight in terms of the primordial curvature perturbation and its canonical conjugate momentum, as well as the corresponding ones in the tensor sector, and the ones mixing scalars and tensors. We also briefly comment on quartic interactions. Our results are important for performing complete calculations of exchange diagrams in inflation, such as the (scalar and tensor) exchange trispectrum and the one-loop power spectrum. Being already written in a form amenable to characterize quantum properties of primordial fluctuations, they also promise to shed light on the non-linear dynamics of quantum states during inflation.

KeldyshQFT: A C++ codebase for real-frequency multiloop functional renormalization group and parquet computations of the single-impurity Anderson model.

We provide a detailed exposition of our computational framework designed for the accurate calculation of real-frequency dynamical correlation functions of the single-impurity Anderson model in the regime of weak to intermediate coupling. Using quantum field theory within the Keldysh formalism to directly access the self-energy and dynamical susceptibilities in real frequencies, as detailed in our recent publication [Ge et al., Phys. Rev. B 109, 115128 (2024)], the primary computational challenge is the full three-dimensional real-frequency dependence of the four-point vertex. Our codebase provides a fully MPI+OpenMP parallelized implementation of the functional renormalization group (fRG) and the self-consistent parquet equations within the parquet approximation. It leverages vectorization to handle the additional complexity imposed by the Keldysh formalism, using optimized data structures and highly performant integration routines. Going beyond the results shown in the previous publication, the code includes functionality to perform fRG calculations in the multiloop framework, up to arbitrary loop order, including self-consistent self-energy iterations. Moreover, implementations of various regulators, such as hybridization, interaction, frequency, and temperature, are supplied.

A hidden 2d CFT for self-dual Yang-Mills on the celestial sphere

Self-dual Yang-Mills theory admits an underlying infinite dimensional symmetry algebra, which has been obtained from mode expansion of Mellin transformed 4d scattering amplitudes and separately, Koszul duality on twistor space. In this paper, we propose to derive an explicit 2d realization of the algebra by performing a particular gauge transformation on the twistor action for self-dual Yang-Mills. The gauge parameter used in the transformation generates pure gauge connections corresponding to large gauge transformations on 4d Minkowski space, which localises part of the twistor action to a ℂℙ1 on ℂ* reduction of twistor space. Under a projection, it can be mapped to the celestial sphere at the light-cone cut of the origin on I\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{I} $$\\end{document}. Geometrically, this is the common boundary celestial sphere shared by Euclidean AdS3 or Lorentzian dS3 slices of Minkowski space. We comment on the geometric meaning of the derivation from the perspective of minitwistor spaces of the 3d slices embedded in 4d Minkowski space. Using the action functional of this 2d CFT, we compute its stress-energy tensor and central charge. By a further marginal deformation, we calculate correlation functions of current algebra generators purely from the 2d side which reproduce full 4d tree-level form factors.

Advanced analysis of single-molecule spectroscopic data

We present Full SMS, a multipurpose graphical user interface (GUI)-based software package for analyzing single-molecule spectroscopy (SMS) data. SMS typically delivers multiparameter data—such as fluorescence brightness, lifetime, and spectra—of molecular- or nanometer-scale particles such as single dye molecules, quantum dots, or fluorescently labeled biological macromolecules. Full SMS allows an unbiased statistical analysis of fluorescence brightness through level resolution and clustering, analysis of fluorescence lifetimes through decay fitting, as well as the calculation of second-order correlation functions and the display of fluorescence spectra and raster-scan images. Additional features include extensive data filtering options, a custom HDF5-based file format, and flexible data export options. The software is open source and written in Python but GUI based so it may be used without any programming knowledge. A multiprocess architecture was employed for computational efficiency. The software is also designed to be easily extendable to include additional import data types and analysis capabilities.

Entanglement Renormalization for Quantum Field Theories with Discrete Wavelet Transforms

We propose an adaptation of Entanglement Renormalization for quantum field theories that, through the use of discrete wavelet transforms, strongly parallels the tensor network architecture of the Multiscale Entanglement Renormalization Ansatz (a.k.a. MERA). Our approach, called wMERA, has several advantages of over previous attempts to adapt MERA to continuum systems. In particular, (i) wMERA is formulated directly in position space, hence preserving the quasi-locality and sparsity of entanglers; and (ii) it enables a built-in RG flow in the implementation of real-time evolution and in computations of correlation functions, which is key for efficient numerical implementations. As examples, we describe in detail two concrete implementations of our wMERA algorithm for free scalar and fermionic theories in (1+1) spacetime dimensions. Possible avenues for constructing wMERAs for interacting field theories are also discussed.

