Neighbor Hopping Research Articles

Genuine multipartite entanglement in a one-dimensional Bose-Hubbard model with frustrated hopping

Frustration and quantum entanglement are two exotic quantum properties in quantum many-body systems. However, despite several efforts, an exact relation between them remains elusive. In this work, we explore the relationship between frustration and quantum entanglement in a physical model describing strongly correlated ultracold bosonic atoms in optical lattices. In particular, we consider the one-dimensional Bose-Hubbard model comprising both nearest-neighbor ($t_{1}$) and frustrated next-nearest neighbor ($t_{2}$) hoppings and examine how the interplay of onsite interaction ($U$) and hoppings results in different quantum correlations dominating in the ground state of the system. We then analyze the behavior of quantum entanglement in the model. In particular, we compute genuine multipartite entanglement as quantified through the generalized geometric measure and make a comparative study with bipartite entanglement and other relevant order parameters. We observe that genuine multipartite entanglement has a very rich behavior throughout the considered parameter regime and frustration does not necessarily favor generating a high amount of it. Moreover, we show that in the region with strong quantum fluctuations, the particles remain highly delocalized in all momentum modes and share a very low amount of both bipartite and multipartite entanglement. Our work illustrates the necessity to give separate attention to dominating ordering behavior and quantum entanglement in the ground state of strongly correlated systems.

Pairing properties of the t−t′−t″−J model

We study the pairing properties of the two-dimensional $t$-$t'$-$t''$-$J$ model, where $t'$ and $t''$ are second and third neighbor hoppings, at a doping level $x\approx0.1$. Recent studies of the $t$-$t'$-$J$ model find strong pairing for $t'>0$, associated with electron doping, but an absence of pairing for $t'<0$ associated with hole doping. This is in contrast to the cuprates, where the highest transition temperatures appear for hole doping. Model parameterizations for the cuprates estimate a $t''$ comparable to $t'$, which, in principle, might fix this discrepancy. However, we find that it does not; we observe a suppression of pairing for the hole-doped system ($t'0$) while for the electron-doped system ($t'>0, t''<0$) $d$-wave pairing is robust. Extended hoppings appear to be insufficient to make the one-band $t$-$t'$-$J$ model capable of describing the pairing in the hole doped system.

Flat band based multifractality in the all-band-flat diamond chain

We study the effect of quasiperiodic Aubry-Andr\'e disorder on the energy spectrum and eigenstates of a one-dimensional all-bands-flat (ABF) diamond chain. The ABF diamond chain possesses three dispersionless flat bands with all the eigenstates compactly localized on two unit cells in the zero disorder limit. The fate of the compact localized states in the presence of the disorder depends on the symmetry of the applied potential. We consider two cases here: a symmetric one, where the same disorder is applied to the top and bottom sites of a unit cell and an antisymmetric one, where the disorder applied to the top and bottom sites are of equal magnitude but with opposite signs. Remarkably, the symmetrically perturbed lattice preserves compact localization, although the degeneracy is lifted. When the lattice is perturbed antisymmetrically, not only is the degeneracy is lifted but compact localization is also destroyed. Fascinatingly, all eigenstates exhibit a multifractal nature below a critical strength of the applied potential. A central band of eigenstates continue to display an extended yet non-ergodic behaviour for arbitrarily large strengths of the potential. All other eigenstates exhibit the familiar Anderson localization above the critical potential strength. We show how the antisymmetric disordered model can be mapped to a $\frac{\pi}{4}$ rotated square lattice with nearest and selective next-nearest neighbour hopping and a staggered magnetic field - such models have been shown to exhibit multifractality. Surprisingly, the antisymmetric disorder (with an even number of unit cells) preserves chiral symmetry - we show this by explicitly writing down the chiral operator.

The Hubbard model: exact constraints on spectral moments in the strong coupling limit

ABSTRACT Exact spectral moment relations are derived and presented for the low temperature, strong coupling limit of the Hubbard model, for any dimension, lattice structure and electron density. These results generate an exact, rigorous and quantitative test for proposed solutions to the Hubbard model that claim to be valid in the strong coupling, low temperature region. The test complements analyses for weak coupling and high temperatures, offering insights into the essential physics of the model, specifically the quasiparticle energy (centroid) and lifetime (width) of the spectral weight function in the infinite coupling, finite hopping limit. Numerical results are given for nearest neighbour hopping in 1, 2 and 3D.

