Long-range Hopping Research Articles

Exact solvable family of discrete Schrödinger operators with long-range hoppings

It is shown that one-dimensional discrete Schrödinger operators, with a uniform electric field and long-range hoppings, form an isospectral family with discrete and simple spectrum (and isospectral operators with eigenfunctions having different decay properties). Explicit relations between hopping decay rates and eigenvectors decay rates are obtained. Small perturbations of exponentially decay hopping operators preserve dynamical localization.

Proton transfer driven by the fluctuation of water molecules in chitin film.

Proton-transfer mechanisms and hydration states were investigated in chitin films possessing the functionality of fuel-cell electrolytes. The absolute hydration number per chitin molecule (N) as a function of relative humidity (RH) was determined from the OH stretching bands of H2O molecules, and the proton conductivity was found to enhance above N = 2 (80%RH). The FIR spectrum at 500-900cm-1 for 20%RH (N < 1) together with first-principles calculations clearly shows that the w1 site has the same hydration strength as the w2 site. The molecular dynamics simulations for N = 2 demonstrate that H2O molecules with tiny fluctuations are localized on w1 and w2, and the hydrogen-bond (HB) network is formed via the CH2OH group of chitin molecules. Shrinkage of the O-O distance (dOO), which synchronizes with the barrier height, is required for proton transfer from H3O+ to adjacent CH2OH groups or H2O molecules. Nevertheless, dOO is hardly modulated for N = 2 because H2O molecules are strongly constrained on w1 and w2, and therefore, the transfer probability becomes small. For N = 3, novel HBs emerged between the additional H2O molecules broadly distributed on the w3 site and H2O molecules on w1 and w2. The transfer probability is enhanced because large fluctuations and diffusions in the whole H2O molecule yield large modulations of dOO. Consequently, long-range proton hopping is driven by the Zundel-type protonated hydrates in the water network.

Interference effects in nonequilibrium quantum transport with long-range interactions

Abstract We investigate how long-range power-law hopping interaction, ∼ 1/r a , affects the characteristics of dissipative quantum transport in a nonequilibrium setting. The model under consideration is a noninteracting bosonic chain subject to thermal baths of differing temperature at its boundaries and dephasing noise which is applied uniformly to all the sites. It is shown that the steady-state current may vary nonmonotonically and has a peak for a finite a depending on the position of the cold bath. This site-specific behaviour stems back to the interference effect caused by the parity of the total sites N and the baths positions. The fractional nature of the system, along with the interplay between coherent and incoherent transport, will affect the steady state current that characterizes the transport.

Optimal light cone for macroscopic particle transport in long-range systems: A quantum speed limit approach

Understanding the ultimate rate at which information propagates is a pivotal issue in nonequilibrium physics. Nevertheless, the task of elucidating the propagation speed inherent in quantum bosonic systems presents challenges due to the unbounded nature of their interactions. In this study, we tackle the problem of macroscopic particle transport in a long-range generalization of the lattice Bose-Hubbard model through the lens of the quantum speed limit. By developing a unified approach based on optimal transport theory, we rigorously prove that the minimum time required for macroscopic particle transport is always bounded by the distance between the source and target regions, while retaining its significance even in the thermodynamic limit. Furthermore, we derive an upper bound for the probability of observing a specific number of bosons inside the target region, thereby providing additional insights into the dynamics of particle transport. Our results hold true for arbitrary initial states under both long-range hopping and long-range interactions, thus resolving an open problem of particle transport in generic bosonic systems.

