Next-nearest Neighbor Coupling Research Articles

Unconventional edge states in a two-leg ladder

Some popular mechanisms for restricting the diffusion of waves include introducing disorder (to provoke Anderson localization) and engineering topologically non-trivial phases (to allow for topological edge states to form). However, other methods for inducing somewhat localized states in elementary lattice models have been historically much less studied. Here we show how edge states can emerge within a simple two-leg ladder of coupled harmonic oscillators, where it is important to include interactions beyond those at the nearest neighbor range. Remarkably, depending upon the interplay between the coupling strength along the rungs of the ladder and the next-nearest neighbor coupling strength along one side of the ladder, edge states can indeed appear at particular energies. In a wonderful manifestation of a type of bulk-edge correspondence, these edge state energies correspond to the quantum number for which additional stationary points appear in the continuum bandstructure of the equivalent problem studied with periodic boundary conditions. Our theoretical results are relevant to a swathe of classical or quantum lattice model simulators, such that the proposed edge states may be useful for applications including waveguiding in metamaterials and quantum transport.

Multiple phase transitions and anomalous non-Hermitian skin effect

Non-Hermiticity is revolutionizing the common understanding in the Hermitian scope by interfacing with topological physics. A single non-Hermitian band can host nontrivial topology that is defined over the nonzero windings of the system's eigenvalues, but not the eigenvectors, as opposed to the Hermitian topological systems. This unique non-Hermitian band topology is responsible for the intriguing non-Hermitian skin effect. Here, we show that the band topology of non-Hermitian one-band models can experience multiple phase transitions. Each transition is identified by a change of the eigenvalue winding. Such an interesting phenomenon is enabled by strategically manipulating the long-range couplings. Associated with the multiple phase transitions, the non-Hermitian skin effect exhibits anomalous behaviors, i.e., in different phases, the skin modes take on different forms of wave localizations. At the transition points, the skin modes evolve into Bloch-wavelike extended states, as if the Hermiticity is restored. For demonstration, we consider a modified Hatano-Nelson model with nonreciprocal next-nearest neighbor couplings. Therein, two phase transitions are identified, corresponding to a stationary and a dynamic one (with respect to the reciprocal nearest-neighbor coupling). Exact analytical derivations are performed to analyze the phase transitions and the associated anomalous non-Hermitian skin effect, which show consistency with the numerical results based on the generalized Brillouin zone method. Our work reveals rich non-Hermitian topological physics in one-band systems, which are considered to be topologically trivial in Hermitian systems. By further showing the anomalous non-Hermitian skin effect, intriguing wave manipulations may inspire experiments in classical realms such as photonics and phononics where versatile non-Hermitian controls are feasible.

Type-II corner modes in topolectrical circuits

We study the rich properties of a topolectrical (TE) circuit array consisting of lossless basic electrical components, such as capacitors and inductors, which can be designed to exhibit higher-order topological phases (HOTP). The HOTP of the circuit exhibits the characteristics of higher-order topology, i.e., unconventional bulk-boundary correspondence with strongly localized corner modes, and higher winding numbers. More interestingly, a type-II corner mode emerges in the presence of long-range interaction, which is realized in the TE circuit by the introduction of next-nearest neighbor (NNN) coupling capacitances. Unlike the usual (i.e., ``type-I'') corner modes that are localized at a particular sublattice node due to the chiral symmetry, the type-II corner modes possess a spatial extent with an exponential decay length. We analytically derive this decay length as a function of the circuit parameters. The NNN coupling is also associated with the tilt parameter in the admittance spectrum of the circuit. The admittance spectrum is reminiscent of that of Dirac fermions. Changing the tilt parameter can lead to a transition from the type-I to the overtilted type-II Dirac dispersion. This overtilting results in a hybridization of the bulk and corner modes in which the distinct corner modes disappear. Furthermore, the type-I and type-II corner modes can be distinguished by their impedance readout. By virtue of their flexibility, the TE circuits provide an ideal platform to demonstrate unusual features of HOTPs arising from long-range interactions, and to engineer different types of robust topological corner modes.

From (S = 1) Spin Hexamer to Spin Tetradecamer by CuO Interstitials in A2Cu3O(CuO)x(SO4)3 (A = alkali).