Modification of Optical, Electronic and Microstructural Properties of PET by 150 keV Cs+ Irradiation

Thick (0.125 mm) sheet samples of PET were irradiated with 150 keV Cs+ ion beam with fluences in the range from 10^13 cm^-2 up to 10^16 cm^-2). Raman and UV-VIS spectroscopy measurements shown destruction of numerous bonds within the polymer – this effect intensifies with fluence. Raman spectroscopy shows the presence of amorphous graphitelike structures as the broad G band appears in the collected spectrum. The analysis of absorbance spectra also confirms formation of numerous carbon clusters leading to a formation of vast conducting structures in the modified layer of the polymer. One can observe the decrease of optical bandgap from 3.85 eV (typical for pristine PET) to 1.05 eV for the sample implanted with the highest fluence, the effect is weaker than for lighter alkali metal ions. The estimated average number of C atom in a clusters reaches in such case values close to 1100. The changes in the polymer structure lead to intense reduction of electrical sheet resistivity of the modified samples by ~ 8 orders of magnitude in the case of severely modified sample. The dependence of resistivity on temperature has also been measured. The plots of ln(σ) vs 1/T show that band conductivity or nearest neighbor hopping between conducting structures prevail in the considered case

Ab initio guided minimal model for the “Kitaev” material BaCo2 ( AsO4)2 : Importance of direct hopping, third-neighbor exchange, and quantum fluctuations

By considering two {\it ab initio}-based complementary approaches, we analyze the electronic structure and extract effective spin models of BaCo$_2$(AsO$_4$)$_2$, a honeycomb material which has been proposed as a candidate for Kitaev physics. Both methods show that the dominant direct hopping makes the bond-dependent Kitaev term negligible averting the material away from the sought-after spin-liquid regime. As a result, we present a simple three-parameter exchange model to describe the interactions of the lowest doublet of the honeycomb cobaltate BaCo$_2$(AsO$_4$)$_2$. Remarkably, it is the third-neighbor interactions, both isotropic and anisotropic, that are responsible for the standout double-zigzag ground state of BaCo$_2$(AsO$_4$)$_2$, stabilized by quantum fluctuations. A significantly large third-nearest neighbor hopping, observed in {\it ab initio}, supports the importance of the third-neighbor interactions in the stabilization of the unique ground state of BaCo$_2$(AsO$_4$)$_2$.

Locating Hop Sets in a Graph

Let G be a connected graph with vertex set V (G) and edge set E(G). The open hop neighborhood of vertex v ∈ V (G) is the set NG(v, 2) = {w ∈ V (G) : dG(v, w) = 2}, where dG(v, w) denotes the distance between v and w. A non-empty set S ⊆ V (G) is a locating hop set of G if NG(u, 2) ∩ S ̸= NG(v, 2) ∩ S for every pair of distinct vertices u, v ∈ V (G) \ S. The smallest cardinality of a locating hop set of G, denoted by lhn(G) is called the locating hop number of G. This study focuses mainly on the concept of locating hop set in graphs. Characterizations of locating hop sets in the join and corona of two graphs are given and bounds for the corresponding locating hop numbers of these graphs are determined.

Grundy Hop Domination in Graphs

Let G be an undirected graph with vertex and edge sets V (G) and E(G), respectively. Let S = (v1, v2, · · · , vk) be a sequence of distinct vertices of G and let Sˆ = {v1, v2, . . . , vk}. Then S is a legal closed hop neighborhood sequence of G if N2 G[vi]\∪i−1j=1N 2 G[vj ] ̸= ∅ for each i ∈ {2, · · · , k}. If, in addition, Sˆ is a hop dominating set of G, then S is called a Grundy hop dominating sequence.The maximum length of a Grundy hop dominating sequence in a graph G, denoted by γ hgr(G), is called the Grundy hop domination number of G. In this paper, we determine some (extreme) values for the Grundy hop domination number. It is pointed out that the Grundy hop domination number is at least equal to the hop domination. Bounds for the Grundy hop domination numbersof some graphs resulting from some binary operations of two graphs are also obtained.

