Nearest-neighbor Interactions Research Articles

Surface wave across crack-tip in a lattice model.

For a triangular lattice of particles, with nearest neighbour interactions and a traction free boundary, there exists a surface wave band for out-of-plane motion. Interactions between such a surface wave and stationary crack tip in mode III are investigated. The discrete Helmholtz equation for scattered waves, that incorporates an anisotropy parameter for unequal spring constants in horizontal versus slant directions, is solved exactly. The coefficient of transmission from one crack face to another, as well as that owing to reflection on the same face, is obtained in a closed form; the same leads to an estimate of energy fraction of incident wave that is leaked at the crack tip via bulk waves. It is found, in terms of surface wave band, that the transmission coefficient attains its maximum magnitude above the mid-band while the energy leak is minimum at the upper-band limit. Besides surface wave propagation across crack tip, surface wave excitation due to incident bulk wave is also discussed. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.

Frustrated Ising Model on D-wave Quantum Annealing Machine

We study the frustrated Ising model on the two-dimensional $L \times L$ square lattice with ferromagnetic (FM) nearest-neighbor and antiferromagnetic diagonal-neighbor interactions using the D-wave quantum annealing machine (D-QAM) with 5000+ qubits composed on structure of the Pegasus graph. As the former Monte Carlo and mean field results, we find the FM to stripe order phase transition, through observations of the magnetization $M$, energy, magnetic susceptibility and structure factor. We also analyze probability which occurs any $M$ at a given interaction for many quantum annealing shots to estimate the shape of objective function $f$. The only one value of $M$ with specific phase is observed in the regions far from phase transition for many quantum annealing shots, while several values of $M$ with different possibilities are appeared in the regimes of phase transition. We guess that $f$ in the regimes of phase transition retains the multi-modal structure with several local minimums, due to the strong degeneracies caused by frustrations. Finally, we discuss fail of the quantum annealing simulations, through analysis of the number of the chains, defined as the same variable with $N$-qubits, as a function of $L$.

Phase Diagram of Hard Core Bosons with Anisotropic Interactions

The phase diagram of lattice hard core bosons with nearest-neighbor interactions allowed to vary independently, from repulsive to attractive, along different crystallographic directions, is studied by Quantum Monte Carlo simulations. We observe a superfluid phase, as well as two crystalline phases at half filling, either checkerboard or striped. Just like in the case of isotropic interactions, no supersolid phase is observed.

Microscopic Phase-Field Simulation of γ′ Precipitation in Ni-Based Binary Alloys Coupled with CALPHAD Method

In the present work, the first (1st) and second (2nd) nearest-neighbor interaction energies are calculated by coupling the microscopic phase-field kinetic model with the calculation of phase diagrams (CALPHAD) method. The morphological evolution of the γ′ precipitate and the variation of its atomic ordering parameter for Ni–X (X = Al, Fe, Mn, Pt, or Si) alloys during aging are studied. The simulation results predict different occupation preferences for solute and solvent atoms in the γ′ phase, i.e., solute atoms are inclined to occupy the corner sites and solvent atoms tend to occupy the face sites. In order to understand the precipitation process of the γ′ phase systematically, the ordering and clustering behaviors of solute atoms are analyzed.

Momentum signatures of site percolation in disordered two-dimensional ferromagnets

In this work, we consider a two-dimensional square lattice of pinned magnetic spins with nearest-neighbour interactions and we randomly replace a fixed proportion of spins with nonmagnetic defects carrying no spin. We focus on the linear spin-wave regime and address the propagation of a spin-wave excitation with initial momentum $k_0$. We compute the disorder-averaged momentum distribution obtained at time $t$ and show that the system exhibits two regimes. At low defect density, typical disorder configurations only involve a single percolating magnetic cluster interspersed with single defects essentially and the physics is driven by Anderson localization. In this case, the momentum distribution features the emergence of two known emblematic signatures of coherent transport, namely the coherent backscattering (CBS) peak located at $-k_0$ and the coherent forward scattering (CFS) peak located at $k_0$. At long times, the momentum distribution becomes stationary. However, when increasing the defect density, site percolation starts to set in and typical disorder configurations display more and more disconnected clusters of different sizes and shapes. At the same time, the CFS peak starts to oscillate in time with well defined frequencies. These oscillation frequencies represent eigenenergy differences in the regular, disorder-immune, part of the Hamiltonian spectrum. This regular spectrum originates from the small-size magnetic clusters and its weight grows as the system undergoes site percolation and small clusters proliferate. Our system offers a unique spectroscopic signature of cluster formation in site percolation problems.

