Finite Size Effects Research Articles

Fractional quantum Hall states with variational projected entangled-pair states: A study of the bosonic Harper-Hofstadter model

An important class of model Hamiltonians for investigation of topological phases of matter consists of mobile, interacting particles on a lattice subject to a semiclassical gauge field, as exemplified by the bosonic Harper-Hofstadter model. A unique method for investigations of two-dimensional quantum systems are the infinite projected-entangled pair states, as they avoid spurious finite-size effects that can alter the phase structure. However, due to no-go theorems in related cases, this was often conjectured to be impossible in the past. In this Letter, we show that upon variational optimization, the infinite projected-entangled pair states can be used to this end by identifying fractional Hall states in the bosonic Harper-Hofstadter model. The obtained states are characterized by showing exponential decay of bulk correlations, as dictated by a bulk gap, as well as chiral edge modes via the entanglement spectrum. Published by the American Physical Society 2024

Improved composable key rates for CV-QKD

Modern security proofs of quantum key distribution (QKD) must take finite-size effects and composable aspects into consideration. This is also the case for continuous-variable (CV) protocols, which are based on the transmission and detection of bosonic coherent states. In this paper, we refine and advance the previous theory in this area providing a more rigorous formulation for the composable key rate of a generic CV-QKD protocol. Thanks to these theoretical refinements, our general formulas allow us to prove more optimistic key rates with respect to previous literature. Published by the American Physical Society 2024

Unveiling chiral states in the XXZ chain: finite-size scaling probing symmetry-enriched c = 1 conformal field theories

We study the low-energy properties of the one-dimensional spin-1/2 XXZ chain with time-reversal symmetry-breaking pseudo-scalar chiral interaction and propose a phase diagram for the model. In the integrable case of the isotropic Heisenberg model with the chiral interaction, we employ the thermodynamic Bethe ansatz to find “chiralization”, the response of the ground state versus the strength of the pseudo-scalar chiral interaction of a chiral Heisenberg chain. Unlike the magnetization case, the chirality of the ground state remains zero until the transition point corresponding to critical coupling αc = 2J/π with J being the antiferromagnetic spin-exchange interaction. The central-charge c = 1 conformal field theories (CFTs) describe the two phases with zero and finite chirality. We show for this particular case and conjecture more generally for similar phase transitions that the difference between two emergent CFTs with identical central charges lies in the symmetry of their ground state (lightest weight) primary fields, i.e., the two phases are symmetry-enriched CFTs. At finite but small temperatures, the non-chiral Heisenberg phase acquires a finite chirality that scales with the temperature quadratically. We show that the finite-size effect around the transition point probes the transition.

Contrasting Views of the Electric Double Layer in Electrochemical CO2 Reduction: Continuum Models vs Molecular Dynamics.

In the field of electrochemical CO2 reduction, both continuum models and molecular dynamics (MD) models have been used to understand the electric double layer (EDL). MD often focuses on the region within a few nm of the electrode, while continuum models can span up to the device level (cm). Still, both methods model the EDL, and for a cohesive picture of the CO2 electrolysis system, the two methods should agree in the regions where they overlap length scales. To this end, we make a direct comparison between state-of-the-art continuum models and classical MD simulations under the conditions of CO2 reduction on a Ag electrode. For continuum modeling, this includes the Poisson-Nernst-Planck formulation with steric (finite ion size) effects, and in MD the electrode is modeled with the constant potential method. The comparison yields numerous differences between the two modeling methods. MD shows cations forming two adsorbed layers, including a fully hydrated outer layer and a partial hydration layer closer to the electrode surface. The strength of the inner adsorbed layer increases with cation size (Li+ < Na+ < K+ < Cs+) and with more negative applied potentials. Continuum models that include steric effects predict CO2 to be mostly excluded within 1 nm of the cathode due to tightly packed cations, yet we find little evidence to support these predictions from the MD results. In fact, MD shows that the concentration of CO2 increases within a few Å of the cathode surface due to interactions with the Ag electrode, a factor not included in continuum models. The EDL capacitance is computed from the MD results, showing values in the range of 7-9 μF cm-2, irrespective of the electrolyte concentration, cation identity, or applied potential. The direct comparison between the two modeling methods is meant to show the areas of agreement and disagreement between the two views of the EDL, so as to improve and better align these models.

