Density-density Correlation Research Articles

Integrability of zero-dimensional replica field theories atβ=1

Building on insights from the theory of integrable lattices, the integrability is claimed for nonlinear replica σ models derived in the context of real symmetric random matrices. Specifically, the fermionic and the bosonic replica partition functions are proven to form a single (supersymmetric) Pfaff-KP hierarchy whose replica limit is shown to reproduce the celebrated nonperturbative formula for the density-density eigenvalue correlation function in the infinite-dimensional Gaussian orthogonal ensemble. Implications of the formalism outlined are briefly discussed.

Theory of fluctuating charge ordering in the pseudogap phase of cuprates via a preformed pair approach

We study the static and dynamic behavior of charge ordering within a $d$-wave pair pseudogap (pg) scenario. This is addressed using a density-density correlation function derived from the standard pg self-energy $\ensuremath{\Sigma}$ and compatible with the longitudinal and transverse sum rules. The broadening factor $\ensuremath{\gamma}$ in $\ensuremath{\Sigma}$ reflects the breaking of pairs into constituent fermions. We apply this form for $\ensuremath{\Sigma}$ (derived elsewhere for high fields) to demonstrate the existence of quantum oscillations in a non-Fermi liquid pg state. Our conclusion is that the pseudogap-induced pair breaking, via $\ensuremath{\gamma}$, allows the underlying fermiology to be revealed; $d$-wave (as distinct from $s$-wave) pairing in YBCO, with finite $\ensuremath{\omega}$ and $\ensuremath{\gamma}$ enables antinodal fluctuations, despite their competition in the static and superconducting limits.

Distribution of local relaxation events in an aging three-dimensional glass: Spatiotemporal correlation and dynamical heterogeneity

We investigate the spatiotemporal distribution of microscopic relaxation events, defined through particle hops, in a model polymer glass using molecular dynamics simulations. We introduce an efficient algorithm to directly identify hops during the simulation, which allows the creation of a map of relaxation events for the whole system. Based on this map, we present density-density correlations between hops and directly extract correlation scales. These scales define collaboratively rearranging groups of particles and their size distributions are presented as a function of temperature and age. Dynamical heterogeneity is spatially resolved as the aggregation of hops into clusters, and we analyze their volume distribution and growth during aging. A direct comparison with the four-point dynamical susceptibility χ(4) reveals the formation of a single dominating cluster prior to the χ(4) peak, which indicates maximally correlated dynamics. An analysis of the fractal dimension of the hop clusters finds slightly noncompact shapes in excellent agreement with independent estimates from four-point correlations.

Friedel oscillations and horizon charge in 1D holographic liquids

In many-body fermionic systems at finite density correlation functions of the density operator exhibit Friedel oscillations at a wavevector that is twice the Fermi momentum. We demonstrate the existence of such Friedel oscillations in a 3d gravity dual to a compressible finite-density state in a (1+1) dimensional field theory. The bulk dynamics is provided by a Maxwell U(1) gauge theory and all the charge is behind a bulk horizon. The bulk gauge theory is compact and so there exist magnetic monopole tunneling events. We compute the effect of these monopoles on holographic density-density correlation functions and demonstrate that they cause Friedel oscillations at a wavevector that directly counts the charge behind the bulk horizon. If the magnetic monopoles are taken to saturate the bulk Dirac quantization condition then the observed Fermi momentum exactly agrees with that predicted by Luttinger’s theorem, suggesting some Fermi surface structure associated with the charged horizon. The mechanism is generic and will apply to any charged horizon in three dimensions. Along the way we clarify some aspects of the holographic interpretation of Maxwell electromagnetism in three bulk dimensions and show that perturbations about the charged BTZ black hole exhibit a hydrodynamic sound mode at low temperature.

Hawking radiation correlations in Bose-Einstein condensates using quantum field theory in curved space

The density-density correlation function is computed for the Bogoliubov pseudoparticles created in a Bose-Einstein condensate undergoing a black hole flow. On the basis of the gravitational analogy, the method used relies only on quantum field theory in curved spacetime techniques. A comparison with the results obtained by ab initio full condensed matter calculations is given, confirming the validity of the approximation used, provided the profile of the flow varies smoothly on scales compared to the condensate healing length.

Dynamics of correlations in shallow optical lattices

We explore the time evolution of correlations in a homogeneous gas of lattice bosons with filling factor ${n}_{0}$, following a sudden reduction in the lattice depth to a regime where the interactions are weak. In the limit of vanishing interactions, we find a simple closed-form expression for the static structure factor. The corresponding real-space density-density correlation function shows multiple spatial oscillations which disperse linearly in time. By perturbatively including the effect of interactions, we study the evolution of boson quasimomentum distribution following the quench. In one dimension, the quasimomentum distribution develops peaks at finite momentum which disperse towards $q=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$. In two dimensions, the momentum occupation rapidly approaches a steady-state distribution characterized by a broad peak at $q=0$. Quasi-long-range order is never found at finite time. Our studies provide insight into the dynamics of isolated quantum systems.