(Na,K)2Cu3O(SO4)3 compounds form structural chains of Cu6 hexameric units with nominal S = 1 spins due to the interplay between inner strong antiferromagnetic and ferromagnetic exchanges. We show here that the lattice relaxation after the replacement of alkali by larger Rb and Cs ones is accompanied by the insertion of neutral CuO species into (Rb,Cs)2Cu3O(CuO)x(SO4)3 phases. Structurally, interstitial CuO links the next two Cu6 units in longer Cu14 tetradecameric ones. For A = Cs (x = 0.5), the cationic ordering is perfect inside a double-cell superstructure. Magnetically, the original Cu14 units consist of frustrated fragments of an S = 1/2 spin ladder, with ferromagnetic rung-like but antiferromagnetic leg-like and next-nearest neighbor couplings. It returns S = 1 Cu14 spin clusters, effective around 100 K. Our density functional theory calculations and susceptibility fits also show that at low temperatures they interact in two-dimensional lattices, despite the existence of short inter-Cu-Cu distances between the next two clusters along pseudo-one-dimensional chains.

Accurate Truncations of Chain Mapping Models for Open Quantum Systems.

The dynamics of open quantum systems are of great interest in many research fields, such as for the interaction of a quantum emitter with the electromagnetic modes of a nanophotonic structure. A powerful approach for treating such setups in the non-Markovian limit is given by the chain mapping where an arbitrary environment can be transformed to a chain of modes with only nearest-neighbor coupling. However, when long propagation times are desired, the required long chain lengths limit the utility of this approach. We study various approaches for truncating the chains at manageable lengths while still preserving an accurate description of the dynamics. We achieve this by introducing losses to the chain modes in such a way that the effective environment acting on the system remains unchanged, using a number of different strategies. Furthermore, we demonstrate that extending the chain mapping to allow next-nearest neighbor coupling permits the reproduction of an arbitrary environment, and adding longer-range interactions does not further increase the effective number of degrees of freedom in the environment.

Exact solution of a quantum spin chain with competing bulk and boundary terms

We obtain the exact solution of an anisotropic quantum spin chain including nearest neighbor (NN), next nearest neighbor (NNN), chiral three-spin interactions and non-diagonal boundary terms. Because the NNN couplings are involved, we find that the off-diagonal boundary reflections can not only induce the anisotropic Dzyloshinsky–Moriya interactions at boundaries but also enhance the anisotropy of first and last bonds. These properties are absent if only the NN spin-exchanging interactions are considered. Due to that the U(1) symmetry is broken, we analytically solve the system by using the off-diagonal Bethe ansatz. The inhomogeneous T − Q relation, energy spectrum and associated Bethe ansatz equations are given explicitly. This paper provides an universal scheme to construct new integrable models with certain interesting interactions.

Realizing topological corner states in two-dimensional Su-Schrieffer-Heeger model with next-nearest neighbor couplings

In the present work, we consider a two-dimensional Su-Schrieffer-Heeger model with alternating positive tunneling couplings between the neighboring sites. We show that introducing next-nearest neighbor couplings results in the emergence of topological corner states for some values of the corresponding tunneling coupling. Our work resolves the contradiction that arose when such corner states absent in the original two-dimensional Su-Schrieffer-Heeger model were observed experimentally in its photonic realization based on the array of cylindrical microwave resonators.

Optical Control of Couplings in Polariton Condensate Lattices.

We demonstrate deterministic control of the nearest and next-nearest neighbor coupling in the unit cell of a square lattice of microcavity exciton-polariton condensates. We tune the coupling in a continuous and reversible manner by optically imprinting potential barriers of variable height, in the form of spatially localized incoherent exciton reservoirs that modify the particle flow between condensates. By controlling the couplings in a 2×2 polariton cluster, we realize ferromagnetic, antiferromagnetic, and paired ferromagnetic phases and demonstrate the potential scalability of the system.

Photonic Anomalous Quantum Hall Effect.