Classical and quantum computing of shear viscosity for (2+1)D SU(2) gauge theory

We perform a nonperturbative calculation of the shear viscosity for (2+1)-dimensional SU(2) gauge theory by using the lattice Hamiltonian formulation. The retarded Green’s function of the stress-energy tensor is calculated from real time evolution via exact diagonalization of the lattice Hamiltonian with a local Hilbert space truncation, and the shear viscosity is obtained via the Kubo formula. When taking the continuum limit, we account for the renormalization group flow of the coupling but no additional operator renormalization. We find the ratio of the shear viscosity and the entropy density ηs is consistent with a well-known holographic result 14π at several temperatures on a 4×4 honeycomb lattice with the local electric representation truncated at jmax=12. We also find the ratio of the spectral function and frequency ρxy(ω)ω exhibits a peak structure when the frequency is small. Both the exact diagonalization method and simple matrix product state classical simulation method beyond jmax=12 on bigger lattices require exponentially growing resources. So we develop a quantum computing method to calculate the retarded Green’s function and analyze various systematics of the calculation including jmax truncation and finite size effects, Trotter errors and the thermal state preparation efficiency. Our thermal state preparation method still requires resources that grow exponentially with the lattice size, but with a very small prefactor at high temperature. We test our quantum circuit on both the Quantinuum emulator and the IBM simulator for a small lattice and obtain results consistent with the classical computing ones. Published by the American Physical Society 2024

The dance of neurons: Exploring nonlinear dynamics in brain networks

The brain is a complex, nonlinear system, exhibiting ever-evolving patterns of activities, whether in the presence or absence of external stimuli or task demands. Nonlinearity can notably obscure the link between structural constraints enforced on the interaction and its dynamical consequences. Suitable nonlinear dynamical models and their analysis serve as essential tools not only for bridging structural and functional understanding of the brain but also for predictably altering the complex dynamical organization of the brain. Here, starting from a large-scale network of threshold Hodgkin–Huxley style neurons, we formulate the average nonlinear dynamics implicitly following from the Wilson–Cowan assumptions. We investigate the influence of biophysical and structural properties on the complexity of neural dynamics at the microscale level and its relationship with the macroscopic Wilson–Cowan model. Incorporating the elements in the model can help identify more realistic regimes of activity and connect the mathematical prediction of increasing nonlinearity to physical manipulations. Our simulations of the temporal profiles reveal dependency on the binary state of interacting subpopulations and the random property of structural network at the transition points, when different synaptic weights are considered. For substantial configurations of stimulus intensity, our model provides further estimates of the neural population’s dynamics, ranging from simple-periodic to aperiodic patterns and phase transition regimes. This reflects the potential contribution of the microscopic nonlinear scheme to the mean-field approximation in studying the collective behaviour of individual neurons with particularly concentrating on the occurrence of critical phenomena. We show that finite-size effects kick the system in a state of irregular modes to evolve differently from predictions of the original Wilson–Cowan reference. Additionally, we report that the complexity and temporal diversity of neural dynamics, especially in terms of limit cycle trajectory, and synchronization can be induced by either small heterogeneity in the degree of various types of local excitatory connectivity or considerable diversity in the external drive to the excitatory pool.

Resolving Nonequilibrium Shape Variations among Millions of Gold Nanoparticles.

Nanoparticles, exhibiting functionally relevant structural heterogeneity, are at the forefront of cutting-edge research. Now, high-throughput single-particle imaging (SPI) with X-ray free-electron lasers (XFELs) creates opportunities for recovering the shape distributions of millions of particles that exhibit functionally relevant structural heterogeneity. To realize this potential, three challenges have to be overcome: (1) simultaneous parametrization of structural variability in real and reciprocal spaces; (2) efficiently inferring the latent parameters of each SPI measurement; (3) scaling up comparisons between 105 structural models and 106 XFEL-SPI measurements. Here, we describe how we overcame these three challenges to resolve the nonequilibrium shape distributions within millions of gold nanoparticles imaged at the European XFEL. These shape distributions allowed us to quantify the degree of asymmetry in these particles, discover a relatively stable "shape envelope" among nanoparticles, discern finite-size effects related to shape-controlling surfactants, and extrapolate nanoparticles' shapes to their idealized thermodynamic limit. Ultimately, these demonstrations show that XFEL SPI can help transform nanoparticle shape characterization from anecdotally interesting to statistically meaningful.

