Bulk Correlation Length Research Articles

Holographic Analysis of Boundary Correlation Functions for the Hyperbolic-Lattice Ising Model

Abstract We analyze boundary spin correlation functions of the hyperbolic-lattice Ising model from the holographic point of view. Using the corner-transfer-matrix renormalization-group (CTMRG) method, we demonstrate that the boundary correlation function exhibits power-law decay with quasiperiodic oscillation, while the bulk correlation function always decays exponentially. On the basis of the geometric relation between the bulk correlation path and distance along the outer edge boundary, we find that scaling dimensions for the boundary correlation function can be well explained by a combination of the bulk correlation length and background curvatures inherent to the hyperbolic lattice. We also investigate the cutoff effect of the bond dimension in CTMRG, revealing that the long-distance behavior of the boundary spin correlation is accurately described even with a small bond dimension. In contrast, the short-distance behavior rapidly loses its accuracy.

Wetting and emergence of long-range couplings in arrays of fluid cells.

Critical wetting is of crucial importance for the phase behavior of a simple fluid or Ising magnet confined between walls that exert opposing surface fields so that one wall favors liquid (spin up), while the other favors gas (spin down). We show that arrays of boxes filled with fluid and linked by channels with appropriately chosen opposing walls can exhibit long-range cooperative effects on a length scale far exceeding the bulk correlation length. We give the theoretical foundations of these long-range couplings by using a lattice gas (Ising model) description of a system.

Variance of the Casimir force in an ideal Bose gas

We consider an ideal Bose gas enclosed in a d-dimensional slab of thickness D. Using the grand canonical ensemble we calculate the variance of the thermal Casimir force acting on the slab’s walls. The variance evaluated per unit wall area is shown to decay like Δvar/D for large D. The amplitude Δvar is a non-universal function of two scaling variables λ/ξ and D/ξ, where λ is the thermal de Broglie wavelength and ξ is the bulk correlation length. It can be expressed via the bulk pressure, the Casimir force per unit wall area, and its derivative with respect to chemical potential. For thermodynamic states corresponding to the presence of the Bose–Einstein condensate the amplitude Δvar retains its non-universal character while the ratio of the mean standard deviation and the Casimir force takes the scaling form , where L is the linear size of the wall.

Exploring Hidden Local Ordering in Microemulsions with a Weak Directive Second Order Parameter

So far, the near-surface ordering of microemulsions was focused on lamellar ordering while the bulk microemulsion was bicontinuous. In a series of different non-ionic surfactants the near-surface ordering of microemulsions at a hydrophilic silicon surface was studied using grazing incidence small angle neutron scattering. For the surfactant C8E3, most likely a gyroid structure was found at the solid–liquid interface, while the more efficient surfactants find lamellar ordering up to lamellar capillary condensation. The ranges for near-surface ordering are deeper than the bulk correlation lengths. These findings point towards theories that use directional order parameters that would lead to deeper near-surface ordering than simple theories with a single scalar order parameter would predict. Rheology experiments display high viscosities at very low shear rates and, therefore, support the existence of a directional order parameter.

Microscopic determination of correlations in the fluid interfacial region in the presence of liquid-gas asymmetry.

In a recent article, we showed how the properties of the density-density correlation function and its integral, the local structure factor, in the fluid interfacial region, in systems with short-ranged forces, can be understood microscopically by considering the resonances of the local structure factor [A. O. Parry and C. Rascón, Nat. Phys. 15, 287 (2019)NPAHAX1745-247310.1038/s41567-018-0361-z]. Here, we illustrate, using mean-field square-gradient theory and the more microscopic Sullivan density functional model, and how this approach generalizes when there is liquid-gas asymmetry, i.e., when the bulk correlation lengths of the coexisting liquid and gas phases are different. In particular, we are able to express the correlation function exactly as a simple average of contributions arising from two effective Ising-symmetric systems referred to as the symmetric gas and symmetric liquid. When combined with our earlier results, this generates analytical approximations for the correlation function and the local structure factor, which are near indistinguishable from the numerical solution to the Ornstein-Zernike equations over the whole range of wave vectors. Our results highlight how asymmetry affects the correlation function structure and describes the crossover from a long-ranged Goldstone mode to short-ranged properties determined by the local density as the wave vector increases.

