Next-nearest Neighbor Hopping Research Articles

Effect of next-nearest neighbor hopping on the single-particle excitations at finite temperature

In the half-filled one-orbital Hubbard model on a square lattice, we study the effect of next-nearest neighbor hopping on the single-particle spectral function at finite temperature using an exact-diagonalization + Monte-Carlo based approach to the simulation process. We find that the pseudogap-like dip, existing in the density of states in between the Néel temperature T_NTN and a relatively higher temperature scale T^*T*, is accompanied with a significant asymmetry in the hole- and particle-excitation energy along the high-symmetry directions as well as along the normal-state Fermi surface. On moving from (\pi/2, \pi/2π/2,π/2) toward (\pi, 0)(π,0) along the normal state Fermi surface, the hole-excitation energy increases, a behavior remarkably similar to what is observed in the dd-wave state and pseudogap phase of high-T_cTc cuprates, whereas the particle-excitation energy decreases. The quasiparticle peak height is the largest near (\pi/2, \pi/2π/2,π/2) whereas it is the smallest near (\pi, 0)(π,0). These spectral features survive beyond T_NTN. The temperature window T_N ≲ T ≲ T^*TN≲T≲T* shrinks with an increase in the next-nearest neighbor hopping, which indicates that the next-nearest neighbor hopping may not be supportive to the pseudogap-like features.

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.

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.

Fate of the reentrant localization phenomenon in the one-dimensional dimerized quasiperiodic chain with long-range hopping

Recently, the exciting reentrant localization transition phenomenon was found in a one-dimensional dimerized lattice with staggered quasiperiodic potentials. Usually, long-range hopping is typically important in actual physical systems. In this work, we study the effect of next-nearest neighbor hopping (NNNH) on the reentrant localization phenomenon. Due to the presence of NNNH, the broken chiral symmetry is further enhanced and the localization properties of electron states in the upper and lower bands become quite different. It is found that the reentrant localization can still persist within a range of NNNH both in Hermitian and non-Hermitian cases. Eventually, the reentrant localization disappears as the strength of NNNH increases to some extent, since the increasing NNNH weakens the dimerization of the system and destroys its competition with the quasiperiodic disorder. Our work thus reveals the effect of long-range hopping in the reentrant localization phenomenon and deepens its physical understanding.

Long time dynamics of a single-particle extended quantum walk on a one-dimensional lattice with complex hoppings: a generalized hydrodynamic description

We study a single-particle continuous-time quantum walk on a one-dimensional spatial lattice with complex nearest neighbour (NN) and next-nearest neighbour (NNN) hopping amplitudes. We show that the model allows for controlled information transfer and directional biasing without a biased initial state. Specifically, we show that for an unbiased initial state, complex couplings lead to chiral propagation and a causal cone structure asymmetric about the origin. We provide a hydrodynamic description for the dynamics in the large space–time limit. We obtain a global ‘quasi-stationary state’ which can be described in terms of the local quasi-particle densities satisfying Euler type of hydrodynamic equations and characterized by an infinite set of conservation laws. Further, we show that higher-order hydrodynamic equations can be used to describe the anomalous sub-diffusive scaling near the extremal fronts. The long-time behaviour for any complex NNN hopping with a nonzero real component is similar to that of purely real hopping; at a critical coupling strength, there is a Lifshitz transition where the topology of the causal structure changes from a regime with one causal cone to a regime with two nested (asymmetric) causal cones. For purely imaginary NNN hopping, there is a transition from one causal cone to a regime with two partially overlapping cones which can be attributed to the existence of degenerate maximal fronts. Both the nature of the Lifshitz transition and the scaling behaviour at the critical coupling are different in the two cases. We also discuss possible experimental realizations of such a model.