D2CRP: A Novel Distributed 2-Hop Cluster Routing Protocol for Wireless Sensor Networks

Typically, wireless sensor networks (WSNs) use limited-capacity batteries that cannot be recharged or replaced. In general, designing an energy-efficient routing protocol has a significant impact on prolonging the network lifetime. In this article, a novel distributed 2-hop cluster-routing protocol (D2CRP) is introduced to achieve energy efficiency in WSNs. In the cluster formation phase, each node obtains the information of its neighbor nodes within the 2-hop range to form the 2-hop cluster in a fully distributed manner. The transmission distance and residual energy are jointly considered to determine the energy-efficient cluster head (CH) in each 2-hop cluster. After the CH is generated, each member node can transmit packets to its 1-hop neighbor or the CH directly. To reduce the overall transmission distance for intercluster communication, multiple chains can be formed among CHs via their adjacent CHs that are closer to the base station (BS). As a result, energy-efficient intracluster and intercluster routing can be achieved for packet transmission. In addition, the optimal cluster number of 2-hop clustering is formulated and derived to minimize the energy consumption for both intracluster and intercluster communications. Simulation results show that the optimal cluster number of D2CRP can be achieved and D2CRP is effectively improved on the performances of network lifetime, energy consumption, and packet transmission than the other four state-of-the-art competitive routing protocols, including low-energy adaptive clustering hierarchy (LEACH), R-LEACH, power-efficient gathering in sensor information system (PEGASIS), and two-tier distributed fuzzy logic-based protocol (TTDFP).

Floquet topological properties in the non-Hermitian long-range system with complex hopping amplitudes

Non-equilibrium phases of matter have attracted much attention in recent years, among which the Floquet phase is a hot point. In this work, based on the periodic driving non-Hermitian model, we reveal that the winding number calculated in the framework of the Bloch band theory has a direct connection with the number of edge states even though the non-Hermiticity is present. Further, we find that the change of the phase of the hopping amplitude can induce the topological phase transitions. Precisely speaking, the increase in the value of the phase can bring the system into a topological phase with a large topological number. Moreover, it can be unveiled that the introduction of the purely imaginary hopping term brings an extremely rich phase diagram. In addition, we can select the even topological invariant exactly from the unlimited winding numbers if we only consider the next-nearest neighbor hopping term. Here, the results obtained may be useful for understanding the periodic driving non-Hermitian theory.

IoT-Enabled Energy-efficient Multipath Power Control for Underwater Sensor Networks

Aims &amp; Background: Energy saving or accurate information transmission within resource limits were major challenges for IoT Underwater Sensing Networks (IoT-UWSNs) on the Internet. Conventional transfer methods increase the cost of communications, leading to bottlenecks or compromising the reliability of information supply. Several routing techniques were suggested using UWSN to ensure uniform transmission of information or reduce communication latency while preserving a data battery (to avoid an empty hole in the network). Objectives &amp; Methodology: In this article, adaptable power networking methods based on the Fastest Route Fist (FRF) method and a smaller amount of the business unit method are presented to solve the problems mentioned above. Both Back Laminated Inter Energy Management One (FLMPC-One) networking method, that employs 2-hop neighborhood knowledge, with the Laminated Inter Energy Management Two (FLMPC-Two) networking procedure, which employs 3-hop neighborhood data, were combined to create such innovative technologies (to shortest path selection). Variable Session Portion (SP) and Information Speed (IS) were also considered to ensure that the suggested method is flexible. Results &amp; Conclusions: These findings show that the suggested methods, Shortest Path First without 3-hop Relatives Data (SPF-Three) or Broadness Initial Searching for Shortest Route. Breadth First Search to 3-hop Relatives Data (BFS-Three) was successfully developed (BFS-SPF-Three). These suggested methods are successful in respect of minimal Electric Cost (EC) and Reduced Transmission Drop Rates (RTDR) given a small number of operational sites at a reasonable latency, according to the simulated findings.

Topological phases of a semi-Dirac Chern insulator in the presence of extended range hopping

We study topological properties and the topological phase transitions therein for a semi-Dirac Haldane model on a honeycomb lattice in presence of an extended range (third neighbour) hopping. While in the absence of a third neighbour hopping, $t_3$, the system exhibits gapless electronic spectrum, its presence creates an energy gap in the dispersion. However, the nature of the spectral gap, that is, whether it is trivial or topological needs to be ascertained. We find that the answer depends on the value of $t_3$, and its interplay with the value of the onsite potential that breaks the sublattice symmetry, namely, Semenoff mass ($\Delta$). To elucidate our findings on the topological phases, we demonstrate two kinds of phase diagrams using the available parameter space, one in which the phases are shown in the $\Delta$-$t_3$ plane, and the other one in a more familiar $\Delta$-$\phi$ plane ($\phi$ being the Haldane flux). The phase diagrams depict the presence of Chern insulating lobes comprising of Chern numbers $\pm2$ and $\pm1$ for certain values of $t_3$, along with trivial insulating regions (zero Chern number). Thus there are phase transitions from one topological regime to another which are characterized by abrupt changes in the values of the Chern number. To support the existence of the topological phases, we compute the counter-propagating chiral edge modes in a ribbon geometry. Finally, the anomalous Hall conductivity shows plateaus either at $e^2/h$ or $2e^2/h$ corresponding to these topological phases.