Surface Phases and Surface Freezing in an Ionic Liquid

Room temperature ionic liquids (RTILs), a novel class of liquid salts, are intensively studied for their basic science and numerous emerging applications. When undercooled, RTILs comprising long alkyl chains often exhibit liquid crystal (LC) bulk phases. However, only one molecular-resolution experimental structure study was published for their LC surface phases. We measured the temperature evolution of another LC surface phase, using surface specific Å-resolution X-ray methods. This phase’s existence range, 90 °C, much exceeds the corresponding bulk phase’s 3 °C. Its thickness, L, confirms the theory-predicted logarithmic temperature dependence, with an amplitude equaling the bulk correlation length. Surprisingly, at L’s divergence temperature, a ∼20 Å thick, hexagonally packed, crystalline monolayer forms at, and fully covers, the sample’s surface. It is identified as a surface-frozen Langmuir–Gibbs film and fundamentally differs from the only reported RTIL surface crystal, a Coulomb-dominated, four-layer, island phase, covering only 5%–15% of the surface.

Understanding of interfacial tension and interface thickness of liquid/liquid interface at a finite concentration of alkyl phosphate by molecular dynamics simulation

The Mulliken charge embedded newly developed OPLS force field has been applied for computation of various structural and dynamical properties of water–dodecane biphasic system. The interface thickness has been investigated in the presence of finite concentration of third component, a lipophilic ligand, tri-isoamyl phosphate (TiAP) and acid employing molecular dynamics simulation. The physical properties at the interface like interface structure, interfacial tension, interface thickness have been studied for a wide range of mole fraction of TiAP and with various aqueous phase acidity. The interfacial tension is found to be decreased with increasing mole fraction of TiAP whereas increased with the acid concentration. The inverse relation between interface thickness and interfacial tension has been established. The surface tension computed from pressure tensor was found to be in excellent agreement with the experimental results, which is then used to determine the interface thickness employing capillary wave theory (CWT) using a simple scheme of finding the bulk correlation length by adopting conductor like screening model for real solvents. Furthermore, a simple equation has been obtained by fitting the MD results of total interface thickness for a wide range of composition of third component. The value of interface thickness calculated from the model equation was found to be in good agreement with the available experimental and MD results for a wide variety of oil-water biphasic systems. Additionally, the stability of the dimer of TiAP with different orientation was established by computing the dimerization energy using DFT which was also captured in the MD simulation. Furthermore, the present MD data shows that the water extraction is enhanced at higher mole fraction of TiAP because of wider interface thickness at higher composition of TiAP which induced the water transport to the organic phase. Again, the calculated values reveal that the water extractability is decreased with increasing aqueous phase acidity as the interface thickness is reduced at higher acidity. The present results might be useful in the frontier area of interfacial science and engineering as well as in partitioning of drug molecules at the biological interfaces.

Order Parameter Profiles near Surfaces of Super-weak Ferrimagnetic Materials Exhibiting a Paramagnetic-Ferrimagnetic Transition

The aim of this paper is to determine the full order parameter profiles close to the surface for a system made of two strongly coupled paramagnetic sublattices of respective moments and . The material exhibits a para-ferrimagnetic transition at some critical temperature Tc greater than the room temperature. The free energy describing the physics of the system is of Landau type, and involves, beside quadratic and quartic terms in both and , a lowest-order coupling, -Co where CoL, and the free energy is then a sum of bulk and surface contributions expanded in terms of the local order parameters. The magnetization at the surface are s and s. As in a recent paper (whom the present work is an extension), we first reduce the model to an effective 4 -theory written in terms of the overall magnetization =+ and the associated fraction of magnetization a=/(+). For the ordinary transition where the extrapolation length is positive s>0, we determine the order parameter profile near surfaces. We show, in particular, that the magnetization behavior is governed, in addition of s and the bulk correlation length b-, by a new length La. We have interpreted this latter as the width of the ordered ferrimagnetic layer close to the surface. Finally, we examine the extraordinary (ss=) and surface (at Tcs>Tc) transitions.