Superfluid–Bose-glass transition in a system of disordered bosons with long-range hopping in one dimension

Superfluid–Bose-glass transition in a system of disordered bosons with long-range hopping in one dimension

Edge modes in finite-size systems with different edge terminals

Abstract We investigate the behavior of edge modes in the presence of different edge terminations and long-range (LR) hopping. Here, we mainly focus on such model crystals with two different types of structures (type I: “…–P–Q–P–Q–…” and type II: “… = P–Q = P–Q = …”), where P and Q represent crystal lines (CLs), while the symbols “–” and “=” denote the distance between the nearest neighbor (NN) CLs. Based on the lattice model Hamiltonian with LR hopping, the existence of edge modes is determined analytically by using the transfer matrix method (TMM) when different edge terminals are taken into consideration. Our findings are consistent with the numerical results obtained by the exact diagonalization method. We also notice that edge modes can exhibit different behaviors under different edge terminals. Our result is helpful in solving novel edge modes in honeycomb crystalline graphene and transition metal dichalcogenides with different edge terminals.

Phase-factor-optimized topological transmission in a dimerized lattice with long-range hopping

Phase-factor-optimized topological transmission in a dimerized lattice with long-range hopping

Different topological phase transitions in the Su–Schrieffer–Heeger model under different disorder structures

Abstract We investigate the topological phase transition in the Su–Schrieffer–Heeger model with the long-range hopping and quasi-periodic modulation. By numerically calculating the real-space winding number, we obtain topological phase diagrams for different disordered structures. These diagrams suggest that topological phase transitions are different by selecting the specific disordered structure. When quasi-periodic modulation is applied to intracell hopping, the resulting disorder induces topological Anderson insulator (TAI) phase with high winding number (W = 2), but the topological states are destroyed as the disorder increases. Conversely, when intercell hoppings are modulated quasi-periodically, both TAI phase and the process of destruction and restoration of topological zero modes can be induced by disorder. These topological states remain robust even under strong disorder conditions. Our work demonstrates that disorder effects do not always disrupt topological states; rather, with a judicious selection of disordered structures, topological properties can be preserved.

Recovery of a Luther-Emery phase in the three-band Hubbard ladder with longer-range hopping

Recovery of a Luther-Emery phase in the three-band Hubbard ladder with longer-range hopping

Effect of sintering temperature on the structural, morphological, optical and electrical properties of Ba1 − xLaxFe12O19

La substituted M-type Barium hexaferrite, Ba(1−x)La(x)Fe12O19, (x = 0.25 and 0.30) were synthesized using ball milling followed by heat treatment at 1150˚C and 1300˚C and the influence of sintering temperature as well as La doping were presented. X-ray diffraction, FESEM, dielectric spectroscopy, and ferroelectric measurements were performed to study the structural, morphological, dielectric, and ferroelectric properties of the prepared samples. Rietveld refinement on the X-ray diffraction measurement reveals the formation of a phase magnetoplumbite structure of barium hexaferrite only for the samples sintered at 1300˚C. The secondary phase, along with the major magnetoplumbite structure, was observed for the sample sintered at 1150˚C. Hexagonal plate-like grains of different sizes were observed, and samples sintered at 1300˚C showed large-size grains. Porosity was observed to decrease with La doping. Impedance spectroscopy reveals that Maxwell-Wagner-type polarisation occurs with the relaxation of mobile charges having long-range hopping. However, the ferroelectric property was suppressed for samples sintered at 1300˚C.

Flat bands in three-dimensional lattice models with non-trivial Hopf index

We report the presence of exactly and nearly flat bands with non-trivial topology in three-dimensional (3D) lattice models. We first show that an exactly flat band can be realized in a 3D lattice model characterized by a 3D topological invariant, namely Hopf invariant. In contrast, we find another distinct 3D model, exhibiting both 2D Chern and 3D Hopf invariant, namely Hopf-Chern insulator, that can host nearly or perfect flat bands across different 2D planes. Such a Hopf-Chern model can be constructed by introducing specific hopping along the orthogonal direction of a simple two-orbital 2D Chern insulator in the presence of in-plane nearest-neighbor and next-nearest hopping among different orbitals. While the Chern planes host nearly perfect flat bands, the orthogonal planes can host both perfect or nearly perfect flat bands with zero Chern number at some special parameter values. Interestingly, such a 3D lattice construction from 2D allows finite Hopf invariant too. Finally, we show that higher Chern models can also be constructed in the same lattice setup with only nearest and next-nearest hopping, but the appearance of flat bands along high-symmetric path in the Brillouin zone requires longer-range hopping. We close with a discussion on possible experimental platforms to realize the models.

