Effects Of Long-range Interactions Research Articles

Robustness of topological corner modes in photonic crystals

We analyze the robustness of corner modes in topological photonic crystals, taking a $C_6$-symmetric breathing honeycomb photonic crystal as an example. First, we employ topological quantum chemistry and Wilson loop calculations to demonstrate that the topological properties of the bulk crystal stem from an obstructed atomic limit phase. We then characterize the topological corner modes emerging within the gapped edge modes employing a semi-analytical model, determining the appropriate real space topological invariants. For the first time, we provide a detailed account of the effect of long-range interactions on the topological modes in photonic crystals, and we quantify their robustness to perturbations. We conclude that, while photonic long-range interactions inevitably break chiral symmetry, the corner modes are protected by lattice symmetries.

Electromechanical Analysis of Flexoelectric Nanosensors Based on Nonlocal Elasticity Theory.

Flexoelectric materials have played an increasingly vital role in nanoscale sensors, actuators, and energy harvesters due to their scaling effects. In this paper, the nonlocal effects on flexoelectric nanosensors are considered in order to investigate the coupling responses of beam structures. This nonlocal elasticity theory involves the nonlocal stress, which captures the effects of nonlocal and long-range interactions, as well as the strain gradient stress. Based on the electric Gibbs free energy, the governing equations and related boundary conditions are deduced via the generalized variational principle for flexoelectric nanobeams subjected to several typical external loads. The closed-form expressions of the deflection and induced electric potential (voltage) values of flexoelectric sensors are obtained. The numerical results show that the nonlocal effects have a considerable influence on the induced electric potential of flexoelectric sensors subjected to general transverse forces. Moreover, the induced electric potential values of flexoelectric sensors calculated by the nonlocal model may be smaller or larger than those calculated by the classical model, depending on the category of applied loads. The present research indicates that nonlocal effects should be considered in order to understand or design basic nano-electromechanical components subjected to various external loads.

Long-Range Interaction Enhanced Adiabatic Quantum ComputersSupported by the National Natural Science Foundation of China (Grant Nos. U1930201, 11574239 and 91836101).

A quantum computer is not necessarily alone, e.g., thousands and millions of quantum computers are simultaneously working together for adiabatic quantum computers based on nuclear spins. Long-range interaction is inevitable between these nuclear spin qubits. Here we investigate the effect of long-range dipolar interaction between different adiabatic quantum computers. Our analytical and numerical results show that the dipolar interaction can enhance the final fidelity in adiabatic quantum computation for solving the factorization problem, when the overall interaction is negative. The enhancement will become more prominent if a single quantum computer encounters an extremely small energy gap which occurs more likely for larger-size systems.

Dynamics of nonlocal thick nano-bars

The thick bar model, accounting for the lateral deformation, shear stiffness, and lateral inertia effect, is the most comprehensive structural theory to study the axial deformation of carbon nanotubes. Physically motivated definition of the axial force field and associated higher order boundary conditions are determined applying a consistent variational framework. The effects of long-range interactions are suitably realized in the framework of the nonlocal integral elasticity. The integral convolutions of the nonlocal constitutive law are determined and suitably resorted with the equivalent nonlocal differential model equipped with non-standard boundary conditions. Preceding contributions on the elastodynamic analysis of the elastic thick bar are, therefore, amended by properly taking into account the higher order and non-standard boundary conditions. The established size-dependent thick bar model is demonstrated to be exempt from the inherent drawbacks of the nonlocal differential formulation and leads to well-posed elastodynamic problems. The wave desperation response and free vibrational behavior of elastic thick bars with kinematic constraints of nano-mechanics interest are rigorously investigated by making recourse to a viable solution approach. New numerical benchmarks are detected for the elastodynamic response of nonlocal thick nano-bars. A consistent approach for nanoscopic study of the field quantities in the nonlocal mechanics is proposed that is capable of properly confirming the smaller-is-softer phenomenon.