Peer-to-Peer Variational Federated Learning Over Arbitrary Graphs

This paper proposes a federated supervised learning framework over a general peer-to-peer network with agents that act in a variational Bayesian fashion. The proposed framework consists of local agents where each of which keeps a local “posterior probability distribution” over the parameters of a global model; the updating of the posterior over time happens in a local fashion according to two subroutines of: 1) variational model training given (a batch of) local labeled data, and 2) asynchronous communication and model aggregation with the 1-hop neighbors. Inspired by the popular federated learning (model averaging), the framework allows the training data to remain distributed on mobile devices while utilizing a peer-to-peer model aggregation in a social network. The proposed framework is shown to allow for a systematic treatment of model aggregation over any arbitrary connected graph with consistent (in general, non-iid) local labeled data. Specifically, under mild technical conditions, the proposed algorithm allows agents with local data to learn a shared model explaining the global training data in a decentralized fashion over an arbitrary peering/connectivity graph. Furthermore, the rate of convergence is characterized and shown to be a function of each individual agent’s data quality weighted by its eigenvector centrality. Empirically, the proposed methodology is shown to work well with efficient variation Bayesian inference techniques to train Bayesian neural networks in a decentralized manner even when the local data batches are not identically distributed.

Thermally driven p–n–p multiple heteromorphic transformation facilitating high Seebeck coefficient for Ca0.8La0.2CeNbWO8+δ

Given that different types of carriers tend to gather at the cold end to offset part of the induced voltage, the high Seebeck coefficient obtained by a single type of carrier brings voltage difference to the automatic sensor. Nevertheless, due to the significant charge compensation effect, the effective mass and average energy of carriers can be improved, and a record high Seebeck coefficient (S &amp;gt; 10 mV K−1) is excavated through heteromorphic transformation. Herein, by introducing Ce4+/Ce3+ redox pairs into the p-type doped scheelite CaCeNbWO8 with excellent structural/thermal stability, we can realize various types of p–n–p conversion under thermal driving, and each transformation ushers in a sharp increase in the Seebeck coefficient and conductivity simultaneously. The heteromorphic transition activates solid solution diffusion, promotes transition from variable range hopping transport to nearest neighbor hopping transport, and induces energy-level degeneracy. In the process of p–n transition, the carrier mobility increases sharply and the Seebeck coefficient is ∼5.75 mV K−1 and the conductivity is ∼0.06 S m−1 at 881 K, while metallization occurs during n–p transition accompanying a surge in carrier concentration, resulting in a maximum Seebeck coefficient of ∼17.35 mV K−1 and a conductivity of ∼0.08 S m−1 at 1068 K. The important role of multiple heteromorphic transformation in improving the Seebeck coefficient is revealed, which is expected to be used in low-cost, low pollution, and low-power thermoelectric devices.

Spin-polarized Majorana zero modes in double zigzag honeycomb nanoribbons

We study the emergence of Majorana zero modes (MZMs) at the ends of a finite double zigzag honeycomb nanoribbon (zHNR). We show that a double zHNR geometry can host spin-polarized MZMs at its ends. We considered a minimal model composed by first nearest neighbor hopping, Rashba spin-orbit coupling (RSOC), p-wave superconducting pairing, and an applied external magnetic field (EMF). The energy spectrum regions with either spin up or down MZMs belong to distinct topological phase transitions characterized by their corresponding winding numbers and can be accessed by tunning the chemical potential of the nanoribbons. Hybrid systems constituted by zHNRs deposited on conventional s-wave superconductors are potential candidates for experimentally realizing the proposal. The spin's discrimination of MZMs suggests a possible route for performing topological-conventional qubit operations using Majorana spintronics.

Topological phases and entanglement in real space for 1D SSH topological insulator: effects of first and second neighbor-hoppings

The hybrid atoms-cell site entanglement in a one-dimensional Su-Schrieffer-Heeger (SSH) topological insulator with first and second neighbor hopping in space representation of finite chains is analyzed. The geometrical phase is calculated by the Resta electric polarization and the entanglement in the atomic basis by the Schmidt number. A relation between entanglement and the topological phase transitions (TPT) is given since the Schmidt number has local critical points of maximal entangled (ME) states in the singularities of the geometrical phase. States with second neighbors have higher entanglement than first-neighbors hopping. The general conditions to produce ME hybrid Bell states and the localization-entanglement relation are given.