Entanglement Entropy of Free Fermions with a Random Matrix as a One-Body Hamiltonian.

We consider a quantum system of large size N and its subsystem of size L, assuming that N is much larger than L, which can also be sufficiently large, i.e., 1≪L≲N. A widely accepted mathematical version of this inequality is the asymptotic regime of successive limits: first the macroscopic limit N→∞, then an asymptotic analysis of the entanglement entropy as L→∞. In this paper, we consider another version of the above inequality: the regime of asymptotically proportional L and N, i.e., the simultaneous limits L→∞,N→∞,L/N→λ>0. Specifically, we consider a system of free fermions that is in its ground state, and such that its one-body Hamiltonian is a large random matrix, which is often used to model long-range hopping. By using random matrix theory, we show that in this case, the entanglement entropy obeys the volume law known for systems with short-range hopping but described either by a mixed state or a pure strongly excited state of the Hamiltonian. We also give streamlined proof of Page's formula for the entanglement entropy of black hole radiation for a wide class of typical ground states, thereby proving the universality and the typicality of the formula.

Superdiffusion in a random two-dimensional system with time-reversal symmetry and long-range hopping

Superdiffusion in a random two-dimensional system with time-reversal symmetry and long-range hopping

Topological phase transitions in the non-Hermitian SSH model with long-range hopping terms induced by gains and losses

The latest progress in the one-dimensional chain SSH model provide the basic understanding of non-Hermitian topological phases. By periodically introducing the gains and losses of imaginary potential ig,-ig,-ig,ig with anti-PT symmetry, we have investigated the topological property of non-Hermitian SSH model with long-range hopping terms. We find that the gains and losses of imaginary potential causes the model to exhibit non-Hermiticity, and the non-Hermiticity induces system to undergo topological phase transitions from topologically trivial phase with non-Hermitian winding number 0 to topologically nontrivial phase with non-Hermitian winding number 1 and −1. The introduction of gains and losses greatly broadens the topological non-trivial region and play a non-trivial role in the model. We fully characterize the topological phase transitions by the band gap closing-reopening, the non-Hermitian winding numbers v and the hidden Chern number C.

Multiple skin transitions in two-band non-Hermitian systems with long-range nonreciprocal hopping

Non-Hermitian skin effect (NHSE) is a prominent feature in non-Hermitian physics, leading to novel topological properties and expanding the traditional energy band theories. In this paper, we investigate a two-band non-Hermitian system in which multiple skin transitions are induced by long-range nonreciprocal hopping. The spectral winding number under periodic boundary conditions reveals the localization directions of skin states. Further, we present the analytical solution of transition points by tracing the self-intersecting points on the complex plane. Interestingly, the current system exhibits the abundant NHSEs, including the normal, W-shaped, and bipolar localization properties, which the eigenstate distributions and the generalized Brillouin zone can clearly illustrate. We also provide a phase diagram to represent the skin transition properties of the system comprehensively. Further, we demonstrate that the multimer non-Hermitian lattices also present the anomalous skin effect and multiple transitions, which occur in the region of the bulk band touching, the same as the two-band lattice. Moreover, a feasible scheme is proposed to realize the current non-Hermitian system with long-range nonreciprocal hopping by a topoelectrical circuit. This work further supplies the content of skin transitions and may help us explore more plentiful localization features in the two-band non-Hermitian systems.

Wave-Function Tomography of Topological Dimer Chains with Long-Range Couplings.