Open-closed string duality, branes, and topological recursion

We consider matrix models exhibiting open-closed string duality in two-dimensional string theories with various amounts of supersymmetry. In particular, a relationship between matrix models in the β = 2 Wigner-Dyson class and models in the (1 + 2Γ, 2) Altland-Zirnbauer class relates the perturbative solutions of the two systems’ string equations. Point-like operator insertions in the closed string theory are mapped to the topological expansion of the free energy in the open string theory. We compute correlation functions of macroscopic loop operators and FZZT branes in a general topological gravity background. The relationship between the topological recursion of moduli space volumes and branes is discussed by analyzing the Virasoro conditions in the matrix models.

Spatial Structure of the Radio‐Frequency Noise Field in a Large City

AbstractThe urban radio‐frequency (RF) noise generated by our cities continues to change with time. Although models exist to describe the RF noise as functions of frequency and urban land use types, very few models describe the spatial character or structure of the noise on the scales of city blocks (50–150 m). The goal of this work is to investigate the connection between urban morphology and the higher‐order spatial statistics of the noise field. To achieve this goal, a large measurement campaign was conducted in Boston, Massachusetts. Many spatial measurements allowed for calculation of spatial correlation functions of noise power in three different neighborhoods, which were used to quantify the spatial structure of the fields. A statistical point source model is then developed, with adjustable parameters relating to urban morphology. Good agreement between the model and the experimental correlation functions suggests the 25 MHz urban noise field is well described by a random network of fixed point sources, radiating with a 1/r power law behavior.

The impacts of spin–orbit coupling and strain on transverse dynamical spin susceptibility in undoped phosphorene: Kane–Mele model study

We present the behaviors of dynamical transverse spin susceptibilities of undoped phosphorene monolayer using the Green’s function approach in the context of Kane–Mele model Hamiltonian. Such dynamical spin susceptibility is proportional to inelastic cross section of neutron beam from the layer. Specially, the effects of magnetic field and spin–orbit coupling strength on the spin excitation modes of phosphorene monolayer are investigated via calculating correlation function of spin density operators. Our results show the increase of magnetic field leads to move the magnetic excitation energy to higher values. Also, the intensity of peaks in inelastic cross section reduces with increase of magnetic field. We also show that applying both uniaxial and biaxial strains causes to decrease the intensity of peaks in dynamical spin susceptibility. Finally the effects of both compressive and tensile strains on frequency dependence of dynamical spin structure factor of phosphorene layer are studied. Moreover, the frequency positions of spin excitation mode of phosphorene layer have been investigated due to the effects of spin orbit coupling strength in details.

Loop diagrams in the kinetic theory of waves

Recent work has given a systematic way for studying the kinetics of classical weakly interacting waves beyond leading order, having analogies with renormalization in quantum field theory. An important context is weak wave turbulence, occurring for waves which are small in magnitude and weakly interacting, such as those on the surface of the ocean. Here we continue the work of perturbatively computing correlation functions and the kinetic equation in this far-from-equilibrium state. In particular, we obtain the next-to-leading-order kinetic equation for waves with a cubic interaction. Our main result is a simple graphical prescription for the terms in the kinetic equation, at any order in the nonlinearity.

Holographic RG from an exact RG: Locality and general coordinate invariance in the bulk

In earlier papers it was shown that the correct kinetic term for scalar, vector gauge field and the spin two field in AdSD+1 space is obtained starting from the exact renormalization group (ERG) equation for a CFTD perturbed by scalar composite, conserved vector current, and conserved traceless energy momentum tensor respectively. In this paper interactions are studied, and it is shown that a flipped version of the Polchinski ERG equation that evolves toward the UV can be written down and is useful for making contact with the usual AdS/CFT prescriptions for correlation function calculations. The scalar-scalar-spin-2 interaction in the bulk is derived from the ERG equation in the large N semiclassical approximation. It is also shown that after mapping to AdS the interaction is local on a scale of the bare cutoff rather than the moving cutoff (which would have corresponded to the anti–de Sitter scale). The map to AdSD+1 plays a crucial role in this locality. The local nature of the coupling ensures that this interaction term in the bulk action is obtained by gauge fixing a general coordinate invariant scalar kinetic term in the bulk action. A wave function renormalization of the scalar field is found to be required for a mutually consistent map of the two fields to AdSD+1. Published by the American Physical Society 2024

Polyakov loop models in the large N limit: Correlation function and screening masses

We explore the ’t Hooft-Veneziano limit of the Polyakov loop models at finite baryon chemical potential. Using methods developed by us earlier we calculate the two- and N-point correlation functions of the Polyakov loops. This gives a possibility to compute the various potentials in the confinement phase and to derive the screening masses outside the confinement region. In particular, we establish the existence of complex masses and an oscillating decay of correlations in a certain range of parameters. Furthermore, it is shown that the calculation of the N-point correlation function in the confinement phase reduces to the geometric median problem. This leads to a large N analog of the Y law for the baryon potential. Published by the American Physical Society 2024