Casimir force in dense confined electrolytes

ABSTRACTUnderstanding the force between charged surfaces immersed in an electrolyte solution is a classic problem in soft matter and liquid-state theory. Recent experiments showed that the force decays exponentially but the characteristic decay length in a concentrated electrolyte is significantly larger than what liquid-state theories predict based on analysing correlation functions in the bulk electrolyte. Inspired by the classical Casimir effect, we consider an additional mechanism for force generation, namely the confinement of density fluctuations in the electrolyte by the walls. We show analytically within the random phase approximation, which assumes the ions to be point charges, that this fluctuation-induced force is attractive and also decays exponentially, albeit with a decay length that is half of the bulk correlation length. These predictions change dramatically when excluded volume effects are accounted for within the mean spherical approximation. At high ion concentrations the Casimir force is found to be exponentially damped oscillatory as a function of the distance between the confining surfaces. Our analysis does not resolve the riddle of the anomalously long screening length observed in experiments, but suggests that the Casimir force due to mode restriction in density fluctuations could be an hitherto under-appreciated source of surface–surface interaction.

Matrix product state description of Halperin states

Many fractional quantum Hall states can be expressed as a correlator of a given conformal field theory used to describe their edge physics. As a consequence, these states admit an economical representation as an exact Matrix Product States (MPS) that was extensively studied for the systems without any spin or any other internal degrees of freedom. In that case, the correlators are built from a single electronic operator, which is primary with respect to the underlying conformal field theory. We generalize this construction to the archetype of Abelian multicomponent fractional quantum Hall wavefunctions, the Halperin states. These latest can be written as conformal blocks involving multiple electronic operators and we explicitly derive their exact MPS representation. In particular, we deal with the caveat of the full wavefunction symmetry and show that any additional SU(2) symmetry is preserved by the natural MPS truncation scheme provided by the conformal dimension. We use our method to characterize the topological order of the Halperin states by extracting the topological entanglement entropy. We also evaluate their bulk correlation length which are compared to plasma analogy arguments.

Tensor network state correspondence and holography

In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can be viewed as a representation of two different quantum many-body states. The two quantum many-body states are said to correspond to each other by means of the tensor network. We apply this "tensor network state correspondence"---a correspondence between quantum many-body states mediated by tensor networks as we describe---to the multi-scale entanglement renormalization ansatz (MERA) representation of ground states of one dimensional (1D) quantum many-body systems. Since the MERA is a 2D hyperbolic tensor network (the extra dimension is identified as the length scale of the 1D system), the two quantum many-body states obtained from the MERA, via tensor network state correspondence, are seen to live in the bulk and on the boundary of a discrete hyperbolic geometry. The bulk state so obtained from a MERA exhibits interesting features, some of which caricature known features of the holographic correspondence of String theory. We show how (i) the bulk state admits a description in terms of "holographic screens", (ii) the conformal field theory data associated with a critical ground state can be obtained from the corresponding bulk state, in particular, how pointlike boundary operators are identified with extended bulk operators. (iii) We also present numerical results to illustrate that bulk states, dual to ground states of several critical spin chains, have exponentially decaying correlations, and that the bulk correlation length generally decreases with increase in central charge for these spin chains.

Solvent-Mediated Interactions Close to the Fisher-Widom Line.

The effective interactions between two hard spheres mediated by a square-well fluid is studied within the framework of classical density functional theory. The main focus of this study is the behavior of the effective interactions in the supercritical regime close to the Fisher-Widom line, where the decay of the bulk correlations of the solvent changes from monotonic to oscillatory, and close to the Widom line, which is the locus of (local) maxima in the bulk correlation length. The effective interactions are calculated by employing the potential distribution theorem.

Many-body topological invariants in fermionic symmetry-protected topological phases: Cases of point group symmetries

We propose the definitions of many-body topological invariants to detect symmetry-protected topological phases protected by point group symmetry, using partial point group transformations on a given short-range entangled quantum ground state. Partial point group transformations $g_D$ are defined by point group transformations restricted to a spatial subregion $D$, which is closed under the point group transformations and sufficiently larger than the bulk correlation length $\xi$. By analytical and numerical calculations,we find that the ground state expectation value of the partial point group transformations behaves generically as $\langle GS | g_D | GS \rangle \sim \exp \Big[ i \theta+ \gamma - \alpha \frac{{\rm Area}(\partial D)}{\xi^{d-1}} \Big]$. Here, ${\rm Area}(\partial D)$ is the area of the boundary of the subregion $D$, and $\alpha$ is a dimensionless constant. The complex phase of the expectation value $\theta$ is quantized and serves as the topological invariant, and $\gamma$ is a scale-independent topological contribution to the amplitude. The examples we consider include the $\mathbb{Z}_8$ and $\mathbb{Z}_{16}$ invariants of topological superconductors protected by inversion symmetry in $(1+1)$ and $(3+1)$ dimensions, respectively, and the lens space topological invariants in $(2+1)$-dimensional fermionic topological phases. Connections to topological quantum field theories and cobordism classification of symmetry-protected topological phases are discussed.