We experimentally realize a photonic analogue of the anomalous quantum Hall insulator using a two-dimensional (2D) array of coupled ring resonators. Similar to the Haldane model, our 2D array is translation invariant, has a zero net gauge flux threading the lattice, and exploits next-nearest neighbor couplings to achieve a topologically nontrivial band gap. Using direct imaging and on-chip transmission measurements, we show that the band gap hosts topologically robust edge states. We demonstrate a topological phase transition to a conventional insulator by frequency detuning the ring resonators and thereby breaking the inversion symmetry of the lattice. Furthermore, the clockwise or the counterclockwise circulation of photons in the ring resonators constitutes a pseudospin degree of freedom. The two pseudospins acquire opposite hopping phases, and their respective edge states propagate in opposite directions. These results are promising for the development of robust reconfigurable integrated nanophotonic devices for applications in classical and quantum information processing.

Temperature-dependent interplay of anisotropic exchange coupling and external fields on metamagnetoelectric multiferroics

We show an analytical study of the magnetoelectric properties of a quasi-two-dimensional multiferroic rare-earth-metal (R) Mn perovskites, RMnO3 spin system with anisotropic exchange interactions. A mechanism to express the nearest neighbor and the next-nearest neighbor couplings as well as the Dzyaloshinskii-Moriya parameter which is defined as the cross-coupling in the plane, in terms of the anisotropic exchange parameter γ is proposed for spiral spin structures. A set of inter-induced metamagnetic and metaelectric transitions is recorded at low temperature with a spin gap, giving rise to a demagnetization field range. A net nonzero polarization is found in spite of this spin gap. This intriguing survival of the ferroelectric order when the ferromagnetism has dropped allows the ferroic order separation in such a magnetoelectric system. The metamagnetoelectric property which arises from the interdependence of the metamagnetism and the metaelectricity in the model is emphasized from TbMnO3, DyMnO3 to YMnO3 (which correspond to an increase in the anisotropic exchange parameter) through the magnetoelectric coupling. The magnetoelectric coupling is shown particularly related to the transition process and then vanishes when saturation occurs. Then, for the spin gap region as expected, as well as for the coercive field values, there is no magnetoelectric coupling at low temperature. This symmetry breaks with the increase of temperature where the magnetoelectric coupling is weakly dependent on the anisotropic exchange parameter and remains at the coercive values of the fields.

Phase Transition in 2D Anisotropic Ising Model with Next-Nearest Neighbor Interactions in a Magnetic Field

The critical behavior at the phase transition of the ferromagnetic two-dimensional anisotropic Ising model with next-nearest neighbor (NNN) couplings in the presence of the field is determined using mainly Monte Carlo (MC) method. This method is used to investigate the phase diagram of the model and to verify the existence of a divergence at null temperature which often appears in two-dimensional systems. We analyze also the influence of the report of the NNN interactions [Formula: see text] and the magnetic field [Formula: see text] on the critical temperature of the system, and we show that the critical temperature depends on the magnetic field for positive values of the interaction. Finally, we have investigated other thermodynamical qualities such as the magnetic susceptibility [Formula: see text]. It has been shown that their thermal behavior depends qualitatively and quantitatively on the strength of NNN interactions and the magnetic field.

Rigorous decoupling between edge states in frustrated spin chains and ladders

We investigate the occurrence of exact zero modes in one-dimensional quantum magnets of finite length that possess edge states. Building on conclusions first reached in the context of the spin-1/2 XY chain in a field, then for the spin-1 $J_1-J_2$ Heisenberg model, we show that the development of incommensurate correlations in the bulk invariably leads to oscillations in the sign of the coupling between edge states, hence to exact zero energy modes at the crossing points where the coupling between the edge states rigorously vanishes. This is true regardless of the origin of the frustration (e.g. next-nearest neighbor coupling or biquadratic coupling for the spin-1 chain), of the value of the bulk spin (we report on spin-1/2, spin-1 and spin-2 examples), and of the value of the edge-state emergent spin (spin-1/2 or spin-1).