Quantum time dynamics employing the Yang-Baxter equation for circuit compression

Quantum time dynamics (QTD) is considered a promising problem for quantum supremacy on near-term quantum computers. However, QTD quantum circuits grow with increasing time simulations. This study focuses on simulating the time dynamics of one-dimensional (1D) integrable spin chains with nearest-neighbor interactions. We have proved the existence of a reflection symmetry in the quantum circuit employed for simulating the time evolution of certain classes of 1D Heisenberg model Hamiltonians by virtue of the quantum Yang-Baxter equation, and how this symmetry can be exploited to compress and produce a shallow quantum circuit. With this compression scheme, the depth of the quantum circuit becomes independent of step size and only depends on the number of spins. We show that the depth of the compressed circuit is rigorously a linear function of the system size for the studied Heisenberg model Hamiltonians in the present work. As a consequence, the number of CNOT gates in the compressed circuit only scales quadratically with the system size, which allows for the simulations of time dynamics of very large 1D spin chains. We derive the compressed circuit representations for different special cases of the Heisenberg Hamiltonian. We compare and demonstrate the effectiveness of this approach by performing simulations on quantum computers.

Effect of next nearest neighbour interactions on compensation temperature in trilayered spin systems

ABSTRACT In this paper we are communicating a Monte-Carlo based numerical study on the ABA type trilayered Ising spin system incorporating next nearest neighbour interactions. The ABA type system is of growing interest because of the existence of compensation temperature. The effect of next nearest neighbour interactions on compensation temperature and phase transition have been studied by focussing on thermal response of some thermodynamic quantities using the Metropolis algorithm. An effort also made to understand the role of intralayer and interlayer interactions in controlling compensation temperature and critical temperature within such a system.

From Asymptotic Freedom to θ Vacua: Qubit Embeddings of the O(3) Nonlinear σ Model.

Conventional lattice formulations of θ vacua in the 1+1-dimensional O(3) nonlinear sigma model suffer from a sign problem. Here, we construct the first sign-problem-free regularization for arbitrary θ. Using efficient lattice MonteCarlo algorithms, we demonstrate how a Hamiltonian model of spin-1/2 degrees of freedom on a two-dimensional spatial lattice reproduces both the infrared sector for arbitrary θ, as well as the ultraviolet physics of asymptotic freedom. Furthermore, as a model of qubits on a two-dimensional square lattice with only nearest-neighbor interactions, it is naturally suited for studying the physics of θ vacua and asymptotic freedom on near-term quantum devices. Our construction generalizes to θ vacua in all CP(N-1) models, solving a long-standing sign problem.

Phase diagram of superconductivity in the integer quantum Hall regime

An interplay between pairing and topological orders has been predicted to give rise to superconducting states supporting exotic emergent particles, such as Majorana particles obeying non-Abelian braid statistics. We consider a system of spin polarized electrons on a Hofstadter lattice with nearest-neighbor attractive interaction and solve the mean-field Bogoliubov-de Gennes equations in a self-consistent fashion, leading to gauge-invariant observables and a rich phase diagram as a function of the chemical potential, the magnetic field, and the interaction. As the strength of the attractive interaction is increased, the system first makes a transition from a quantum Hall phase to a skyrmion lattice phase that is fully gapped in the bulk but has topological chiral edge current, characterizing a topologically nontrivial state. This is followed by a vortex phase in which the vortices carrying Majorana modes form a lattice; the spectrum contains a low-energy Majorana band arising from the coupling between neighboring vortex-core Majorana modes but does not have chiral edge currents. For some parameters, a dimer vortex lattice occurs with no Majorana band. The experimental feasibility and the observable consequences of skyrmions as well as Majorana modes are indicated.