Zero-energy states in the Kitaev finite and semi-infinite model

The Kitaev chain models a p -wave superconductor and hosts two Majorana bound states at the ends of the chain in the topological phase, for example if μ = 0 , Δ = t , where μ , Δ and t are chemical potential, superconducting pairing potential, and the next-nearest neighbor hopping amplitude, respectively. We consider finite and semi-infinite chains with close parameters μ = 0 and Δ = t + ɛ where ɛ is small, near the point Δ − t = 0 . Using the Dyson equation and the Green’s function for the infinite Kitaev chain, we analytically study the conditions for the appearance of zero-energy states, as well as their wave functions. We proove that in the finite chain such states exist only if Δ > t and the number of sites is odd. Zero-energy states disappear in the finite chain in the presence of an impurity potential, which indicates their instability. But in the semi-infinite chain, for Δ > t there is a single Majorana state and it is robust against an impurity.Thus the bulk-boundary correspondence may be violated for the Kitaev chain near the singular point. • We study the Kitaev chain with the pair potential close to the hopping amplitude. • Zero-energy states exist only for odd sites number and a large enough pair potential. • For a large pair potential there is Majorana state in the semi-infinite Kitaev chain. • The bulk-boundary correspondence is not always satisfied for the Kitaev chain.

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.

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.

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.

Proximity-driven ferromagnetism and superconductivity in the triangular Rashba-Hubbard model

Bilayer Moir\'e structures are a highly tunable laboratory to investigate the physics of strongly correlated electron systems. Moir\'e transition metal dichalcogenides at low-energies, in particular, are believed to be described by a single narrow band Hubbard model on a triangular lattice with spin-orbit coupling. Motivated by recent experimental evidence for superconductivity in twisted bilayer materials, we investigate the possible superconducting pairings in a two-dimensional single band Rashba-Hubbard model. Using a random-phase approximation in the presence of nearest and next-nearest neighbor hopping, we analyze the structure of spin fluctuations and the symmetry of the superconducting gap function. We show that Rashba spin-orbit coupling favors ferromagnetic fluctuations which strengthen triplet superconductivity. If parity is violated due to the absence of spatial inversion symmetry, singlet (d-wave) and triplet (p-wave) channels of superconductivity will be mixed. Moreover, we show that time-reversal symmetry can be spontaneously broken leading to a chiral superconducting state. Finally, we consider quasiparticle interference as a possible experimental technique to observe the superconducting gap symmetry.

Density-matrix renormalization group study of optical conductivity of the Mott insulator for two-dimensional clusters

The real part of optical conductivity $\text{Re}\sigma(\omega)$ of the Mott insulators has a large amount of information on how spin and charge degrees of freedom interact with each other. By using the time-dependent density-matrix renormalization group, we study $\text{Re}\sigma(\omega)$ of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of $\text{Re}\sigma(\omega)$ not only for the two-dimensional square lattice but also for two- and four-leg ladders. For the square lattice, however, we do not clearly find a gap between an excitonic peak and continuum band, which indicates that a bound state is not well defined. The emergence of an excitonic peak in $\text{Re}\sigma(\omega)$ implies the formation of a spin polaron. Examining the dependence of $\text{Re}\sigma(\omega)$ on the on-site Coulomb interaction and next-nearest neighbor hoppings, we confirm that an excitonic peak is generated from a magnetic effect. Electron scattering due to an electron-phonon interaction is expected to easily suppress an excitonic peak since spectral width of an excitonic peak is very narrow. Introducing a large broadening in $\text{Re}\sigma(\omega)$ by modeling the electron-phonon coupling present in La$_{2}$CuO$_{4}$ and Nd$_{2}$CuO$_{4}$, we obtain $\text{Re}\sigma(\omega)$ comparable with experiments.

Engineering the topological state transfer and topological beam splitter in an even-sized Su-Schrieffer-Heeger chain

The usual Su-Schrieffer-Heeger model with an even number of lattice sites possesses two degenerate zero energy modes. The degeneracy of the zero energy modes leads to the mixing between the topological left and right edge states, which makes it difficult to implement the state transfer via topological edge channel. Here, enlightened by the Rice-Male topological pumping, we find that the staggered periodic next-nearest neighbor hoppings can also separate the initial mixed edge states, which ensures the state transfer between topological left and right edge states. Significantly, we construct an unique topological state transfer channel by introducing the staggered periodic on-site potentials and the periodic next-nearest neighbor hoppings added only on the odd sites simultaneously, and find that the state initially prepared at the last site can be transfered to the first two sites with the same probability distribution. This special topological state transfer channel is expected to realize a topological beam splitter, whose function is to make the initial photon at one position appear at two different positions with the same probability. Further, we demonstrate the feasibility of implementing the topological beam splitter based on the circuit quantum electrodynamic lattice. Our scheme opens up a new way for the realization of topological quantum information processing and provides a new path towards the engineering of new type of quantum optical device.

