Next-nearest Neighbor Research Articles

Counterdiabatic optimized driving in quantum phase sensitive models

State preparation plays a pivotal role in numerous quantum algorithms, including quantum phase estimation. This paper extends and benchmarks counterdiabatic driving protocols across three one-dimensional spin systems characterized by phase transitions: the axial next-nearest neighbor Ising, XXZ, and Haldane–Shastry models. We perform a shallow quantum optimal control over the counterdiabatic protocols by optimizing an energy cost function. Moreover, we provide a code package for computing symbolically various adiabatic gauge potentials. This protocol consistently surpasses standard annealing schedules, often achieving performance improvements of several orders of magnitude. The axial next-nearest neighbor Ising model stands out as a notable example, where fidelities exceeding 0.5 are attainable in most cases. Furthermore, the optimized paths exhibit promising generalization capabilities to higher-dimensional systems, allowing for the extension of parameters from smaller models. Nevertheless, our investigations reveal limitations in the case of the XXZ and Haldane–Shastry models, particularly when transitioning away from the ferromagnetic phase. This suggests that finding optimal diabatic gauge potentials for specific systems remains an important research direction.

Magnetic properties of the frustrated Ising chain

Using the Kramers–Wannier transfer matrix method, we studied several decorated Ising chains. The exact expressions for thermodynamic characteristics, including the ground state characteristics, were obtained. We considered several modeling chains with different signs and absolute values of exchange constants for the nearest- and the next-nearest neighbors. For these models, we calculated the magnetization curves. The critical values of magnetic fields and corresponding magnetization plateau parameters were obtained. Analytic expressions for the ground state entropy were obtained for the chains with different interaction constants. The dependencies of the number of states with minimum energy (the degeneration of the ground state) as the function of the number of particles were found. It was shown that these dependencies are expressed in terms of well-known numerical sequences, namely Lucas numbers and Pell numbers, which, in the limit of a large number of particles, are proportional to the powers of the golden and silver sections. Therefore, the ground state entropy (per particle) of the systems under consideration can be described in terms of these sections and, therefore, is nonzero.

Absence of the impurity-resonance spot at a Bi defect located near the Zn impurity in Bi2Sr2Ca(Cu1-xZnx)2O8+δ

Zn dopants to Cu sites in high-Tc cuprates strongly suppress superconductivity and act as impurities with a strong quasiparticle scattering resonance. Using the scanning tunneling microscope, we investigate the electronic structure in the atomic scale around Zn impurities in Bi2Sr2Ca(Cu1-xZnx)2O8+δ. The intense scattering resonance of the Zn impurity in the CuO2 layer strongly affects the measured local density of states of the BiO layer on the surface. The pattern of the bound state induced by a Zn impurity consists of a central spot at the Bi atom just above the Zn impurity and eight symmetric spots at the next nearest neighboring (NNN) and the third nearest neighboring (3NN) sites of Bi atoms. When the Bi atom above the NNN Cu atom is missing, the corresponding scattering spot is absent simultaneously. Our results indicate that the measured impurity-induced bound state pattern is strongly influenced by Bi atoms on the surface and therefore supports the “filter” theoretical model of the nonlocal interlayer tunneling effect from the CuO2 layer to the BiO layer on the surface. Our research provides extra information about the impurity-induced bound state by Zn impurities.

Atomic-scale environment of niobium in ore minerals as revealed by XANES and EXAFS at the Nb K-edge

Abstract. The mineralogy of niobium (Nb) is characterized by multicomponent oxides such as AB2O6, A2B2O7, ABO4, and ABO3 in which Nb is incorporated in the B site. Such complex crystal-chemistry prevents their unambiguous identification in ore deposits such as hydrothermal rocks and laterites which exhibit complex and fine-grained textures. The understanding of the processes controlling Nb ore deposit formation in various geological settings is therefore limited, although Nb is a critical element. In this study, we use X-ray absorption spectroscopy (XAS) at the Nb K-edge to investigate the local atomic-scale structure around Nb in a large set of natural and synthetic minerals of geological and technological importance. Our X-ray absorption near-edge structure (XANES) data at the Nb K-edge show three major features of variable position and intensity and then can be related to the local distortion and coordination number of the Nb site. Shell-by-shell fits of the extended X-ray absorption fine structure (EXAFS) data reveal that the NbO6 octahedra are distorted in a variety of pyrochlore species. At least two distinct first shells of O atoms are present while reported crystallographic data yield regular octahedra in the same minerals. Next-nearest Nb–Nb distances in pyrochlore and Nb-bearing perovskite mirror a corner-sharing NbO6 network, whereas the two Nb–Nb distances in columbite are typical of edge- and corner-sharing NbO6 octahedra. Such a resolution on the Nb site geometry and the intersite relationships between the next-nearest NbO6 octahedra is made possible by collecting EXAFS data under optimal conditions at 20 K and up to 16 Å−1. The local structure around substituted Nb5+ in Fe3+, Ti4+, and Ce4+ oxides suffers major changes relative to the unsubstituted structures. The substitution of Nb5+ for Ti4+ in anatase leads to the increase in the interatomic distances between Nb and its first and second Ti4+ neighbors. The substitution of Nb5+ for Ce4+ in cerianite reduces the coordination number of the cation from eight to four, and the Nb–O bonds are shortened compared to Ce–O ones. In hematite, Nb5+ occupies a regular site, whereas the Fe3+ site is strongly distorted suggesting major site relaxation due to charge mismatch. The sensitivity of XANES and EXAFS spectroscopies at the Nb K-edge to the local site geometry and next-nearest neighbors demonstrated in this study would help decipher Nb speciation and investigate mineralogical reactions of Nb minerals in deposit-related contexts such as hydrothermal and lateritic deposits.