Efficient simulation of moiré materials using the density matrix renormalization group

We present an infinite density-matrix renormalization group (DMRG) study of an interacting continuum model of twisted bilayer graphene (tBLG) near the magic angle. Because of the long-range Coulomb interaction and the large number of orbital degrees of freedom, tBLG is difficult to study with standard DMRG techniques -- even constructing and storing the Hamiltonian already poses a major challenge. To overcome these difficulties, we use a recently developed compression procedure to obtain a matrix product operator representation of the interacting tBLG Hamiltonian which we show is both efficient and accurate even when including the spin, valley and orbital degrees of freedom. To benchmark our approach, we focus mainly on the spinless, single-valley version of the problem where, at half-filling, we find that the ground state is a nematic semimetal. Remarkably, we find that the ground state is essentially a k-space Slater determinant, so that Hartree-Fock and DMRG give virtually identical results for this problem. Our results show that the effects of long-range interactions in magic angle graphene can be efficiently simulated with DMRG, and opens up a new route for numerically studying strong correlation physics in spinful, two-valley tBLG, and other moire materials, in future work.

Universality in incompressible active fluid: Effect of nonlocal shear stress.

Phase transitions in active fluids attracted significant attention within the last decades. Recent results show [L. Chen etal., New J. Phys. 17, 042002 (2015)10.1088/1367-2630/17/4/042002] that an order-disorder phase transition in incompressible active fluids belongs to a new universality class. In this work, we further investigate this type of phase transition and focus on the effect of long-range interactions. This is achieved by introducing a nonlocal shear stress into the hydrodynamic description, which leads to superdiffusion of the velocity field, and can be viewed as a result of the active particles performing Lévy walks. The universal properties in the critical region are derived by performing a perturbative renormalization group analysis of the corresponding response functional within the one-loop approximation. We show that the effect of nonlocal shear stress decreases the upper critical dimension of the model, and can lead to the irrelevance of the active fluid self-advection with the resulting model belonging to an unusual long-range Model A universality class not reported before, to our knowledge. Moreover, when the degree of nonlocality is sufficiently high all nonlinearities become irrelevant and the mean-field description is valid in any spatial dimension.

Linear and nonlinear rheology of oil in liquid crystal emulsions

While the majority of experimental and numerical studies focus on yield stress fluids with short-range repulsive interactions, the effect of long-range interaction is rarely known. In this work, we studied the linear and nonlinear rheological behavior of a model oil in nematic liquid crystal emulsions, which exhibit long-range droplet-droplet interaction. The characteristic of long-range interaction, attractive at large droplet separation and repulsive at a small surface distance, was inferred from the morphology and thixotropy of emulsions. We suggested a model accounting for the plateau modulus purely due to the long-range repulsive interaction. We further illustrated that neither the yield stress nor the relaxation time followed a simple power-law scaling with respect to the distance to jamming. The rescaled steady and dynamic flow curves could not collapse on master curves above jamming transition when the long-range and short-range repulsive interactions contribute simultaneously.

Extrinsic spin Hall effect in inhomogeneous systems

Charge-to-spin conversion in inhomogeneous systems is studied theoretically. We consider free electrons subject to impurities with spin-orbit interaction and with spatially modulated distribution, and calculate spin accumulation and spin current induced by an external electric field. It is found that the spin accumulation is induced by the vorticity of electron flow through the side-jump and skew-scattering processes, and the differences of the two processes are discussed. The results can be put in a form of generalized spin diffusion equation with a spin source term given by the divergence of the spin Hall current. This spin source term reduces to the form of spin-vorticity coupling when the spin Hall angle is independent of impurity concentration. We also study the effects of long-range Coulomb interaction, which is indispensable when the process involves charge inhomogeneity and accumulation as in the present problem.

Long-Range Multibody Interactions and Three-Body Antiblockade in a Trapped Rydberg Ion Chain.