Flat-band superconductivity for tight-binding electrons on a square-octagon lattice

The discovery of superconductivity in twisted bilayer graphene has triggered a resurgence of interest in flat-band superconductivity. Here, we investigate the square-octagon lattice, which also exhibits two perfectly flat bands when next-nearest neighbour hopping or an external magnetic field are added to the system. We calculate the superconducting phase diagram in the presence of on-site attractive interactions and find two superconducting domes, as observed in several types of unconventional superconductors. The critical temperature shows a linear dependence on the coupling constant, suggesting that superconductivity might reach high temperatures in the square-octagon lattice. Our model could be experimentally realized using photonic or ultracold atoms lattices.

Topological and nontopological features of generalized Su-Schrieffer-Heeger models

The (one-dimensional) Su-Schrieffer-Heeger Hamiltonian, augmented by spin-orbit coupling and longer-range hopping, is studied at half filling for an even number of sites. The ground-state phase diagram depends sensitively on the symmetry of the model. Charge-conjugation (particle-hole) symmetry is conserved if hopping is only allowed between the two sublattices of even and odd sites. In this case (of BDI symmetry) we find a variety of topologically non-trivial phases, characterized by different numbers of edge states (or, equivalently, different quantized Zak phases). The transitions between these phases are clearly signalled by the entanglement entropy. Charge-conjugation symmetry is broken if hopping within the sublattices is admitted (driving the system into the AI symmetry class). We study specifically next-nearest-neighbor hopping with amplitudes $t_a$ and $t_b$ for the $A$ and $B$ sublattices, respectively. For $t_a=t_b$ parity is conserved, and also the quantized Zak phases remain unchanged in the gapped regions of the phase diagram. However, metallic patches appear due to the overlap between conduction and valence bands in some regions of parameter space. The case of alternating next-nearest neighbor hopping, $t_a=-t_b$, is also remarkable, as it breaks both charge-conjugation $C$ and parity $P$ but conserves the product $CP$. Both the Zak phase and the entanglement spectrum still provide relevant information, in particular about the broken parity. Thus the Zak phase for small values of $t_a$ measures the disparity between bond strengths on $A$ and $B$ sublattices, in close analogy to the proportionality between the Zak phase and the polarization in the case of the related Aubry-Andr\'e model.

ZQ Berry phase for higher-order symmetry-protected topological phases

We propose the $\mathbb{Z}_Q$ Berry phase as a topological invariant for higher-order symmetry-protected topological (HOSPT) phases for two- and three-dimensional systems. It is topologically stable for electron-electron interactions assuming the gap remains open. As a concrete example, we show that the Berry phase is quantized in $\mathbb{Z}_4$ and characterizes the HOSPT phase of the extended Benalcazar-Bernevig-Hughes (BBH) model, which contains the next-nearest neighbor hopping and the intersite Coulomb interactions. In addition, we introduce the $\mathbb{Z}_4$ Berry phase for the spin-model-analog of the BBH model, whose topological invariant has not been found so far. Furthermore, we demonstrate the Berry phase is quantized in $\mathbb{Z}_4$ for the three-dimensional version of the BBH model. We also confirm the bulk-corner correspondence between the $\mathbb{Z}_4$ Berry phase and the corner states in the HOSPT phases.

Edge states, corner states, and flat bands in a two-dimensional PT -symmetric system

We study corner states on a flat band in the square lattice. To this end, we introduce a two dimensional model including Su-Schrieffer-Heeger type bond alternation responsible for corner states as well as next-nearest neighbor hoppings yielding flat bands. The key symmetry of the model for corner states is space-time inversion ($\cal PT$) symmetry, which guarantees quantized Berry phases. This implies that edge states as well as corner states would show up if boundaries are introduced to the system. We also argue that an infinitesimal $\cal PT$ symmetry-breaking perturbation could drive flat bands into flat Chern bands.