Study on the local and global performance of homogeneous platoon with a bidirectional ring interconnection

This paper investigates the local and global performance of the platoon where multiple identical vehicles move in a closed roadway and cooperate based on nearest-neighbour interactions. The information from the front neighbour, namely position, speed, and acceleration, is weighted non-equally component-wise to that from the back neighbour, which is quantified by the asymmetry level on each component. The local performance refers to the locally propagating attenuation for the bidirectional control, which captures whether the disturbance is amplified when propagating from a vehicle to its immediate neighbours. The global performance refers to the system transfer scalability, which characterises the scalability of system transfer matrix. Based on forward and backward wave transfer functions, several analytical necessary conditions of the locally propagating attenuation are obtained. Furthermore, two of these necessary conditions happen to be the same with the conditions for scalably asymptotic stability. Under mild assumptions, the locally propagating attenuation is sufficient for scalably asymptotic stability, the latter of which in turn implies the system transfer scalability. Numerical calculations further show that it is favourable for both performance measures to select the asymmetry levels on speed and acceleration with small magnitudes and located around the centre line of the band-like region of scalably asymptotic stability.

Anisotropic deconfined criticality in Dirac spin liquids

We analyze a Higgs transition from a U(1) Dirac spin liquid to a gapless ℤ2 spin liquid. This ℤ2 spin liquid is of relevance to the spin S = 1/2 square lattice antiferromagnet, where recent numerical studies have given evidence for such a phase existing in the regime of high frustration between nearest neighbor and next-nearest neighbor antiferromagnetic interactions (the J1-J2 model), appearing in a parameter regime between the vanishing of Néel order and the onset of valence bond solid ordering. The proximate Dirac spin liquid is unstable to monopole proliferation on the square lattice, ultimately leading to Néel or valence bond solid ordering. As such, we conjecture that this Higgs transition describes the critical theory separating the gapless ℤ2 spin liquid of the J1-J2 model from one of the two proximate ordered phases. The transition into the other ordered phase can be described in a unified manner via a transition into an unstable SU(2) spin liquid, which we have analyzed in prior work. By studying the deconfined critical theory separating the U(1) Dirac spin liquid from the gapless ℤ2 spin liquid in a 1/Nf expansion, with Nf proportional to the number of fermions, we find a stable fixed point with an anisotropic spinon dispersion and a dynamical critical exponent z ≠ 1. We analyze the consequences of this anisotropic dispersion by calculating the angular profiles of the equal-time Néel and valence bond solid correlation functions, and we find them to be distinct. We also note the influence of the anisotropy on the scaling dimension of monopoles.

Benchmark calculations of multiloop pseudofermion fRG

The pseudofermion functional renormalization group (pffRG) is a computational method for determining zero-temperature phase diagrams of frustrated quantum magnets. In a recent methodological advance, the commonly employed Katanin truncation of the flow equations was extended to include multiloop corrections, thereby capturing additional contributions from the three-particle vertex (Thoenniss et al. https://arxiv.org/abs/2011.01268; Kiese et al. https://arxiv.org/abs/2011.01269). This development has also stimulated significant progress in the numerical implementation of pffRG, allowing one to track the evolution of pseudofermion vertices under the renormalization group flow with unprecedented accuracy. However, cutting-edge solvers differ in their integration algorithms, heuristics to discretize Matsubara frequency grids, and more. To lend confidence in the numerical robustness of state-of-the-art multiloop pffRG codes, we present and compare results produced with two independently developed and algorithmically distinct solvers for Heisenberg models on three-dimensional lattice geometries. Using the cubic lattice Heisenberg (anti)ferromagnet with nearest and next-nearest neighbor interactions as a generic benchmark model, we find the two codes to quantitatively agree, often up to several orders of magnitude in digital precision, both on the level of spin-spin correlation functions and renormalized fermionic vertices for varying loop orders. These benchmark calculations further substantiate the usage of multiloop pffRG solvers to tackle unconventional forms of quantum magnetism.Graphic abstract

Entanglement diagnostics for efficient VQA optimization

We consider information spreading measures in randomly initialized variational quantum circuits and introduce entanglement diagnostics for efficient variational quantum/classical computations. We establish a robust connection between entanglement measures and optimization accuracy by solving two eigensolver problems for Ising Hamiltonians with nearest-neighbor and long-range spin interactions. As the circuit depth affects the average entanglement of random circuit states, the entanglement diagnostics can identify a high-performing depth range for optimization tasks encoded in local Hamiltonians. We argue, based on an eigensolver problem for the Sachdev–Ye–Kitaev model, that entanglement alone is insufficient as a diagnostic to the approximation of volume-law entangled target states and that a large number of circuit parameters is needed for such an optimization task.