Magnetism and superconductivity in the layered hexagonal transition metal pnictides

We investigate the electronic and magnetic structures of the 122 (AM$_2$B$_2$) hexagonal transition-metal pnictides with A=(Sr, Ca), M=(Cr, Mn, Fe, Co, Ni) and B=(As, P, Sb). It is found that the family of materials share critical similarities with those of tetragonal structures that include the famous iron-based high temperature superconductors. In both families, the next nearest neighbor(NNN) effective antiferromagnetic(AFM) exchange couplings reach the maximum value in the iron-based materials. While the NNN couplings in the latter are known to be responsible for the C-type AFM state and to result in the extended s-wave superconducting state upon doping, they cause the former to be extremely frustrated magnetic systems and can lead to an time reversal symmetry broken $d+id$ superconducting state upon doping. The iron-based compounds with the hexagonal structure, thus if synthesized, can help us to determine the origin of high temperature superconductivity.

Continuum of compensation points in the mixed spin Ising ferrimagnet with four-spin interaction and next-nearest neighbor coupling

ABSTRACTWe investigate the magnetic properties of the mixed spin-1/2 and spin-1 Ising ferrimagnetic system with four-spin interaction J4 and next-nearest neighbor (NNN) coupling J′. We perform exact ground-state calculations and use the finite cluster approximation, based on a single cluster theory, to derive the state equations for the two-dimensional square lattice. The main attention has been paid to the study of the phase diagram for both the transition and compensation temperatures. We find a number of characteristic behaviors. The model with only NNNs induces one compensation point while the four-spin interaction does not. The investigation of the model with both interactions shows a number of characteristic behaviors. In particular, the presence of the four-spin interaction, according to J4 and J′, may lead to one, two or possibly a continuum of compensation points. This phenomenon may have important applications in technology such as thermomagnetic writing and erasing at the compensation point.

Competing magnetic orders and spin liquids in two- and three-dimensional kagome systems: Pseudofermion functional renormalization group perspective

Quantum magnets on kagome lattice geometries in two and three spatial dimensions are archetypal examples of spin systems in which geometric frustration inhibits conventional magnetic ordering and instead benefits the emergence of long-range entangled spin liquids at low temperature. Here we employ a recently developed pseudo-fermion functional renormalization group (pf-FRG) approach to study the low-temperature quantum magnetism of kagome and hyperkagome spin systems with exchange interactions beyond the nearest neighbor coupling. We find that next-nearest neighbor couplings stabilize a variety of magnetic orders as well as induce additional spin liquid regimes giving rise to rather rich phase diagrams, which we characterize in detail. On a technical level, we find that the pf-FRG approach is in excellent quantitative agreement with high-temperature series expansions over their range of validity and it exhibits a systematic finite-size convergence in the temperature regime below. We discuss notable advantages and some current limitations of the pf-FRG approach in the ongoing search for unconventional forms of quantum magnetism.

Spontaneous dimerization, critical lines, and short-range correlations in a frustrated spin-1 chain

We report on a detailed investigation of the spin-1 $J_1-J_2-J_3$ Heisenberg model, a frustrated model with nearest-neighbor coupling $J_1$, next-nearest neighbor coupling $J_2$, and a three site interaction $J_3\left[({\bf S}_{i-1}\cdot {\bf S}_i)({\bf S}_i\cdot {\bf S}_{i+1})+{\mathrm H.c.}\right]$ previously studied in [Phys. Rev. B 93, 241108(R) (2016)]. Using DMRG and exact diagonalizations, we show that the phase boundaries between the Haldane phase, the next-nearest neighbor Haldane phase and the dimerized phase can be very accurately determined by combining the information deduced from the dimerization, the ground-state energy, the entanglement spectrum and the Berry phase. By a careful investigation of the finite-size spectrum, we also show that the transition between the next-nearest neighbor Haldane phase and the dimerized phase is in the Ising universality class all along the critical line. Furthermore, we justify the conformal embedding of the $SU(2)_2$ Wess-Zumino-Witten conformal field theory in terms of a boson and an Ising field, and we explicitly derive a number of consequences of this embedding for the spectrum along the $SU(2)_2$ transition line between the Haldane phase and the dimerized phase. We also show that the solitons along the first-order transition line between the Haldane phase and the dimerized phase carry a spin-1/2, while those between different dimerization domains inside the dimerized phase carry a spin 1. Finally, we show that short-range correlations change character in the Haldane and dimerized phases through disorder and Lifshitz lines, as well as through the development of short-range dimer correlations in the Haldane phase, leading to a remarkably rich phase diagram.