From 2D to 3D: Critical Casimir interactions and phase behavior of colloidal hard spheres in a near-critical solvent.

Colloids dispersed in a binary solvent mixture experience long-ranged solvent-mediated interactions (critical Casimir forces) upon approaching the critical demixing point of the solvent mixture. The range of the interaction is set by the bulk correlation length of the solvent mixture, which diverges upon approaching the critical point. This presents a great opportunity to realize the reversible self-assembly of colloids by tuning the proximity to the critical point of the solvent. Here, we develop a rejection-free geometric cluster algorithm to study the full ternary mixture of colloidal hard spheres suspended in an explicit three-dimensional lattice model for the solvent mixture using extensive Monte Carlo simulations. The phase diagram displays stable colloidal gas, liquid, and crystal phases, as well as broad gas-liquid and gas-crystal phase coexistence, and pronounced fractionation of the solvent in the coexisting colloid phases. The topology of the phase diagram in our three-dimensional study shows striking resemblance to that of our previous studies carried out in two dimensions.

Трехмерная $O(n)$-$\phi^4$-модель в плоско-параллельном слое со свободными граничными условиями: точные результаты для нетривиального размерного кроссовера в пределе $n\to\infty$

Дан краткий обзор недавних результатов точных расчетов критических сил Казимира в $O(n)$-$\phi^4$-модели при $n\to\infty$ для трехмерного слоя ширины $L$, ограниченного двумя параллельными плоскостями со свободными граничными условиями. В этой модели дальний порядок имеет место при температурах ниже критической точки $T_{\mathrm c}$ объемного фазового перехода только в пределе $L\to\infty$, однако дальний порядок в модели отсутствует при всех температурах $T>0$ при произвольной конечной ширине слоя $L<\infty$. Последовательное описание скейлингового поведения системы вблизи $T_{\mathrm c}$ оказывается весьма сложной задачей, так как наряду с объемным и поверхностным скейлингом, а также конечно-размерным скейлингом необходимо учитывать нетривиальный размерный кроссовер. Модель допускает точное решение в пределе $n\to\infty$ в терминах собственных значений и собственных функций самосогласованного уравнения Шредингера. Это решение содержит потенциал $v(z)$, который имеет при $z\to +0$ сингулярное поведение $v(z)\approx-1/(4z^2)+4m/(\pi^2z)$ в приграничном слое, где $m=1/\xi_+(|t|)$ - обратная корреляционная длина в объемной системе, $t\sim(T-T_{\mathrm c})/T_{\mathrm c}$, и аналогичная сингулярность имеет место вблизи второй граничной плоскости. В недавней работе нами совместно с соавторами численными методами с высокой точностью были вычислены потенциал $v(z)$, избыточная свободная энергия и сила Казимира. Дано объяснение того, как эти численные результаты могут быть дополнены точными аналитическими результатами для целого ряда величин (коэффициенты разложения потенциала $v(z)$, данные рассеяния для потенциала $v(z)$ в полубесконечной геометрии $L=\infty$ при всех значениях $m\gtreqless 0$, низкотемпературная асимптотика избыточной свободной энергии и силы Казимира). Эти аналитические результаты были получены сочетанием таких методов, как операторные разложения, обобщенная теория обратной задачи рассеяния, новая формула следов и квазиклассические (ВКБ) разложения.

