Density-density Correlation Function Research Articles

Pair correlation functions and the wavevector-dependent surface tension in a simple density functional treatment of the liquid–vapour interface

We study the density-density correlation function G(r, r′) in the interfacial region of a fluid (or Ising-like magnet) with short-ranged interactions using square gradient density functional theory. Adopting a simple double parabola approximation for the bulk free-energy density, we first show that the parallel Fourier transform G(z, z′; q) and local structure factor S(z; q) separate into bulk and excess contributions. We attempt to account for both contributions by deriving an interfacial Hamiltonian, characterised by a wavevector dependent surface tension σ(q), and then reconstructing density correlations from correlations in the interface position. We show that the standard crossing criterion identification of the interface, as a surface of fixed density (or magnetization), does not explain the separation of G(z, z′; q) and the form of the excess contribution. We propose an alternative definition of the interface position based on the properties of correlations between points that ‘float’ with the surface and show that this describes the full q and z dependence of the excess contributions to both G and S. However, neither the ‘crossing-criterion’ nor the new ‘floating interface’ definition of σ(q) are quantities directly measurable from the total structure factor Stot(q) which contains additional q dependence arising from the non-local relation between fluctuations in the interfacial position and local density. Since it is the total structure factor that is measured experimentally or in simulations, our results have repercussions for earlier attempts to extract and interpret σ(q).

Dynamics of many-body localization

Following the field theoretic approach of Basko et al., Ann. Phys. 321, 1126 (2006), we study in detail the real-time dynamics of a system expected to exhibit many-body localization. In particular, for time scales inaccessible to exact methods, we demonstrate that within the second-Born approximation that the temporal decay of the density-density correlation function is non-exponential and is consistent with a finite value for $t\to\infty$, as expected in a non-ergodic state. This behavior persists over a wide range of disorder and interaction strengths. We discuss the implications of our findings with respect to dynamical phase boundaries based both on exact diagonalization studies and as well as those established by the methods of Ref. 1.

Optical properties of plasmons in a multiple quantum well semiconductor superlattice under electric and magnetic fields

The behavior of multiple quantum well GaAs/AlxGa1−xAs semiconductor superlattices with different dielectric interfaces are considered under magnetic and electric fields perpendicular and parallel to the superlattice axis, respectively. The parabolic confining potential well was varied with the compositional rate of the AlxGa1−xAs barrier. Taking into account intrasubband and intersubband transitions and using random phase approximation, the density-density correlation function is calculated as a function of the magnetic field strength, compositional rate, and averaged electric field strength over the quantum well. In this way, the dispersion of the surface and bulk state energies are obtained. The Raman intensities for these states are also obtained as a function of incoming light energy for various averaged electric field strengths over the quantum well.

Dynamics of colloidal aggregation in microgravity by critical Casimir forces

By combining static and dynamic structure factor measurements under microgravity conditions, we obtain for the first time direct insight into the internal structure of colloidal aggregates formed over a wide range of particle attractions under ideal diffusion-limited conditions. By means of near-field scattering we measure the time-dependent density-density correlation function as the aggregation process evolves, and we determine the ratio of the hydrodynamic and gyration radius to elucidate the aggregate's internal structure as a function of its fractal dimension. Surprisingly, we find that despite the large variation of particle interactions, the mass is always evenly distributed in all objects with fractal dimension ranging from 2.55 for shallow potentials to 1.78 for deep ones.

Multireference symmetry-projected variational approximation for the ground state of the doped one-dimensional Hubbard model

The few determinant (FED) approximation introduced in our previous work [Phys. Rev. B 87, 235129 (2013)] is used to describe the ground state, characterized by well-defined spin and space group symmetry quantum numbers as well as doping fractions ${N}_{e}/{N}_{\mathrm{sites}}$, of one-dimensional Hubbard lattices with nearest-neighbor hopping and periodic boundary conditions. Within this multireference scheme, each ground state is expanded in a given number of nonorthogonal and variationally determined symmetry-projected configurations. The results obtained for the ground-state and correlation energies of half-filled and doped lattices with 30, 34, and 50 sites compare well with the exact Lieb-Wu solutions as well as with those obtained with other state-of-the-art approximations. The structure of the intrinsic symmetry-broken determinants resulting from the variational procedure is interpreted in terms of solitons whose translational and breathing motions can be regarded as basic units of quantum fluctuations. It is also shown that in the case of doped one-dimensional lattices, a part of such fluctuations can also be interpreted in terms of polarons. In addition to momentum distributions, both spin-spin and density-density correlation functions are studied as functions of doping. The spectral functions and density of states, computed with an ansatz whose quality can be well controlled by the number of symmetry-projected configurations used to approximate the ${N}_{e}\ifmmode\pm\else\textpm\fi{}1$ electron systems, display features beyond a simple quasiparticle distribution, as well as spin-charge separation trends.