Trapped Rydberg ions represent a flexible platform for quantum simulation and information processing that combines a high degree of control over electronic and vibrational degrees of freedom. The possibility to individually excite ions to high-lying Rydberg levels provides a system where strong interactions between pairs of excited ions can be engineered and tuned via external laser fields. We show that the coupling between Rydberg pair interactions and collective motional modes gives rise to effective long-range and multibody interactions consisting of two, three, and four-body terms. Their shape, strength, and range can be controlled via the ion trap parameters and strongly depends on both the equilibrium configuration and vibrational modes of the ion crystal. By focusing on an experimentally feasible quasi one-dimensional setup of ^{88}Sr^{+} Rydberg ions, we demonstrate that multibody interactions are enhanced by the emergence of soft modes associated with, e.g., a structural phase transition. This has a striking impact on many-body electronic states and results-for example-in a three-body antiblockade effect that can be employed as a sensitive probe to detect structural phase transitions in Rydberg ion chains. Our study unveils the possibilities offered by trapped Rydberg ions for studying exotic phases of matter and quantum dynamics driven by enhanced multibody interactions.

Skyrmion and tetarton lattices in twisted bilayer graphene

Recent experiments on twisted bilayer graphene show an anomalous quantum Hall (AQH) effect at filling of $3$ electrons per moir\`e unit cell. The AQH effect arises in an insulating state with both valley- and ferromagnetic order. We argue, that weak doping of such a system leads to the formation of a novel topological spin texture, a `double-tetarton lattice'. The building block of this lattice, the `double-tetarton', is a spin configuration which covers $1/4$ of the unit-sphere twice. In contrast to skyrmion lattices, the net magnetization of this magnetic texture vanishes. Only at large magnetic fields more conventional skyrmion lattices are recovered. But even for large fields the addition of a single charge to the ferromagnetic AQH state flips hundreds of spins. Our analysis is based on the investigation of an effective non-linear sigma model which includes the effects of long-ranged Coulomb interactions.

Precise measurement of particle size in colloid system based on the development of multiple-angle dynamic light scattering apparatus

Dynamic light scattering (DLS) is a widely used, non-invasive and in-situ method for particle size measurement. However, the precision of the measurement results is still under discussion. Theoretically, the apparent hydrodynamic diameter measured by DLS varies with scattering angle due to Mie scattering as well as long-distance interaction between particles. In this paper, a multiple-angle dynamic light scattering (MDLS) apparatus is established. After determining the critical concentration at which multiple scattering occurs at different scattering angle, polystyrene latex (PSL) particles sized from 23 to 500 nm diluted with different concentrations are precisely measured at different scattering angles. By introducing special pin-holes, precise alignment design and beam-stops at all scattering angles, the precision of the MDLS apparatus is highly improved. DLS results are strongly angular and concentration dependent, and the trends vary with particle size. DLS results at infinite dilution and zero angle are obtained after extrapolation, which eliminates the effects of long-range interactions and intraparticle interference. The present optical design extends the application validity of this method from nano particle to submicron particle.

Emergence of generalized hydrodynamics in the non-local Luttinger model

We propose the Luttinger model with finite-range interactions as a simple tractable example in 1+1 dimensions to analytically study the emergence of Euler-scale hydrodynamics in a quantum many-body system. This non-local Luttinger model is an exactly solvable quantum field theory somewhere between conformal and Bethe-ansatz integrable models. Applying the recent proposal of generalized hydrodynamics, we show that the model allows for fully explicit yet non-trivial solutions of the resulting Euler-scale hydrodynamic equations. Comparing with exact analytical non-equilibrium results valid at all time and length scales, we show perfect agreement at the Euler scale when the interactions are short range. A formal proof of the emergence of generalized hydrodynamics in the non-local Luttinger model is also given, and effects of long-range interactions are briefly discussed.

Limit cycles in the spectra of mass imbalanced many-boson system

The independence between few-body scales beyond the van der Waals universality is demonstrated for the extreme mass-imbalanced case of a specific many-boson system. This finding generalizes the scaling properties of universal tetramers to a broader class of heterogeneous few-boson systems. We assume two heavy atoms interacting with (N − 2)-lighter ones at the unitary limit, using a particular case where no interactions are active between identical particles, by investigating the interwoven spectra of this many-body system for an arbitrary number of light bosons. A large mass-ratio between the particles allows us to treat this N-body system analytically, by solving an effective inverse-squared long-range interaction which is stablished for the two heavy bosons. For a cluster with N − 2 light bosons (N ⩾ 4), we discuss the implications of the corresponding long-range potentials associated with different subsystem thresholds, implying in independent interwoven limit cycles for the correlation between the energies of excited N-body system. Our study with extreme mass-imbalanced few-boson bound states provides a fundamental understanding of the scaling behavior of their interwoven spectra. The novel insights enlarge the well-known Efimov physics paradigm and show the existence of different limit cycles, which could be probed by new experiments.