Emergent facilitation and glassy dynamics in supercooled liquids

In supercooled liquids, dynamical facilitation refers to a phenomenon where microscopic motion begets further motion nearby, resulting in spatially heterogeneous dynamics. This is central to the glassy relaxation dynamics of such liquids, which show super-Arrhenius growth of relaxation timescales with decreasing temperature. Despite the importance of dynamical facilitation, there is no theoretical understanding of how facilitation emerges and impacts relaxation dynamics. Here, we present a theory that explains the microscopic origins of dynamical facilitation. We show that dynamics proceeds by localized bond-exchange events, also known as excitations, resulting in the accumulation of elastic stresses with which new excitations can interact. At low temperatures, these elastic interactions dominate and facilitate the creation of new excitations near prior excitations. Using the theory of linear elasticity and Markov processes, we simulate a model, which reproduces multiple aspects of glassy dynamics observed in experiments and molecular simulations, including the stretched exponential decay of relaxation functions, the super-Arrhenius behavior of relaxation timescales as well as their two-dimensional finite-size effects. The model also predicts the subdiffusive behavior of the mean squared displacement (MSD) on short, intermediate timescales. Furthermore, we derive the phonon contributions to diffusion and relaxation, which when combined with the excitation contributions produce the two-step relaxation processes, and the ballistic-subdiffusive-diffusive crossover MSD behaviors commonly found in supercooled liquids.

Atomistic insights into argon clusters and nucleation dynamics

Accurate predictions of nucleation and atomic-level estimates of cluster properties in gas-phase chemical physics have proven challenging. These challenges arise from two primary sources: finite-size effects associated with nanoscopic particles and the emergence of non-standard thermodynamics, particularly at elevated temperatures. This study reexamines the formation of argon clusters using established methodologies such as atomistic simulations, configurational sampling, and statistical thermochemistry. To enhance the representation of condensed-phase argon, we employ an ab initio-based two-body potential, complemented by a three-body Axilrod–Teller potential. Additionally, we address the impact of anharmonicities on cluster stabilities using a recently developed extension to the standard statistical cluster model. The employed anharmonic model is rigorously benchmarked against molecular dynamics simulations. The subsequent analysis demonstrates a robust and consistent agreement between our model and experimental data. Our analysis covers nearly every experimental data point collected between 1971 and 2010, offering valuable insights into the predictive capabilities of the model. Moreover, in contrast to previous studies, our findings indicate that individual measurements are consistently in alignment with each other.

Linear Electro-Optic Effect in 2D Ferroelectric for Electrically Tunable Metalens.

The advent of 2D ferroelectrics, characterized by their spontaneous polarization states in layer-by-layer domains without the limitation of a finite size effect, brings enormous promise for applications in integrated optoelectronic devices. Comparing with semiconductor/insulator devices, ferroelectric devices show natural advantages such as non-volatility, low energy consumption and high response speed. Several 2D ferroelectric materials have been reported, however, the device implementation particularly for optoelectronic application remains largely hypothetical. Here, the linear electro-optic effect in 2D ferroelectrics is discovered and electrically tunable 2D ferroelectric metalens is demonstrated. The linear electric-field modulation of light is verified in 2D ferroelectric CuInP2S6. The in-plane phase retardation can be continuously tuned by a transverse DC electric field, yielding an effective electro-optic coefficient rc of 20.28 pm V-1. The CuInP2S6 crystal exhibits birefringence with the fast axis oriented along its (010) plane. The 2D ferroelectric Fresnel metalens shows efficacious focusing ability with an electrical modulation efficiency of the focusing exceeding 34%. The theoretical analysis uncovers the origin of the birefringence and unveil its ultralow light absorption across a wide wavelength range in this non-excitonic system. The van der Waals ferroelectrics enable room-temperature electrical modulation of light and offer the freedom of heterogeneous integration with silicon and another material system for highly compact and tunable photonics andmetaoptics.

Quantum Dichotomies and Coherent Thermodynamics beyond First-Order Asymptotics

We address the problem of exact and approximate transformation of quantum dichotomies in the asymptotic regime, i.e., the existence of a quantum channel E mapping ρ1⊗n into ρ2⊗Rnn with an error ϵn (measured by trace distance) and σ1⊗n into σ2⊗Rnn exactly, for a large number n. We derive second-order asymptotic expressions for the optimal transformation rate Rn in the small-, moderate-, and large-deviation error regimes, as well as the zero-error regime, for an arbitrary pair (ρ1,σ1) of initial states and a commuting pair (ρ2,σ2) of final states. We also prove that for σ1 and σ2 given by thermal Gibbs states, the derived optimal transformation rates in the first three regimes can be attained by thermal operations. This allows us, for the first time, to study the second-order asymptotics of thermodynamic state interconversion with fully general initial states that may have coherence between different energy eigenspaces. Thus, we discuss the optimal performance of thermodynamic protocols with coherent inputs and describe three novel resonance phenomena allowing one to significantly reduce transformation errors induced by finite-size effects. What is more, our result on quantum dichotomies can also be used to obtain, up to second-order asymptotic terms, optimal conversion rates between pure bipartite entangled states under local operations and classical communication. Published by the American Physical Society 2024

Numerical tests of the large charge expansion

We perform Monte-Carlo measurements of two and three-point functions of charged operators in the critical O(2) model in 3 dimensions. Our results are compatible with the predictions of the large charge superfluid effective field theory. To obtain reliable measurements for large values of the charge, we improved the Worm algorithm and devised a measurement scheme which mitigates the uncertainties due to lattice and finite size effects.