CoX2Y4: a family of two-dimensional magnets with versatile magnetic order.

Two-dimensional (2D) magnetic materials offer a promising platform for nanoscale spintronics and for exploration of novel physical phenomena. Here, we predict a diverse range of magnetic orders in cobalt-based 2D single septuple layers CoX2Y4, namely, CoBi2Te4, CoBi2Se2Te2, CoBi2Se4, and CoSb2Te4. Notably, CoBi2Te4 presents intrinsic non-collinear antiferromagnetism (AFM), while the others display collinear AFM. The emergence of AFM in all CoX2Y4 materials is attributed to the antiferromagnetic 90° Co-Te(Se)-Co superexchange coupling. The origin of non-collinear/collinear orders lies in competing Heisenberg exchange interactions within the Co triangular lattice. A pivotal factor governing the non-collinear order of CoBi2Te4 is the vanishingly small ratio of exchange coupling between next-nearest neighbour Co and the nearest neighbour Co (J2/J1 ∼ 0.01). Furthermore, our investigation into strain effects on CoX2Y4 lattices demonstrates the tunability of the magnetic state of CoSb2Te4 from collinear to non-collinear. Our prediction of the unique non-collinear AFM in 2D suggests the potential for observing extraordinary magnetic phenomena in 2D, including non-collinear scattering and magnetic domain walls.

Every atom counts: predicting sites of reaction based on chemistry within two bonds

How much chemistry can be described by looking only at each atom, its neighbours and its next-nearest neighbours?

Geometry induced domain-walls of dipole lattices on curved structures

We investigate the ground state (GS) properties of rectangular dipole lattices on curved surfaces. The curved geometry can ‘distort’ the lattice and lead to dipole equilibrium configurations that strongly depend on the local geometry of the surface. We find that the system’s GS can exhibit domain-walls separating domains with different dipole configurations. Furthermore, we show how, regardless of the surface geometry, the domain-walls (DWs) locate along the lattice sites for which the (Euclidean) distances to nearest and next-nearest neighbors are equal. We analyze the response of the DWs to an external electric field and observe displacements and splittings thereof below and above a critical electric field, respectively. We further show that the DW acts as a boundary that traps low-energy excitations within a domain.

Spin-polarized superconducting phase in semiconducting system with next-nearest-neighbor hopping on the honeycomb lattice

The particles in the honeycomb lattice with on-site s-wave pairing exhibit many interesting behaviors, which can be described in the framework of the Hubbard model. Among others, at the half-filling, some critical value |Uc| of pairing interaction U<0 exists that, for U<Uc, the superconducting phase becomes unstable. Introduction of the nonzero hopping t′ between next-nearest-neighbor sites strongly modifies the physical properties of the system. Here, we discuss the behavior of the system for t′≠0 (at the ground state), where the hopping between next-nearest neighbors leads to change of the order of phase transition between superconducting and normal phases from discontinuous to continuous one in the external magnetic field h. We show that this behavior is strongly dependent on t′ and associated with the Dirac cones in the non-interacting band structure of the system. For non-zero magnetic field and for some range of t′, a spin-polarized superconducting phase occurs in the ground state phase diagram (only at the half-filling and for h≠0).

Ising nematic in &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;–&lt;i&gt;J&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt; square-lattice Heisenberg model within self-consistent spin-wave theory

We study the Ising nematic ordering, the Ising nematic phase transition, and the temperature behavior of the short-range order parameters in spin 1/2 quantum Heisenberg model on two-dimensional square-lattice with exchange parameters of nearest and next-nearest neighbors. Two versions of the self-consistent spin-wave theory with and without auxiliary pseudofermions are considered.