Phase separation of polymer-bound particles induced by loop-mediated one dimensional effective long-range interactions

The cellular cytoplasm is organized into compartments. Phase separation is a simple manner to create membrane-less compartments in order to confine and localize particles like proteins. In many cases these particles are bound to fluctuating polymers like DNA or RNA. We propose a general theoretical framework for such polymer-bound particles and derive an effective 1D lattice gas model with both nearest-neighbor and emergent long-range interactions arising from looped configurations of the fluctuating polymer. We argue that 1D phase transitions exist in such systems for both Gaussian and self-avoiding polymers and, using a variational method that goes beyond mean-field theory, we obtain the complete mean occupation-temperature phase diagram. To illustrate this model we apply it to the biologically relevant case of ParABS, a prevalent bacterial DNA segregation system.

Coupling between Particle Shape and Long-Range Interaction in the High-Density Regime**Supported by the National Natural Science Foundation of China (Grant Nos. 11774059 and 11734014).

We experimentally probe the coupling between particle shape and long-range interaction, using long-range interacting polygons. For two typical space-filling polygons, square and triangle, we find two types of coupling modes that predominantly control the structure formation. Specifically, the rotational ordering of squares brings a lattice deformation that produces a hexagonal-to-rhombic transition in the high density regime, whereas the alignment of triangles introduces a large geometric frustration that causes an order-to-disorder transition. Moreover, the two coupling modes lead to small and large “internal roughness” of the two systems, and thus predominantly control their structure relaxations. Our study thus provides a physical picture to the coupling between long-range interaction effect and short-range shape effect in the high-density regime unexplored before.

Quantum phase transitions in a spin-1 antiferromagnetic chain with long-range interactions and modulated single-ion anisotropy

We study the phase diagram of spin-1 antiferromagnetic chain with isotropic antiferromagnetic interactions decaying with a power-law $\propto r^{-\alpha}$ ($\alpha\ge 1$) accompanied by modulated single-ion anisotropy. Employing the techniques of the density-matrix renormalization group, effects of long-range interactions and single-ion anisotropy on a variety of correlations are investigated. In order to check the consistency, the fidelity susceptibilities are evaluated across quantum phase transitions. The quantum critical points are faithfully detected and orders of phase transitions are determined. The correlation-length critical exponent is extracted from scaling functions of the fidelity susceptibility. The presence of long-range interactions leads to quantitative change of the phase boundaries and reduces the order of phase transition under certain conditions. A direct first-order transition between the periodic N\'eel phase and the large-$D$ phase occurs for slowly decaying antiferromagnetic interactions.

Two-electron selective coupling in an edge-state based conditional phase shifter

We investigate the effect of long-range Coulomb interaction on the two-electron scattering in the integer quantum Hall regime at bulk filling factor 2. A parallel version of the Split-Step Fourier method evolves the exact two-particle wave function in a 2D potential background reproducing the effect of depleting gates in a realistic heterostructure, with the charge carrier represented by a localized wavepacket of edge states. We compare the spatial shift induced by Coulomb repulsion in the final two-electron wave function for two indistinguishable electrons initialized in different configurations according to their Landau index, and analyze their bunching probability and the effect of screening. We finally prove the feasibility of the present operating regime as a two-qubit conditional phase shifter to generate entanglement from product states.

Exciton localization in tubular molecular aggregates: Size effects and optical response.