Enhancement and suppression of nonsequential double ionization by spatially inhomogeneous fields

Using the three-dimensional classical ensemble approach, we theoretically investigate the nonsequential double ionization of argon atoms in an intense laser field enhanced by bowtie-nanotip. We observe an anomalous decrease in the double ionization yield as the laser intensity increases, along with a significant gap in the low momentum of photoelectrons. According to our theoretical analysis, the finite range of the induced field by the nanostructure is the fundamental cause of the decline in double ionization yield. Driven by the enhanced inhomogeneous field, energetic electrons can escape from the finite range of nanotips without returning. This reduces the possibility of re-scattering on the nucleus and imprints the finite size effect into the double ionization yield and momentum distribution of photoelectrons in the form of yield decline and a gap in the photoelectron-momentum distribution.

Novel barostat implementation for molecular dynamics.

We propose a novel implementation of the extended-dynamics equations for isothermal-isobaric ensemble in molecular dynamics, as the Martyna-Tobias-Klein thermostat and barostat. This method is suitable for systems with constraints and the Verlet-family integrators. Instead of iterations or the Trotter-expansion-based methods, both velocities and box sizes (scaling of bond lengths) are predicted. The algorithm begins with force calculation, requiring neither quarter nor half time steps, and necessitating iterations only inside SHAKE. Several tests demonstrate that the quality is comparable to other implementations. It is found that the formula relating the extended barostat mass to the characteristic time of volume fluctuations is inaccurate for condensed systems, which has consequences for the parameter setup. Emphasis is also put on the verification of the precise isothermal-isobaric ensemble and finite-size effects.

Microwave analogy of Förster resonance energy transfer and effect of finite antenna length

The near-field interaction between quantum emitters, governed by Förster resonance energy transfer (FRET), plays a pivotal role in nanoscale energy transfer mechanisms. However, FRET measurements in the optical regime are challenging as they require nanoscale control of the position and orientation of the emitters. To overcome these challenges, microwave measurements were proposed for enhanced spatial resolution and precise orientation control. However, unlike in optical systems for which the dipole can be taken to be infinitesimal in size, the finite size of microwave antennas can affect energy transfer measurements, especially at short distances. This highlights the necessity to consider the finite antenna length to obtain accurate results. In this study, we advance the understanding of dipole–dipole energy transfer in the microwave regime by developing an analytical model that explicitly considers finite antennas. Unlike previous works, our model calculates the mutual impedance of finite-length thin-wire dipole antennas without assuming a uniform current distribution. We validate our analytical model through experiments investigating energy transfer between antennas placed adjacent to a perfect electric conductor mirror. This allows us to provide clear guidelines for designing microwave experiments, distinguishing conditions where finite-size effects can be neglected and where they must be taken into account. Our study not only contributes to the fundamental physics of energy transfer but also opens avenues for microwave antenna impedance-based measurements to complement optical FRET experiments and quantitatively explore dipole–dipole energy transfer in a wider range of conditions.

Analysis of the co-rotating vortex pair as a test case for computational aeroacoustics

The co-rotating vortex pair arrangement is a frequently applied test case in computational aeroacoustics. Its flow quantities and far-field radiated sound pressure can be computed analytically, assuming delta-distribution potential vortices. When this configuration is used for verification in a numerical computation, the singular vortex cores cannot be modeled directly; they have to be desingularized, which affects the associated flow and acoustical fields. Closed-form expressions for the aeroacoustic source terms are derived for the Scully vortex model and used for detailed numerical computations of the radiated sound pressure. The effects of desingularization and finite source region size are analyzed in the frequency domain for Lighthill’s equation and the perturbed convective wave equation by means of an efficient numerical approach that computes the convolution of the aeroacoustic source terms and the 2D free-field Green’s function. It is shown that the deviations of the far-field radiated sound pressure from the idealized analytical solution depend on the Mach number, vortex core radius, and truncation limit of the source region. A significant increase in the effective size of the source region due to the desingularization is demonstrated. Minimal error bounds compared to the analytic far-field pressure solution are established. The presented converged numerical results serve as reference solutions for validating implementations of hybrid computational aeroacoustic workflows.