Two-dimensional extended Hubbard model: doping, next-nearest neighbor hopping and phase diagrams

Using the strong coupling diagram technique, we investigate the extended Hubbard model on a two-dimensional square lattice. This approach allows for charge and spin fluctuations and a short-range antiferromagnetic order at nonzero temperatures. The model features the first-order phase transition to states with alternating site occupations (SAO) at the intersite repulsion v = v c . In this work, we show that doping decreases v c . For a nonzero next-nearest neighbor hopping , less mobile carriers produce a stronger fall in v c . For half-filling and , we consider phase diagrams for a fixed temperature T, on-site U, and intersite repulsions. The diagrams contain regions of SAO, Mott insulator, and several metallic states distinguished by their densities of states. Two of them are characterized by a dip and a peak at the Fermi level. The dip originates from the Slater mechanism for itinerant electrons, while the peak to bound states of electrons with localized magnetic moments. The existence of these two metallic regions in the phase diagram is a manifestation of the Pomeranchuk effect. The boundary between these regions reveals itself as a kink in the curve v c (T) and as a maximum in the T dependence of the double occupancy D. Our calculated D for different values of v, U, and T are in semiquantitative agreement with Monte Carlo results.

X-ray and molecular dynamics study of the temperature-dependent structure of FLiNaK

The atomic structure of FLiNaK and its evolution with temperature are examined with x-ray scattering and molecular dynamics (MD) simulations in the temperature range 460–636 °C. In accord with previous studies, it’s observed that the average nearest-neighbor (NN) cation-anion coordination number increases with increasing cation size, going from ∼4 for Li-F to ∼6.4 for K-F. In addition, we find that there is a coupled change in local coordination geometry – going from tetrahedral for Li-F to octahedral for Na to very disordered quasi-cuboidal for K. The varying geometry and coordination distances for the cation-anion pairs cause a relatively constant F-F next-nearest neighbor (NNN) distance of approximately 3.1 Å. This relatively fixed distance allows the F anions to assume an overall correlated structure very similar to that of a hard-sphere liquid with an extended radius which is beyond the normal F ion size but reflects the cation-anion coordination requirements. Careful consideration of the evolution of the experimental atomic distribution functions with increasing temperature shows that the changes in correlation at each distance can be understood within the context of broadening asymmetric neighbor distributions. Within the temperature range studied, the evolution of F-F correlations with increasing temperature is consistent with changes expected in a hard-sphere liquid simply due to decreasing density.

Off-stoichiometry and molybdenum substitution effects on elastic moduli of B1-type titanium carbide

B1-type MX ceramics are composed of transition metals (M) and C, N, and/or O (X) occupying the M and X sites, respectively, and having M–X nearest neighbor (NN) bonds and M–M and X–X next nearest neighbor (NNN) bonds. Substitution of the elements and the formation of structural vacancies in B1-type ceramics change the numbers and strengths of the bonds, leading to novel properties. The change in elastic modulus of off-stoichiometric TiC in equilibrium with a Ti–Mo solid solution phase was experimentally investigated based on the rule of mixtures from the Voigt model. The experimentally obtained values agreed well with the results of density functional theory calculations. The bulk modulus (K) of TiC increased from 205.6 to 239.2 GPa as the fraction of Ti sites occupied by Mo increased from 0.11 to 0.33, whereas the Young’s modulus (E) and the shear modulus (G) remained nearly constant. On the other hand, all three elastic moduli decreased with increasing vacancy fraction at the C sites. These results suggest that the M–X bond strength should be the dominant factor in these moduli and the effect of M–M bond on K is greater than that of G and E.

Coexistence of Cationic and Anionic Phosphate Moieties in Solids: Unusual but Not Impossible.

Phosphoric acid is commonly known either as a neutral molecule or as an anion (phosphate). We theoretically confirm by ab initio molecular dynamics simulations (AIMD) that a cationic form H4PO4+ coexists with the anionic form H2PO4- in the same salt. This paradoxical situation is achieved by partial substitution of Cs+ by H4PO4+ in CsH2PO4. Thus, HnPO4 acts simultaneously as both the positive and the negative ion of the salt. We analyze the dynamical protonation pattern within the unusual hydrogen bond network that is established between the ions. Our AIMD simulations show that a conventional assignment of protonation states of the phosphate groups is not meaningful. Instead, a better description of the protonation situation is achieved by an efficiently fractional assignment of the strongly hydrogen-bonded protons to both its nearest and next-nearest oxygen neighbors.