Two approaches for describing the Casimir interaction in graphene: Density-density correlation function versus polarization tensor

The comparison studies of theoretical approaches to the description of the Casimir interaction in layered systems including graphene is performed. It is shown that at zero temperature the approach using the polarization tensor leads to the same results as the approach using the longitudinal density-density correlation function of graphene. An explicit expression for the zero-temperature transverse density-density correlation function of graphene is provided. We further show that the computational results for the Casimir free energy of graphene-graphene and graphene-Au plate interactions at room temperature, obtained using the temperature-dependent polarization tensor, deviate significantly from those using the longitudinal density-density correlation function defined at zero temperature. We derive both the longitudinal and transverse density-density correlation functions of graphene at nonzero temperature. The Casimir free energy in layered structures including graphene, computed using the temperature-dependent correlation functions, is exactly equal to that found using the polarization tensor.

Keldysh approach to the renormalization group analysis of the disordered electron liquid

We present a Keldysh nonlinear sigma-model approach to the renormalization group analysis of the disordered electron liquid. We include both the Coulomb interaction and Fermi-liquid type interactions in the singlet and triplet channels into the formalism. Based on this model, we reproduce the coupled renormalization group equations for the diffusion coefficient, the frequency, and interaction constants previously derived with the replica model in the imaginary time technique. With the help of source fields coupling to the particle-number and spin densities, we study the density-density and spin density-spin density correlation functions in the diffusive regime. This allows us to obtain results for the electric conductivity and the spin susceptibility and thereby to re-derive the main results of the one-loop renormalization group analysis of the disordered electron liquid in the Keldysh formalism.

Analytic results for a quantum quench from free to hard-core one-dimensional bosons

It is widely believed that the stationary properties after a quantum quench in integrable systems can be described by a generalized Gibbs ensemble (GGE), even if all of the analytical evidence is based on free theories in which the pre- and postquench modes are linearly related. In contrast, we consider the experimentally relevant quench of the one-dimensional Bose gas from zero to infinite interaction, in which the relation between modes is nonlinear, and consequently Wick's theorem does not hold. We provide exact analytical results for the time evolution of the dynamical density-density correlation function at any time after the quench and we prove that its stationary value is described by a GGE in which Wick's theorem is restored.

Optimally focused cold atom systems obtained using density-density correlations

Resonant absorption imaging is a common technique for detecting the two-dimensional column density of ultracold atom systems. In many cases, the system's thickness along the imaging direction greatly exceeds the imaging system's depth of field, making the identification of the optimally focused configuration difficult. Here we describe a systematic technique for bringing Bose-Einstein condensates (BEC) and other cold-atom systems into an optimal focus even when the ratio of the thickness to the depth of field is large: a factor of 8 in this demonstration with a BEC. This technique relies on defocus-induced artifacts in the Fourier-transformed density-density correlation function (the power spectral density, PSD). The spatial frequency at which these artifacts first appear in the PSD is maximized on focus; the focusing process therefore both identifies and maximizes the range of spatial frequencies over which the PSD is uncontaminated by finite-thickness effects.

Manifestation of random first-order transition theory in Wigner glasses

We use Brownian dynamics simulations of a binary mixture of highly charged spherical colloidal particles to test some of the predictions of the random first-order transition (RFOT) theory [Phys. Rev. Lett. 58, 2091 (1987); Phys. Rev. A 40, 1045 (1989)]. In accord with mode-coupling theory and RFOT, we find that as the volume fraction of the colloidal particles ϕ approaches the dynamical transition value ϕ(A), three measures of dynamics show an effective ergodic to nonergodic transition. First, there is a dramatic slowing down of diffusion, with the translational diffusion constant decaying as a power law as ϕ→ϕ(A)(-). Second, the energy metric, a measure of ergodicity breaking in classical many-body systems, shows that the system becomes effectively nonergodic as ϕ(A) is approached. Finally, the time t(*), at which the four-point dynamical susceptibility achieves a maximum, also increases as a power law near ϕ(A). Remarkably, the translational diffusion coefficients, ergodic diffusion coefficient, and (t(*))(-) all vanish as (ϕ(-1)-ϕ(A)(-1))(γ) with both ϕ(A)(≈0.1) and γ being the roughly the same for all three quantities. Above ϕ(A), transport involves crossing free energy barriers. In this regime, the density-density correlation function decays as a stretched exponential [exp-(t/τ(α))(β)] with β≈0.45. The ϕ dependence of the relaxation time τ(α) could be fit using the Vogel-Tamman-Fulcher law with the ideal glass transition at ϕ(K)≈0.47. By using a local entropy measure, we show that the law of large numbers is not obeyed above ϕ(A), and gives rise to subsample to subsample fluctuations in all physical observables. We propose that dynamical heterogeneity is a consequence of violation of law of large numbers.

Correlation lengths of the repulsive one-dimensional Bose gas

We investigate the large-distance asymptotic behavior of the static density-density and field-field correlation functions in the one-dimensional Bose gas at finite temperature. The asymptotic expansions of the Bose gas correlators are obtained performing a specific continuum limit in the similar low-temperature expansions of the longitudinal and transversal correlation functions of the $XXZ$ spin chain. In the lattice system the correlation lengths are computed as ratios of the largest and next-largest eigenvalues of the $XXZ$ spin chain quantum transfer matrix. In both cases, lattice and continuum, the correlation lengths are expressed in terms of solutions of Yang-Yang type [C. N. Yang and C. P. Yang, J. Math. Phys. 10, 1151 (1969)] nonlinear integral equations which are easily implementable numerically.

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.

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.

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.

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.

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.