Ionic hydration at ambient and higher pressures: Computed chemical potentials from simulations and finite-size effects

For the chemical potential of a hydrated mono-atomic ion, finite- size effects on simulation results obtained using molecular potential truncation are investigated. Free energy perturbation (FEP) calculations were carried out by scaling in two processes the Lennard-Jones (LJ) ion-water parameters and the ion-charge (q) for Br−, K+ and Ca2+ interacting with TIP4P water. Corrections which scale with q2 enable us to reduce finite-size effects. However, at ambient conditions, discrepancies which depend on q are shown by the corrected values when comparison is made with the experimental data of the Marcus compilation. Similar behavior was observed by extrapolating the original FEP results to an infinitely large system. Hence, these errors were assumed to depend on water density and corrected at high pressures. Consistency, within statistical uncertainties, is shown when comparing with results derived from computed volumetric quantities. Results are also compared with those derived from experimental values of excess volumes at ambient conditions.

Collective dynamics and shot-noise-induced switching in a two-population neural network.

Neural mass models are a powerful tool for modeling of neural populations. Such models are often used as building blocks for the simulation of large-scale neural networks and the whole brain. Here, we carry out systematic bifurcation analysis of a neural mass model for the basic motif of various neural circuits, a system of two populations, an excitatory, and an inhibitory ones. We describe the scenarios for the emergence of complex collective behavior, including chaotic oscillations and multistability. We also compare the dynamics of the neural mass model and the exact microscopic system and show that their agreement may be far from perfect. The discrepancy can be interpreted as the action of the so-called shot noise originating from finite-size effects. This shot noise can lead to the blurring of the neural mass dynamics or even turn its attractors into metastable states between which the system switches recurrently.

Three-phase equilibria of hydrates from computer simulation. I. Finite-size effects in the methane hydrate.

Clathrate hydrates are vital in energy research and environmental applications. Understanding their stability is crucial for harnessing their potential. In this work, we employ direct coexistence simulations to study finite-size effects in the determination of the three-phase equilibrium temperature (T3) for methane hydrates. Two popular water models, TIP4P/Ice and TIP4P/2005, are employed, exploring various system sizes by varying the number of molecules in the hydrate, liquid, and gas phases. The results reveal that finite-size effects play a crucial role in determining T3. The study includes nine configurations with varying system sizes, demonstrating that smaller systems, particularly those leading to stoichiometric conditions and bubble formation, may yield inaccurate T3 values. The emergence of methane bubbles within the liquid phase, observed in smaller configurations, significantly influences the behavior of the system and can lead to erroneous temperature estimations. Our findings reveal finite-size effects on the calculation of T3 by direct coexistence simulations and clarify the system size convergence for both models, shedding light on discrepancies found in the literature. The results contribute to a deeper understanding of the phase equilibrium of gas hydrates and offer valuable information for future research in this field.

Three-phase equilibria of hydrates from computer simulation. II. Finite-size effects in the carbon dioxide hydrate.

In this work, the effects of finite size on the determination of the three-phase coexistence temperature (T3) of the carbon dioxide (CO2) hydrate have been studied by molecular dynamic simulations and using the direct coexistence technique. According to this technique, the three phases involved (hydrate-aqueous solution-liquid CO2) are placed together in the same simulation box. By varying the number of molecules of each phase, it is possible to analyze the effect of simulation size and stoichiometry on the T3 determination. In this work, we have determined the T3 value at 8 different pressures (from 100 to 6000bar) and using 6 different simulation boxes with different numbers of molecules and sizes. In two of these configurations, the ratio of the number of water and CO2 molecules in the aqueous solution and the liquid CO2 phase is the same as in the hydrate (stoichiometric configuration). In both stoichiometric configurations, the formation of a liquid drop of CO2 in the aqueous phase is observed. This drop, which has a cylindrical geometry, increases the amount of CO2 available in the aqueous solution and can in some cases lead to the crystallization of the hydrate at temperatures above T3, overestimating the T3 value obtained from direct coexistence simulations. The simulation results obtained for the CO2 hydrate confirm the sensitivity of T3 depending on the size and composition of the system, explaining the discrepancies observed in the original work by Míguez et al. [J. Chem Phys. 142, 124505 (2015)]. Non-stoichiometric configurations with larger unit cells show a convergence of T3 values, suggesting that finite-size effects for these system sizes, regardless of drop formation, can be safely neglected. The results obtained in this work highlight that the choice of a correct initial configuration is essential to accurately estimate the three-phase coexistence temperature of hydrates by direct coexistence simulations.