Magnetic phase diagram of the infinite- U Hubbard model with nearest- and next-nearest-neighbor hoppings

We study the infinite-U Hubbard model on ladders of 2, 4 and 6 legs with nearest (t) and next-nearest (t') neighbor hoppings by means of the density-matrix renormalization group algorithm. In particular, we analyze the stability of the Nagaoka state for several values of t' when we vary the electron density $(\rho)$ from half-filling to the low-density limit. We build the two-dimensional phase diagram, where the fully spin-polarized and paramagnetic states prevail. We find that the inclusion of a non-frustrating next nearest neighbor hopping stabilizes the fully spin-polarized phase up until |t'/t|=0.5. Surprisingly, for this value of t', the ground state is fully spin-polarized for almost any electron density 1 $\gtrsim \rho \gtrsim$ 0, connecting the Nagaoka state to itinerant ferromagnetism at low density. Also, we find that the previously found checkerboard insulator phase at t'=0 and $\rho$=0.75 is unstable against t'.

Light-cone and local front dynamics of a single-particle extended quantum walk

We study the light-cone and front dynamics of a single particle continuous time extended quantum walk on a one dimensional lattice with finite range hopping. We show that, in general, for an initially localized state, propagating wave fronts can be characterized as ordinary or extremal fronts with the latter exhibiting an anomalous sub-diffusive scaling behaviour in the front region. We investigate the dynamical global and local scaling properties of the cumulative probability distribution function for the extended walk with nearest and next-nearest neighbour hopping using analytical and numerical methods. The global scaling shows the existence of a 'causal light-cone' corresponding to excitations travelling with a velocity smaller than a maximal 'light velocity'. Maximal fronts moving with fixed 'light velocity' bound the causal cone. The front regions spread with time sub-diffusively exhibiting a local Airy scaling which leads to an internal staircase structure. At a certain critical next-nearest neighbour hopping strength, there is a transition from a phase with one 'causal cone' to a phase with two nested 'causal cones' and the existence of an internal staircase structure in the corresponding cumulative distribution profiles. We also connect the study to that in spin chain systems and indicate that a single particle quantum walk on the one dimensional lattice already captures the many body physics of a spin chain system. In particular, we suggest that the time evolution of a single particle quantum walk on the one dimensional lattice with an initially localized state is equivalent to the time evolution of a domain wall initial state in a corresponding spin chain system.

Manipulating quantum materials with quantum light

We show that the macroscopic magnetic and electronic properties of strongly correlated electron systems can be manipulated by coupling them to a cavity mode. As a paradigmatic example we consider the Fermi-Hubbard model and find that the electron-cavity coupling enhances the magnetic interaction between the electron spins in the ground-state manifold. At half filling this effect can be observed by a change in the magnetic susceptibility. At less than half filling, the cavity introduces a next-nearest neighbour hopping and mediates a long-range electron-electron interaction between distant sites. We study the ground state properties with Tensor Network methods and find that the cavity coupling can induce a new phase characterized by a momentum-space pairing effect for electrons.

Temperature-filling phase diagram of the two-dimensional Holstein model in the thermodynamic limit by self-consistent Migdal approximation

We study the temperature-filling phase diagram of the single-band Holstein model in two dimensions using the self-consistent Migdal approximation, where both the electron and phonon self-energies are treated on an equal footing. By employing an efficient numerical algorithm utilizing fast Fourier transforms to evaluate momentum and Matsubara frequency summations, we determine the charge-density-wave (CDW) and superconducting transition temperatures in the thermodynamic limit using lattice sizes that are sufficient to eliminate significant finite size effects present at lower temperatures. We obtain the temperature-filling phase diagrams for a range of coupling strengths and phonon frequencies for the model defined on a square lattice with and without next-nearest neighbor hopping. We find the appearance of a superconducting dome with a critical temperature that decreases before reaching the $\mathbf{q}_{\text{max}} = (\pi,\pi)$ CDW phase boundary. For very low phonon frequencies, we also find an incommensurate CDW phase with the ordering vector $\mathbf{q}_{\text{max}} \approx (\pi,\pi)$ appearing between the commensurate CDW and superconducting phases. Our numerical implementation can be easily extended to treat momentum-dependent electron-phonon coupling, as well as dispersive phonon branches, and has been made available to the public.