Analysis of spin-polaron formation in hund lattices

We consider a one-dimensional Hund lattice model where a conducting band is coupled with localized spins s = 1/2 interacting antiferromagnetically, with coupling constant J, and investigate the ground state phase diagram as a function of both the exchange coupling J and the band filling, n. From spin structure factor measurements we found different evolving magnetic orderings in the ground state related to the particle distribution in the systems, although no charge density waves are formed, as found from density-density correlation function measurements. We study the quasiparticle formation and phase separation using the density-matrix renormalization group method, which is a highly efficient method to investigate quasi-one-dimensional strongly correlated systems.

Proposed Imaging of the Ultrafast Electronic Motion in Samples using X-Ray Phase Contrast

Tracing the motion of electrons has enormous relevance to understanding ubiquitous phenomena in ultrafast science, such as the dynamical evolution of the electron density during complex chemical and biological processes. Scattering of ultrashort x-ray pulses from an electronic wave packet would appear to be the most obvious approach to image the electronic motion in real time and real space with the notion that such scattering patterns, in the far-field regime, encode the instantaneous electron density of the wave packet. However, recent results by Dixit et al. [Proc. Natl. Acad. Sci. U.S.A. 109, 11636 (2012)] have put this notion into question and have shown that the scattering in the far-field regime probes spatiotemporal density-density correlations. Here, we propose a possible way to image the instantaneous electron density of the wave packet via ultrafast x-ray phase contrast imaging. Moreover, we show that inelastic scattering processes, which plague ultrafast scattering in the far-field regime, do not contribute in ultrafast x-ray phase contrast imaging as a consequence of an interference effect. We illustrate our general findings by means of a wave packet that lies in the time and energy range of the dynamics of valence electrons in complex molecular and biological systems. This present work offers a potential to image not only instantaneous snapshots of nonstationary electron dynamics, but also the laplacian of these snapshots which provide information about the complex bonding and topology of the charge distributions in the systems.

Two-dimensional dipolar Bose gas with the roton-maxon excitation spectrum

We discuss fluctuations in a dilute two-dimensional Bose-condensed dipolar gas, which has a roton-maxon character of the excitation spectrum. We calculate the density-density correlation function, fluctuation corrections to the chemical potential, compressibility, and the normal (superfluid) fraction. It is shown that the presence of the roton strongly enhances fluctuations of the density, and we establish the validity criterion of the Bogoliubov approach. At T=0 the condensate depletion becomes significant if the roton minimum is sufficiently close to zero. At finite temperatures exceeding the roton energy, the effect of thermal fluctuations is stronger and it may lead to a large normal fraction of the gas and compressibility.

Quantum quenches in one-dimensional gapless systems

We present a comparison between the bosonization results for quantum quenches and exact diagonalizations in microscopic models of interacting spinless fermions in a one-dimensional lattice. The numerical analysis of the long-time averages shows that density-density correlations at small momenta tend to a non-zero limit, mimicking a thermal behavior. These results are at variance with the bosonization approach, which predicts the presence of long-wavelength critical properties in the long-time evolution. By contrast, the numerical results for finite momenta suggest that the singularities at 2k F in the density-density correlations and at k F in the momentum distribution are preserved during the time evolution. The presence of an interaction term that breaks integrability flattens out all singularities, suggesting that the time evolution of one-dimensional lattice models after a quantum quench may differ from that of the Luttinger model.

Off-resonant light scattering from ultracold gases in optical lattices

We examine the possibility to study the statistical properties of trapped ultracold bosons with light scattering. We derive general effective hamiltonian and show that the spectrum of scattered photons contains information about density-density correlations. As a specific example we discuss light scattering as a potential tool to probe the Mott transition in optical lattice and Anderson localization in incommensurate superlattice.

Many-body Landau-Zener transition in cold-atom double-well optical lattices

Ultracold atoms in optical lattices provide an ideal platform for exploring many-body physics of a large system arising from the coupling among a series of small identical systems whose few-body dynamics is exactly solvable. Using Landau-Zener (LZ) transition of bosonic atoms in double-well optical lattices as an experimentally realizable model, we investigate such few- to many-body routes by exploring the relation and difference between the small few-body (in one double well) and the large many-body (in double-well lattice) nonequilibrium dynamics of cold atoms in optical lattices. We find the many-body coupling between double wells greatly enhances the LZ transition probability. The many-body dynamics in the double-well lattice shares both similarity and difference from the few-body dynamics in one and two double wells. The sign of the on-site interaction plays a significant role in the many-body LZ transition. Various experimental signatures of the many-body LZ transition, including atom density, momentum distribution, and density-density correlation, are obtained.

Density-density correlation in quasi two-dimensional free expanding Bose-Einstein condensates

The effective Lagrangian density function and the quantum fluctuation of the wave function in the form of quantized operators are presented for a quasi two-dimensional Bose-Einstein condensate by means of Madelung transformation. This paper calculates the two-point density-density correlation function of the condensate during its free expansion after its confinement potential is removed. Results show that the two-point density-density correlation function in the long-wave limit is proportional to the wave number k and it tends to be a constant in the short-wave limit.