Evolution of magnetic phase in two-dimensional van der Waals Mn1−x Ni x PS3 single crystals

Metal thio(seleno)phosphates MPX3 have attracted considerable attentions with wide spanned band gaps and rich magnetic properties. In this series, two neighboring members MnPS3 and NiPS3 differ in magnetic atoms, magnetic easy axes, spin anisotropy, as well as nearest-neighbor magnetic interactions. The competition between these components may cause intriguing physical phenomena. In this article, the evolution of magnetism of Mn1−x Ni x PS3 series is reported. Despite the incompatible antiferromagnetic orders of two end members, the antiferromagnetism persists as the ground state in the whole substitution region. The magnetic ordering temperature T N show nonmonotonic V-shape behavior, and the reentrant spin glass phase at x= 0.5 is observed. In addition, abnormal bifurcation of T N occurs at x = 0.75, which may be due to the temperature-dependent spin reorientation or phase separation. The evolution of magnetism is further confirmed semi-quantitatively by our density functional theory calculations. Our study indicates that exotic magnetism can be intrigued when multi-degrees of freedom are involved in these low-dimensional systems, which call for more in-depth microscopic studies in future.

ON THE EXISTENCE OF BOUND STATES OF A SYSTEM OF TWO FERMIONS ON THE ONE DIMENSIONAL LATTICE

We study the two-particle discrete Schrodinger operator associated of a system of two fermions on the one dimensional lattice with nearest-neighbour interaction . We prove the existence of eigenvalues below the essential spectrum of the operator in the following two cases: in the case for all and in the case of for large .

Hydrophobic Cluster Formation in Aqueous Ethanol Solutions Probed by Soft X-ray Absorption Spectroscopy.

Hydrophobic cluster structures in aqueous ethanol solutions at different concentrations have been investigated by soft X-ray absorption spectroscopy (XAS). In the O K-edge XAS, we have found that hydrogen bond structures among water molecules are enhanced in the middle-concentration region by the hydrophobic interaction of the ethyl groups in ethanol. In the C K-edge XAS, the lower energy features arise from a transition from the terminal methyl C 1s electron to an unoccupied orbital of 3s Rydberg character, which is sensitive to the nearest-neighbor intermolecular interactions. From the comparison of C K-edge XAS with the inner-shell calculations, we have found that ethanol clusters are easily formed in the middle-concentration region due to the hydrophobic interaction of the ethyl group in ethanol, resulting in the enhancement of the hydrogen bond structures among water molecules. This behavior is different from aqueous methanol solutions, where the methanol-water mixed clusters are more predominant in the middle-concentration region due to the relatively weak hydrophobic interactions of the methyl group in methanol.

Density of states in antiferromagnetic nanowire superconductors

The coexistence of different order parameters and the pairing symmetry is the major issue in the study of one dimensional wires. We adopt a tight-binding model, for the coexistence of superconductivity and antiferromagnetism in s-wave pairing symmetry, which is consistent and most favourable for the nearest-neighbour pairing interaction, and derive a set of gap equations which are solved numerically and self-consistently. The effects of the order parameters on one another are studied. We have also calculated the density of states and band energies. The density of states shows the defined interference peaks on either side of the Fermi level corresponding to the order parameters with van Hove singularities.