We study the exciton localization and resulting optical response for disordered tubular aggregates of optically active molecules. It has previously been shown that such tubular structures allow for excitons delocalized over more than a thousand molecules, owing to the combined effects of long-range dipole-dipole interactions and the higher-dimensional (not truly one-dimensional) nature of the aggregate. Such large delocalization sizes prompt the question to what extent in experimental systems the delocalization may still be determined by the aggregate size (diameter and length) and how this affects the aggregate's optical response and dynamics. We perform a systematic study of the size effects on the localization properties using numerical simulations of the exciton states in a cylindrical model structure inspired by the previously derived geometry of a cylindrical aggregate of cyanine dye molecules (C8S3). To characterize the exciton localization, we calculate the participation ratio and the autocorrelation function of the exciton wave function. We also calculate the density of states and absorption spectrum. We find strong effects of the tube's radius on the localization and optical properties in the range of parameters relevant to the experiment. In addition, surprisingly, we find that even for tubes as long as 750 nm, the localization size is limited by the tube's length for disorder values that are relevant to experimental circumstances, while observable effects of the tube's length in the absorption spectrum still occur for tube lengths up to about 150 nm. The latter may explain the changes in the optical spectra observed during the aging process of bromine-substituted C8S3 aggregates. For weak disorder, the exciton wave functions exhibit a scattered, fractal-like nature, similar to the quasi-particles in two-dimensional disordered systems.

Observation of Spin-Spin Fermion-Mediated Interactions between Ultracold Bosons.

Interactions in an ultracold boson-fermion mixture are often manifested by elastic collisions. In a mixture of a condensed Bose gas (BEC) and spin polarized degenerate Fermi gas (DFG), fermions can mediate spin-spin interactions between bosons, leading to an effective long-range magnetic interaction analogous to Ruderman-Kittel-Kasuya-Yosida [Phys. Rev. 96, 99 (1954); Prog. Theor. Phys. 16, 45 (1956); Phys. Rev. 106, 893 (1957)] interaction in solids. We used Ramsey spectroscopy of the hyperfine clock transition in a ^{87}Rb BEC to measure the interaction mediated by a ^{40}K DFG. By controlling the boson density we isolated the effect of mediated interactions from mean-field frequency shifts due to direct collision with fermions. We measured an increase of boson spin-spin interaction by a factor of η=1.45±0.05^{stat}±0.13^{syst} in the presence of the DFG, providing clear evidence of spin-spin fermion mediated interaction. Decoherence in our system was dominated by inhomogeneous boson density shift, which increased significantly in the presence of the DFG, again indicating mediated interactions. We also measured a frequency shift due to boson-fermion interactions in accordance with a scattering length difference of a_{bf_{2}}-a_{bf_{1}}=-5.36±0.44^{stat}±1.43^{syst}a_{0} between the clock-transition states, a first measurement beyond the low-energy elastic approximation [R. Côté, A. Dalgarno, H. Wang, and W. C. Stwalley, Phys. Rev. A 57, R4118 (1998); A. Dalgarno and M. Rudge, Proc. R. Soc. A 286, 519 (1965)] in this mixture. This interaction can be tuned with a future use of a boson-fermion Feshbach resonance.Fermion-mediated interactions can potentially give rise to interesting new magnetic phases and extend the Bose-Hubbard model when the atoms are placed in an optical lattice.

Energy current correlation in solvable long-range interacting systems.

We consider heat transfer in one-dimensional systems with long-range interactions. It is known that typical short-range interacting systems shows anomalous behavior in heat transport when total momentum is conserved, whereas momentum-nonconserving systems do not exhibit anomaly. In this study, we focus on the effect of long-range interaction. We propose an exactly solvable model that reduces to the so-called momentum-exchange model in the short-range interaction limit. We exactly calculate the asymptotic time decay in the energy current correlation function, which is related to the thermal conductivity via the Green-Kubo formula. From the time decay of the current correlation, we show three qualitatively crucial results. First, the anomalous exponent in the time-decay continuously changes as a function of the index of the long-range interaction. Second, there is a regime where the current correlation diverges with increasing the system size with fixed time, and hence, the exponent of the time decay cannot be defined. Third, even momentum-nonconserving systems can show the anomalous exponent indicating anomalous heat transport. Higher dimensions are also considered, and we found that long-range interaction can induce the anomalous exponent even in three-dimensional systems.