The ability to tailor with a high accuracy the intersite connectivity in a lattice is a crucial tool for realizing novel topological phases of matter. Here, we report the experimental realization of photonic dimer chains with long-range hopping terms of arbitrary strength and phase, providing a rich generalization of the Su-Schrieffer-Heeger model which, in its conventional form, is limited to nearest-neighbor couplings only. Our experiment is based on a synthetic dimension scheme involving the frequency modes of an optical fiber loop platform. This setup provides direct access to both the band dispersion and the geometry of the Bloch wave functions throughout the entire Brillouin zone allowing us to extract the winding number for any possible configuration. Finally, we highlight a topological phase transition solely driven by a time-reversal-breaking synthetic gauge field associated with the phase of the long-range hopping, providing a route for engineering topological bands in photonic lattices belonging to the AIII symmetry class.

Ubiquitous light real-space pairing from long-range hopping and interactions

We systematically examine how long-range hopping and its synergy with extended interactions leads to light bound pairs. Pair properties are determined for a dilute extended Hubbard model with large on-site repulsion (U) and both near- and next-nearest neighbor hopping (t and t′) and attraction (V and V′), for cubic and tetragonal lattices. The presence of t′ and V′ promotes light pairs. For tetragonal lattices, t′<0 pairs can be lighter than non-interacting particles, and d-symmetric pairs form. Close packing transition temperatures, T⁎, are estimated for the Bose-Einstein condensation (BEC) of pairs to be kBT⁎∼0.1t‾, where t‾ is the geometric mean of the hoppings on the Cartesian axes. When pairs have d-symmetry, the condensate has d-wave character. Thus, the presence of both t′ and V′ leads ubiquitously to small strongly bound pairs with an inverse mass that is linear in hopping, which could lead to high temperature BECs.

Impact of dephasing on nonequilibrium steady-state transport in fermionic chains with long-range hopping

Impact of dephasing on nonequilibrium steady-state transport in fermionic chains with long-range hopping

Acoustic Higher-Order Topological Insulators Induced by Orbital-Interactions.

The discovery of higher-order topological insulator metamaterials, in analogy with their condensed-matter counterparts, has enabled various breakthroughs in photonics, mechanics, and acoustics. A common way of inducing higher-order topological wave phenomena is through pseudo-spins, which mimic the electron spins as a symmetry-breaking degree of freedom. Here, this work exploits degenerate orbitals in acoustic resonant cavities to demonstrate versatile, orbital-selective, higher-order topological corner states. Type-II corner states are theoretically investigated and experimentally demonstrated based on tailored orbital interactions, without the need for long-range hoppings that has so far served as a key ingredient for Type-II corner states in single-orbital systems. Due to the orthogonal nature of the degenerate p orbitals, this work also introduces a universal strategy to realize orbital-dependent edge modes, featuring high-Q edge states identified in bulk bands. These findings provide an understanding of the interplay between acoustic orbitals and topology, shedding light on orbital-related topological wave physics, as well as its applications for acoustic sensing and trapping.

Coexistence of localized and extended states in the Anderson model with long-range hopping

We study states arising from fluctuations in the disorder potential in systems with long-range hopping. Here, contrary to systems with short-range hopping, the optimal fluctuations of disorder responsible for the formation of the states in the gap, are not rendered shallow and long-range when E approaches the band edge (E→0). Instead, they remain deep and short-range. The corresponding electronic wave functions also remain short-range-localized for all E<0. This behavior has striking implications for the structure of the wave functions slightly above E=0. By a study of finite systems, we demonstrate that the wave functions ΨE transform from a localized to a quasi-localized type upon crossing the E=0 level, forming resonances embedded in the E>0 continuum. The quasi-localized ΨE>0 consists of a short-range core that is essentially the same as ΨE=0 and a delocalized tail extending to the boundaries of the system. The amplitude of the tail is small, but it decreases with r slowly. Its contribution to the norm of the wave function dominates for sufficiently large system sizes, L≫Lc(E); such states behave as delocalized ones. In contrast, in small systems, L≪Lc(E), quasi-localized states are overwhelmingly dominated by the localized cores and are effectively localized.