Correlation between Si-Al disorder and hydrogen-bonding distance variation in ussingite (Na2AlSi3O8OH) revealed by one- and two-dimensional multi-nuclear NMR and first-principles calculation

Abstract Ussingite (Na2AlSi3O8OH) is a mineral with a unique interrupted framework structure and strong hydrogen bonding. It contains 4-, 6-, and 8-membered tetrahedral rings resembling feldspars, but, unlike the latter, is partially depolymerized. There are four crystallographically distinct tetrahedral (T) sites, two of which (T1, T2) are Q4 [i.e., having 4 next nearest neighbor (NNN) T sites], and the other two (T3, T4) are Q3 (i.e., having 3 NNN T sites), each with NNN (in brackets) of T1(1T2, 1T3, 2T4), T2(1T1, 2T3, 1T4), T3(1T1, 2T2), and T4(2T1, 1T2). There is one unique OH site in the T4-O8-H···O2-T3 configuration, where O8 and O2 are nonbridging O atoms (NBO). In the ordered structure, T1 is fully occupied by Al, and the other three T sites by Si. Previous X-ray and neutron diffraction and 1H and 29Si NMR studies gave contradictory conclusions regarding Si-Al disorder. In this study, we were able to unambiguously clarify the issue via comprehensive one- and two-dimensional 1H, 29Si, 27Al, and 23Na NMR and first-principles calculation. It was revealed that there is ~3% Si-Al disorder that occurs between neighboring T1-(O)-T2 sites, such that the formation of Al-O-Al linkage and Al(Q3) are avoided. The disorder was found to result in the development of Si(Q3) sites with various NNN, including 3Al and 3Si, and neighboring OH sites having significantly shorter and longer hydrogen-bonding distances than in the ordered structure, with 1H chemical shifts near 15~16 ppm and 11 ppm, in addition to a main peak near 13.9 ppm. Good correlation was found between 1H chemical shift, hydrogen-bonding (O-H, H···O, and O···O) distances, and Si-O distances in the Si-O-H···O-Si linkage. This suggests that Si-Al disorder is correlated with variation in hydrogen-bonding distances via through-bond transmission of bond valence variations. This could be a universal phenomenon also applicable to other hydrous minerals. The revelation of preferential partition of Al in Q4 over Q3 sites to avoid the formation of Al-OH and Al-NBO provides insight into their behavior in other partially depolymerized hydrous aluminosilicate systems, such as glasses and melts.

A simple theory for quantum quenches in the ANNNI model

In a recent numerical study by Haldar et al. [Phys. Rev. X 11, 031062] it was shown that signatures of proximate quantum critical points can be observed at early and intermediate times after certain quantum quenches. Said work focused mainly on the case of the axial next-nearest neighbour Ising (ANNNI) model. Here we construct a simple time-dependent mean-field theory that allows us to obtain a quantitatively accurate description of these quenches at short times, which for reasons we explain remains a fair approximation at late times (with some caveats). Our approach provides a simple framework for understanding the reported numerical results as well as fundamental limitations on detecting quantum critical points through quench dynamics. We moreover explain the origin of the peculiar oscillatory behaviour seen in various observables as arising from the formation of a long-lived bound state.

Gauge-invariant measure of the magnon orbital angular momentum

Unlike the Berry phase, the orbital angular momentum (OAM) of magnons with two-dimensional wave vector $\mathbf{k}$ in band $n$ is not gauge invariant for arbitrary phase ${\ensuremath{\lambda}}_{n}(\mathbf{k})$ and so is not physically observable. However, by integrating the OAM over the orientation $\ensuremath{\phi}$ of wave vector $\mathbf{k}$, we construct a gauge-invariant function ${F}_{n}(k)$. Like ${F}_{n}(k)$, the average OAM for magnon band $n$ in a circle of radius $k$ is also gauge invariant and can be directly observed. We demonstrate these results for a ferromagnet on a honeycomb lattice with Dzyalloshinskii-Moriya interactions between next-nearest neighbor spins. With wave vectors $\mathbf{k}$ restricted to the first Brillouin zone, the angular averaged OAM ${F}_{n}(k)$ then has opposite signs for lower and upper bands $n=1$ and 2 for all $k$.