Phase diagram of the ferrimagnetic mixed-spin Blume-Capel model with four-spin and next-nearest neighbor interactions

A finite cluster approximation based on a single cluster theory is developed for a ferrimagnetic mixed spin-1/2 and spin-1 Blume-Capel model with four-spin interaction J4 and next-nearest neighbor couplings J’. The state equations are derived for the two-dimensional square lattice and the phase diagram is explored. We found that the system can exhibits both critical and tricritical behavior according to appropriate values of J’, D and J4.

Optical conductivity of the spin Lieb nanolattice

An optical absroption in the ferromagnetic insulator with the Dzyaloshinskii–Moriya interaction (DMI), theoretically and numerically is investigated. In other words, we investigate the optical absroption, σ(ω), of the spin Lieb nanolattice (SLN) a face-centered square lattice, subjected to a light spectrum with frequency ω. Using linear response theory and Green's function approach, the frequency dependence of optical conductivity (OC) has been obtained in the context of Heisenberg Hamiltonian. At low frequencies, the OC is found to be monotonically increasing with frequency for next-nearest neighbor (NNN) coupling, DMI strength (DMIS) and temperature. Also we have found that OC has a peak (absorption). Eventually, we are investigated the effect of magnetic field on the OC of this system.

A goal-oriented adaptive procedure for the quasi-continuum method with cluster approximation

We present a strategy for adaptive error control for the quasi-continuum (QC) method applied to molecular statics problems. The QC-method is introduced in two steps: Firstly, introducing QC-interpolation while accounting for the exact summation of all the bond-energies, we compute goal-oriented error estimators in a straight-forward fashion based on the pertinent adjoint (dual) problem. Secondly, for large QC-elements the bond energy and its derivatives are typically computed using an appropriate discrete quadrature using cluster approximations, which introduces a model error. The combined error is estimated approximately based on the same dual problem in conjunction with a hierarchical strategy for approximating the residual. As a model problem, we carry out atomistic-to-continuum homogenization of a graphene monolayer, where the Carbon---Carbon energy bonds are modeled via the Tersoff---Brenner potential, which involves next-nearest neighbor couplings. In particular, we are interested in computing the representative response for an imperfect lattice. Within the goal-oriented framework it becomes natural to choose the macro-scale (continuum) stress as the "quantity of interest". Two different formulations are adopted: The Basic formulation and the Global formulation. The presented numerical investigation shows the accuracy and robustness of the proposed error estimator and the pertinent adaptive algorithm.

Quantum phase transition as an interplay of Kitaev and Ising interactions

We study the interplay between the Kitaev and Ising interactions on both ladder and two dimensional lattices. We show that the ground state of the Kitaev ladder is a symmetry-protected topological (SPT) phase, which is protected by a $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry. It is confirmed by the degeneracy of the entanglement spectrum and non-trivial phase factors (inequivalent projective representations of the symmetries), which are obtained within infinite matrix-product representation of numerical density matrix renormalization group. We derive the effective theory to describe the topological phase transition on both ladder and two-dimensional lattices, which is given by the transverse field Ising model with/without next-nearest neighbor coupling. The ladder has three phases, namely, the Kitaev SPT, symmetry broken ferro/antiferromagnetic order and classical spin-liquid. The non-zero quantum critical point and its corresponding central charge are provided by the effective theory, which are in full agreement with the numerical results, i.e., the divergence of entanglement entropy at the critical point, change of the entanglement spectrum degeneracy and a drop in the ground-state fidelity. The central charge of the critical points are either c=1 or c=2, with the magnetization and correlation exponents being 1/4 and 1/2, respectively. In the absence of frustration, the 2D lattice shows a topological phase transition from the $\mathbb{Z}_2$ spin-liquid state to the long-range ordered Ising phase at finite ratio of couplings, while in the presence of frustration, an order-by-disorder transition is induced by the Kitaev term. The 2D classical spin-liquid phase is unstable against the addition of Kitaev term toward an ordered phase before the transition to the $\mathbb{Z}_2$ spin-liquid state.