Queue Length and Mobility aware Routing Protocol for Mobile Ad hoc Network

A mobile ad-hoc network (MANET) is different from other wireless networks in many ways. One of the key differences is that a MANET is a multihop wireless network,i.e., a routing path is composed of intermediate mobile nodes and wireless links connecting them. In this paper, heterogeneous Mobile Ad-hoc Networks (H-MANETs) are considered. H-MANETs are composed of nodes with different transmission range. We propose an improvement of AODV protocol called AMAODV (Adaptative Mobility aware AODV). This protocol is based on new metric combine more routing metrics (distance, relative velocity, queue length and hop count) between each node and one hop neighbor. Which permits to avoid losing route. Through the simulation, it is confirmed that this improvement has higher packet delivery ratio and less average end-to-end delay than basic AODV protocol.

Link Quality and MAC-Overhead aware Predictive Preemptive Multipath Routing Protocol for Mobile Ad hoc Networks

In Ad Hoc networks, route failure may occur due to less received power, mobility, congestion and node failures. Many approaches have been proposed in literature to solve this problem, where a node predicts pre-emptively the route failure that occurs with the less received power. However, these approaches encounter some difficulties, especially in scenario without mobility where route failures may arise. In this paper, we propose an improvement of AOMDV protocol called LO-PPAOMDV (Link Quality and MAC-Overhead aware Predictive Preemptive AOMDV). This protocol is based on new metric combine two routing metrics (Link Quality, MAC Overhead) between each node and one hop neighbor. Also we propose a cross-layer networking mechanism to distinguish between both situations, failures due to congestion or mobility, and consequently avoiding unnecessary route repair process. The LO-PPAOMDV was implemented using NS-2. The simulation results demonstrate the merits of our proposed LO-PPAOMDV with approximately 10-15% increase in the packet delivery ratio while average end-to-end delay is reduced by 20%, and normalized routing load is reduced about 45%, also with 7% increase in the throughput, when compared with PPAOMDV.

Variable range hopping conduction mechanisms in reduced rutile TiO2

In this study, obtained samples via reducing Rutile TiO2 by Mg are analyzed to determine the titanium suboxide phases and the dominant structural phase in each sample. By increasing the heat treatment temperature or the amount of reducing agent (Mg), the amount of suboxide phases Ti n O2n−1 (1 ≤ n < 10) with the lower n values increases, and TiO is the main phase in the samples with a low electrical resistivity. The hopping conduction mechanism is also investigated in the temperature range of 11.5–300 K, and the characteristic parameters describing the conduction mechanism are determined and discussed. For samples with a low electrical resistivity, the nearest neighbor hopping (NNH) conduction mechanism governs the charge transport properties below 220 K, and a transition from the NNH to the Mott-variable range hopping (VRH) conduction regimes is observed at ∼65 K. In addition, the Efros-Shklovskii (ES)-VRH conduction process governs at low temperatures below 18 K, and the last crossover from the Mott-VRH to the ES-VRH models illustrates the strong electron-electron Coulomb interaction, which leads to the Coulomb gap (∼1 meV) at low temperatures. According to the obtained hopping parameters, the low resistivity samples are close to the metal-insulator transition. For samples with a high electrical resistivity, the hopping conduction relations are not fitted to the resistivity-temperature curves, and probably it is related to the resistive switching behavior of the material, which changes the nature and conductivity properties, and is depicted in the current-voltage (I-V) curve.

Modulated structure and hopping transport mechanism involving a defect-induced localization–delocalization transition in a Ca–Ce(La)–Nb–W–O system

CaCeNbWO8-δ (CCNWO) oxide is a three-dimensional semiconductor with potential applications in electronic devices. It has been reported that the temperature dependence of the resistivity of CCNWO deviates from that predicted by the Arrhenius equation over a wide temperature range. However, its complex hopping transport mechanism has remained unclear due to unknown defect structures. A combination of transmission electron microscopy and the density functional theory showed that CaCeNbWO8-δ and CaCe0.5La0.5NbWO8-δ have a modulated defect structure, and the carriers mainly undergo a Nb4d→W5d transition. At low temperatures, anisotropic defects promote the diversification of transport properties, variable-range hopping, and nearest neighbor hopping. With increasing temperature, isotropic defects promote simplification of the transport property. Compared with CCNWO, CaCe0.5La0.5NbWO8-δ, with a more stable structure, has stronger electron–electron interactions and shifts the localization–delocalization transition point to a higher temperature. The proposed hopping transport mechanism involving a defect-induced localization–delocalization transition allows semiconductor design and device integration schemes, thus impacting a variety of applications.