Simultaneous single-qubit driving of semiconductor spin qubits at the fault-tolerant threshold

Practical Quantum computing hinges on the ability to control large numbers of qubits with high fidelity. Quantum dots define a promising platform due to their compatibility with semiconductor manufacturing. Moreover, high-fidelity operations above 99.9% have been realized with individual qubits, though their performance has been limited to 98.67% when driving two qubits simultaneously. Here we present single-qubit randomized benchmarking in a two-dimensional array of spin qubits, finding native gate fidelities as high as 99.992(1)%. Furthermore, we benchmark single qubit gate performance while simultaneously driving two and four qubits, utilizing a novel benchmarking technique called N-copy randomized benchmarking, designed for simple experimental implementation and accurate simultaneous gate fidelity estimation. We find two- and four-copy randomized benchmarking fidelities of 99.905(8)% and 99.34(4)% respectively, and that next-nearest neighbor pairs are highly robust to cross-talk errors. These characterizations of single-qubit gate quality are crucial for scaling up quantum information technology.

Evaluation of Neel Temperatures from Fully Self-Consistent Broken-Symmetry GW and High-Temperature Expansion: Application to Cubic Transition-Metal Oxides

Using fully self-consistent thermal broken-symmetry GW, we construct effective magnetic Heisenberg Hamiltonians for a series of transition metal oxides (NiO, CoO, FeO, and MnO), capturing a rigorous but condensed description of the magnetic states. Then applying high-temperature expansion, we find the decomposition coefficients for spin susceptibility and specific heat. The radius of convergence of the found series determines the Neel temperature. The NiO, CoO, and FeO contain a small ferromagnetic interaction between the nearest neighbors (NNs) and the dominant antiferromagnetic interaction between the next-nearest neighbors (NNNs). For them, the derived Neel temperatures are in good agreement with experiment. The case of MnO is different because both NN and NNN couplings are antiferromagnetic and comparable in magnitude, for which the error in the estimated Neel temperature is larger, which is a signature of additional effects not captured by electronic structure calculations.

Electro-Elastic Modeling of Multi-Step Transitions in Two Elastically Coupled and Sterically Frustrated 1D Spin Crossover Chains

One-dimensional spin crossover (SCO) solids that convert between the low spin (LS) and the high spin (HS) states are widely studied in the literature due to their diverse thermal and optical characteristics which allow obtaining many original behaviors, such as large thermal hysteresis, incomplete spin transitions, as multi-step spin transitions with self-organized states. In the present work, we investigate the thermal behaviors of a system of two elastically coupled 1D mononuclear chains, using the electro-elastic model, by including an elastic frustration in the nearest neighbors (nn) bond length distances of each chain. The chains are made of SCO sites that are coupled elastically through springs with their nn and next-nearest neighbors. The elastic interchain coupling includes diagonal springs, while the nn inter-chain distance is fixed to that of the high spin state. The model is solved using MC simulations, performed on the spin states and the lattice distortions. When we only frustrate the first chain, we found a strong effect on the thermal dependence of the HS fraction of the second chain, which displays an incomplete spin transition with a significantly lowered transition temperature. In the second step, we frustrate both chains by imposing different frustration rates. Here, we demonstrate that for high frustration values, the thermal dependence of the total HS fraction exhibits multi-step spin transitions. The careful examination of the spin state structures in the plateau regions showed the coexistence of special dimerized ferro–antiferro patterns of type LL-HH-LL-HH along the first chain and HH-LL-HH-LL (H=HS and L=LS) along the second one, revealing that the two chains are antiferro-elastically coupled. This type of spatial modulation of the spin state and bond length distances is very attractive because it anticipates the possible existence of periodic structures in 2D lattices, made of alternate 1D SCO strings with HLHLHL structures, coupled in the ferro-like fashion along the interchain direction.

Extreme sensitivity of the magnetic ground state to halide composition in FeCl3−xBrx

Mixed halide chemistry has recently been utilized to tune the intrinsic magnetic properties of transition-metal halides---one of the largest families of magnetic van der Waals materials. Prior studies have shown that the strength of exchange interactions, hence the critical temperature, can be tuned smoothly with halide composition for a given ground state. Here we show that the ground state itself can be altered by a small change of halide composition in ${\mathrm{FeCl}}_{3\ensuremath{-}x}{\mathrm{Br}}_{x}$. Specifically, we find a threefold jump in the N\'eel temperature and a sign change in the Weiss temperature at $x=0.08$ corresponding to only $3%$ bromine doping. Using neutron scattering, we reveal a change of the ground state from spiral order in ${\mathrm{FeCl}}_{3}$ to $A$-type antiferromagnetic order in ${\mathrm{FeBr}}_{3}$. From first-principles calculations, we show that a delicate balance between nearest and next-nearest neighbor interactions is responsible for such a transition. These results demonstrate how varying the halide composition can tune the competing interactions and change the ground state of a spiral spin liquid system.