Dynamic density-density correlations in interacting Bose gases on optical lattices

In order to identify possible experimental signatures of the superfluid to Mott-insulator quantum phase transition we calculate the charge structure factor S(k, ω) for the one-dimensional Bose-Hubbard model using the dynamical density-matrix renormalisation group (DDMRG) technique. Particularly we analyse the behaviour of S(k, ω) by varying – at zero temperature–the Coulomb interaction strength within the first Mott lobe. For strong interactions, in the Mott-insulator phase, we demonstrate that the DDMRG results are well reproduced by a strong-coupling expansion, just as the quasi-particle dispersion. In the super-fluid phase we determine the linear excitation spectrum near k = 0. In one dimension, the amplitude mode is absent which mean-field theory suggests for higher dimensions.

Pseudopotential-based first-principles approach to the magneto-optical Kerr effect: From metals to the inclusion of local fields and excitonic effects

We propose a first-principles scheme for the description of the magneto-optical kerr effect within density functional theory (DFT). Though the computation of Kerr parameters is often done within DFT, starting from the conductivity or the dielectric tensor, there is no formal justification to this choice. As a first steps, using as reference materials iron, cobalt and nickel we show that pseudo-potential based calculations give accurate predictions. Then we derive a formal expression for the full dielectric tensor in terms of the density-density correlation function. The derived equation is exact in systems with an electronic gap, with the possible exception of Chern insulators, and whenever the time reversal symmetry holds and can be used as a starting point for the inclusion of local fields and excitonic effects within time-dependent DFT for such systems. In case of metals instead we show that, starting from the density-density correlation function, the term which describes the anomalous Hall effect is neglected giving a wrong conductivity.

Mode-coupling theory of the glass transition for confined fluids

We present a detailed derivation of a microscopic theory for the glass transition of a liquid enclosed between two parallel walls relying on a mode-coupling approximation. This geometry lacks translational invariance perpendicular to the walls, which implies that the density profile and the density-density correlation function depends explicitly on the distances to the walls. We discuss the residual symmetry properties in slab geometry and introduce a symmetry adapted complete set of two-point correlation functions. Since the currents naturally split into components parallel and perpendicular to the walls the mathematical structure of the theory differs from the established mode-coupling equations in bulk. We prove that the equations for the nonergodicity parameters still display a covariance property similar to bulk liquids.

Density-density correlations on a gelatin films surface

The spatial correlations on the surface of films obtained from aqueous solutions of gelatin during cooling from 320 to 293 K have been studied using electron microscopy. It has been shown that the total density fluctuation correlation function on the scale R > 4 nm can be represented in the form h(R) ∼ R−nexp(−R/ζ), where the correlation radius ζ coincides with the hydrodynamic radius of a macromolecule. Unfolding of macromolecules in the coil → helix transformation leads to a decrease in the density and the fractal dimension of the physical network of pinnings of macromolecules and to variation in the index n of the power term in the function h(R) from n = 1 to 2, due to the transition from a continual type of disorder to a cellular type in a solid.

Induced superfluidity of imbalanced Fermi gases near unitarity

The induced intraspecies interactions among the majority species, mediated by the minority species, is computed for a population-imbalanced two-component Fermi gas. Although the Feshbach-resonance mediated interspecies interaction is dominant for equal populations, leading to singlet s-wave pairing, we find that in the strongly imbalanced regime the induced intraspecies interaction leads to p-wave pairing and superfluidity of the majority species. Thus, we predict that the observed spin-polaron Fermi liquid state in this regime is unstable to p-wave superfluidity, in accordance with the results of Kohn and Luttinger, below a temperature that, near unitarity, we find to be within current experimental capabilities. Possible experimental signatures of the p-wave state using radio-frequency spectroscopy as well as density-density correlations after free expansion are presented.

Correction to the chiral magnetic effect from axial-vector interaction

The recent lattice calculation at finite axial chemical potential suggests that the induced current density of the chiral magnetic effect (CME) is somehow suppressed comparing with the standard analytical formula. We show in a NJL-type model of QCD that such a suppression is a natural result when considering the influence of the attractive axial-vector interaction. We point out that the lattice result doesn't need to be quantitatively consistent with the analytical formula due to the chirality density-density correlation. We also investigate the nonperturbative effect of instanton molecules on the CME. Since an unconventional repulsive axial-vector interaction is induced, the CME will be enhanced significantly by the instanton-anti-instanton pairings. Such a prediction needs to be tested by more improved lattice simulations. We further demonstrate that the axial-vector interaction plays an important role on the $T-\mu_A$ phase diagram.

Scaling behavior of trapped bosonic particles in two dimensions at finite temperature

In the framework of the trap-size scaling theory, we study the scaling properties of the Bose-Hubbard model in two dimensions in the presence of a trapping potential at finite temperature. In particular, we provide results for the particle density and the density-density correlator at the Mott transitions and within the superfluid phase. For the former quantity, numerical outcomes are also extensively compared to local density approximation predictions.