Complex coacervates formed across liquid interfaces: A self-consistent field analysis

The Scheutjens–Fleer self-consistent field (SF-SCF) theory is used to study complexation between two oppositely charged polyelectrolytes across an interface formed by two solvents, here called oil and water. The focus is on the composition and the lateral stability of such interfacial coacervate. One polyelectrolyte is chosen to be oil soluble and the other one prefers water, whereas the counter and salt ions are taken to distribute ideally over all phases. There exists an electrostatic associative driving force for the formation of the coacervate phase which increases with decreasing ionic strength and may be assisted by some specific affinity between the associating units and an effective poor solvency for the coacervate. As with respect to the lateral stability an unusual wetting scenario, called pseudo-partial wetting, presents itself, which results from interactions on two different length scales. On the segmental length the screening of oil–water contacts promotes the wetting by the coacervate: a pre-wetting jump-like transition takes place off-coexistence from a microscopically thin to a mesoscopically thin film. Usually this implies complete wetting. However, the mesoscopically thin film is exposed to long-ranged attractive electrostatic interactions and therefore cannot grow to macroscopic dimensions upon approach towards coexistence. Hence the system remains partial wet. The bulk correlation length controls the thickness of the mesoscopically thin film and as a result the wetting transition occurs extremely close to the bulk critical point. We therefore expect that a thick coacervate film typically is laterally inhomogeneous: there are drops on top of a mesoscopically thin coacervate film. This conclusion qualitatively explains the experimental observation that such a coacervate film scatters visible light.

Interface localization near criticality

The theory of interface localization in near-critical planar systems at phase coexistence is formulated from first principles. We show that mutual delocalization of two interfaces, amounting to interfacial wetting, occurs when the bulk correlation length critical exponent $\nu$ is larger than or equal to 1. Interaction with a boundary or defect line involves an additional scale and a dependence of the localization strength on the distance from criticality. The implications are particularly rich in the boundary case, where delocalization proceeds through different renormalization patterns sharing the feature that the boundary field becomes irrelevant in the delocalized regime. The boundary delocalization (wetting) transition is shown to be continuous, with surface specific heat and layer thickness exponents which can take values that we determine.

Nonadditivity of critical Casimir forces.

In soft condensed matter physics, effective interactions often emerge due to the spatial confinement of fluctuating fields. For instance, microscopic particles dissolved in a binary liquid mixture are subject to critical Casimir forces whenever their surfaces confine the thermal fluctuations of the order parameter of the solvent close to its critical demixing point. These forces are theoretically predicted to be nonadditive on the scale set by the bulk correlation length of the fluctuations. Here we provide direct experimental evidence of this fact by reporting the measurement of the associated many-body forces. We consider three colloidal particles in optical traps and observe that the critical Casimir force exerted on one of them by the other two differs from the sum of the forces they exert separately. This three-body effect depends sensitively on the distance from the critical point and on the chemical functionalisation of the colloid surfaces.

Nematic ordering of SWNT in meso-structured thin liquid films of polystyrenesulfonate.

The formation of nematic-like islands of single-walled carbon nanotubes (SWNT) in polystyrenesulfonate (PSS) dispersions confined into nanometrically thin films is reported. The SWNT are observed to assemble into orientationally ordered phases, where the intertube distance, as measured via transmission electron microscopy at cryogenic temperatures, matches the polyelectrolyte's bulk correlation length deduced from X-ray scattering. The micrometers-long islands of orientationally ordered carbon nanotubes are observed in both SWNT and double-walled carbon nanotubes (DWNT) but not in specimens prepared from similar dispersions of multiwalled carbon nanotubes (MWNT). These observations, together with relaxation and rheological experiments, suggest that the orientational ordering may result from coupling between confinement of the polymer-wrapped SWNT and DWNT and the microstructure of the solvated polyelectrolyte.

Disjoining Pressure, Healing Distance, and Film Height Dependent Surface Tension of Thin Wetting Films

In this work, we simulate the adsorption of wetting liquid argon films on a model substrate. We calculate the disjoining pressure isotherm and show that it is completely dominated by the long-range van der Waals interactions. Thick films exhibit the expected Hamaker power law decay, but a quantitative description of thin films requires consideration of the detailed structure of the adsorbed layer. The spectrum of film height fluctuations is calculated and shown to provide reliable estimates of the disjoining pressure for all films studied. However, it is observed that the full spectrum can only be reproduced provided that we account for a film height dependent surface tension proportional to the derivative of the disjoining pressure. A simple theory is worked out that describes well the observed film height dependence. Having at hand both the surface tension and the disjoining pressure, we calculate the healing distance of the liquid films, which differs from the classical expectation by a constant of the same order of magnitude as the bulk correlation length. We show these findings have important implications on the behavior of adsorbed liquids and determine corrections to the augmented Young–Laplace equation at the subnanometer length scale.