Surface criticality of the antiferromagnetic Potts model

We study the three-state antiferromagnetic Potts model on the simple-cubic lattice, paying attention to the surface critical behaviors. When the nearest neighboring interactions of the surface is tuned, we obtain a phase diagram similar to the XY model, owing to the emergent O(2) symmetry of the bulk critical point. For the ordinary transition, we get $y_{h1}=0.780(3)$, $\eta_\parallel=1.44(1)$, and $\eta_\perp=0.736(6)$; for the special transition, we get $y_s=0.59(1)$, $y_{h1}=1.693(2)$, $\eta_\parallel=-0.391(4)$, and $\eta_\perp=-0.179(5)$; in the extraordinary-log phase, the surface correlation function $C_\parallel(r)$ decays logarithmically, with decaying exponent $q=0.60(2)$, however, the correlation $C_\perp(r)$ still decays algebraically, with critical exponent $\eta_\perp=-0.442(5)$. If the ferromagnetic next nearest neighboring surface interactions are added, we find two transition points, the first one is a special point between the ordinary phase and the extraordinary-log phase, the second one is a transition between the extraordinary-log phase and the $Z_6$ symmetry-breaking phase, with critical exponent $y_{\rm s}=0.41(2)$. The scaling behaviors of the second transition is very interesting, the surface spin correlation function $C_\parallel(r)$ and the surface squared staggered magnetization at this point decays logarithmically, with exponent $q=0.37(1)$; however, the surface structure factor with the smallest wave vector and the correlation function $C_\perp(r)$ satisfy power-law decaying, with critical exponents $\eta_\parallel=-0.69(1)$ and $\eta_\perp=-0.37(1)$, respectively.

Phase diagram and thermodynamic properties of the frustrated ferro-antiferromagnetic spin system on the octahedral lattice

The influence of anisotropy generated by the competition between the ferromagnetic and antiferromagnetic nearest-neighbor interactions on the magnetic and thermodynamic properties of the classical spin system on the octahedral lattice is investigated in the framework of the exactly solvable Ising-like model on the recursive octahedral lattice. The phase diagram of the model is found and the nature of all phase transitions is determined. It is shown that the model exhibits the existence of the intermediate phase that separates the ferromagnetic phase from the antiferromagnetic one. Moreover, it is also shown that while the intermediate phase and the antiferromagnetic one are separated by the critical curve of the second-order phase transitions the transitions between the ferromagnetic phase and the intermediate one have the first-order nature on the coexistence line. The magnetization and entropy properties of all phases of the model are studied. Depending on the value of the frustration parameter, four different ground states are identified with formation of a strict residual entropy hierarchy. Due to the frustration nature of the model the specific heat capacity exhibits anomalous (Schottky) behavior at low temperatures in the vicinity of the value of the frustration parameter, for which two highly macroscopically degenerated single-point-like ground states are formed. The presence of the intermediate phase in the model also leads to the existence of the series of even three successive second-order phase transitions in the temperature dependence of the magnetization as well as of the specific heat capacity.

As-Se Pentagonal Linkers to Induce Chirality and Polarity in Mixed-Valent Fe-Se Tetrahedral Chains Resulting in Hidden Magnetic Ordering.

A novel mixed-valent hybrid chiral and polar compound, Fe7As3Se12(en)6(H2O), has been synthesized by a single-step solvothermal method. The crystal structure consists of 1D [Fe5Se9] chains connected via [As3Se2]-Se pentagonal linkers and charge-balancing interstitial [Fe(en)3]2+ complexes (en = ethylenediamine). Neutron powder diffraction verified that interstitial water molecules participate in the crystal packing. Magnetic polarizability of the produced compound was confirmed by X-ray magnetic circular dichroism (XMCD) spectroscopy. X-ray absorption spectroscopy (XAS) and 57Fe Mössbauer spectroscopy showed the presence of mixed-valent Fe2+/Fe3+ in the Fe-Se chains. Magnetic susceptibility measurements reveal strong antiferromagnetic nearest neighbor interactions within the chains with no apparent magnetic ordering down to 2 K. Hidden short-range magnetic ordering below 70 K was found by 57Fe Mössbauer spectroscopy, showing that a fraction of the Fe3+/Fe2+ in the chains are magnetically ordered. Nevertheless, complete magnetic ordering is not achieved even at 6 K. Analysis of XAS spectra demonstrates that the fraction of Fe3+ in the chain increases with decreasing temperature. Computational analysis points out several competing ferrimagnetic ordered models within a single chain. This competition, together with variation in the Fe oxidation state and additional weak intrachain interactions, is hypothesized to prevent long-range magnetic ordering.