Next-nearest Neighbor Hopping Research Articles

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.

Fermi surface pockets in electron-doped iron superconductor by Lifshitz transition

The Fermi surface pockets that lie at the corner of the two-iron Brillouin zone in heavily electron-doped iron selenide superconductors are accounted for by an extended Hubbard model over the square lattice of iron atoms that includes the principal 3dxz and 3dyz orbitals. At half filling, and in the absence of intra-orbital next-nearest neighbor hopping, perfect nesting between electron-type and hole-type Fermi surfaces at the the center and at the corner of the one-iron Brillouin zone is revealed. It results in hidden magnetic order in the presence of magnetic frustration within mean field theory. An Eliashberg-type calculation that includes spin-fluctuation exchange finds that the Fermi surfaces undergo a Lifshitz transition to electron/hole Fermi surface pockets centered at the corner of the two-iron Brillouin zone as on-site repulsion grows strong. In agreement with angle-resolved photoemission spectroscopy on iron selenide high-temperature superconductors, only the two electron-type Fermi surface pockets remain after a rigid shift in energy of the renormalized band structure by strong enough electron doping. At the limit of strong on-site repulsion, a spin-wave analysis of the hidden-magnetic-order state finds a ‘floating ring’ of low-energy spin excitations centered at the checkerboard wavenumber . This prediction compares favorably with recent observations of low-energy spin resonances around (π, π) in intercalated iron selenide by inelastic neutron scattering.

Correlation between charge-order state and next nearest-neighbor hopping in electron-doped cuprate superconductors

Within the framework of the t-t[Formula: see text]J model, the evolution of the charge-order state with the next nearest-neighbor (NN) hopping in the electron-doped cuprate superconductors is studied. It is shown that although the magnitude of the charge-order wave vector increases with the increase of the next NN hopping in the hole-doped case, the charge-order wave vector in the electron-doped side decreases with the increase of the next NN hopping, reflecting an asymmetric next NN hopping dependence of the charge-order state between the hole- and electron-doped cuprate superconductors.

Optimal doping for d-wave superconducting ground states within the generalized Hubbard model

A single-band generalized Hubbard model that describes two-dimensional superconductivity with d-wave symmetry on a square lattice within the BCS formalism is considered. For a set of Hamiltonian parameters and varying the ratio between nearest-neighbor and next-nearest neighbor hoppings (t'/t), an optimal doping (nop) can be found for each t'/t value, where the critical temperature is maximum (Tc-max). After calculating the superconducting gap at T=0K and the corresponding ground state (Eg ) for all the carrier concentrations, a ground state energy minimum (Eg-min) is found close to half filling. Since Tc-max is the highest critical temperature for a given ratio t'/t, the minimum of all the Tc-max values defines a supreme of this set of temperatures, named as Tc-max-sup. The corresponding optimal doping for Tc-max-sup will be called nop-sup, and the the results show that Eg-min is located at nop-sup. The Fermi surface (FS) is analyzed for carrier concentrations close to nop-sup and it is suggested that the location for over (OD) and under (UD) doping regimes (nOD>nop-sup>nUD) could define a pseudogap zone for high critical temperature superconductors.

A dynamical mean-field study of orbital-selective Mott phase enhanced by next-nearest neighbor hopping

The dynamical mean-field theory is employed to study the orbital-selective Mott transition (OSMT) of the two-orbital Hubbard model with nearest neighbor hopping and next-nearest neighbor (NNN) hopping. The NNN hopping breaks the particle-hole symmetry at half filling and gives rise to an asymmetric density of states (DOS). Our calculations show that the broken symmetry of DOS benefits the OSMT, where the region of the orbital-selective Mott phase significantly extends with the increasing NNN hopping integral. We also find that Hund's rule coupling promotes OSMT by blocking the orbital fluctuations, but the influence of NNN hopping is more remarkable.

Higher first Chern numbers in one-dimensional Bose–Fermi mixtures

We propose to use a one-dimensional system consisting of identical fermions in a periodically driven lattice immersed in a Bose gas, to realise topological superfluid phases with Chern numbers larger than 1. The bosons mediate an attractive induced interaction between the fermions, and we derive a simple formula to analyse the topological properties of the resulting pairing. When the coherence length of the bosons is large compared to the lattice spacing and there is a significant next-nearest neighbour hopping for the fermions, the system can realise a superfluid with Chern number ±2. We show that this phase is stable in a large region of the phase diagram as a function of the filling fraction of the fermions and the coherence length of the bosons. Cold atomic gases offer the possibility to realise the proposed system using well-known experimental techniques.

Theory of electron spin resonance in one-dimensional topological insulators with spin-orbit couplings: Detection of edge states

Edge/surface states often appear in a topologically nontrivial phase, when the system has a boundary. The edge state of a one-dimensional topological insulator is one of the simplest examples. Electron Spin Resonance (ESR) is an ideal probe to detect and analyze the edge state for its high sensitivity and precision. We consider ESR of the edge state of a generalized Su-Schrieffer-Heeger model with a next-nearest neighbor (NNN) hopping and a staggered spin-orbit coupling. The spin-orbit coupling is generally expected to bring about nontrivial changes on the ESR spectrum. Nevertheless, in the absence of the NNN hoppings, we find that the ESR spectrum is unaffected by the spin-orbit coupling thanks to the chiral symmetry. In the presence of both the NNN hopping and the spin-orbit coupling, on the other hand, the edge ESR spectrum exhibits a nontrivial frequency shift. We derive an explicit analytical formula for the ESR shift in the second order perturbation theory, which agrees very well with a non-perturbative numerical calculation.

Vortex-core order and field-driven supersolidity

Superconductivity occurs in the proximity of other competing orders in a wide variety of materials. Such competing phases may reveal themselves when superconductivity is locally suppressed by a magnetic field in the core of a vortex. We explore the competition between superconductivity and charge density wave order in the attractive Hubbard model on a square lattice. Using Bogoliubov-deGennes mean field theory, we study how vortex structures form and evolve as the magnetic flux is tuned. Each vortex seeds a CDW region whose size is determined by the energy cost of the competing phase. The vortices form a lattice whose lattice parameter shrinks with increasing flux. Eventually, their charge-ordered vortex cores overlap, leading to a field-driven coexistence phase exhibiting both macroscopic charge order and superconductivity -- a `supersolid'. Ultimately, superconductivity disappears via a first-order phase transition into a purely charge ordered state. We construct a phase diagram containing these multiple ordered states, using $t'$, the next-nearest neighbour hopping, to tune the competition between phases.

Tight binding calculation of tunneling conductance of a metal/ferromagnetic junction

A tight binding approximation was used to describe the electronic properties of a metal/ ferromagnetic junction in a one-dimensional system. The appropriate boundary conditions were calculated to describe the quality of the interface, the non-spin-flip and spin-flip scattering potential. The BTK model was used to compute the reflection and transmission probabilities, and the Landauer formulation was used to calculate the conductance spectrum. It was found that the conductance spectrum changes slope at the bias voltage that reached the bottom of the minority band and the top of the majority band of the ferromagnetic. The conductance spectrum was suppressed for all energies when either the non-spin-flip or spin-flip scattering at the interface increased. However, the conductance spectrum can be enhanced when the interface was taken into account for the appropriate value of the spin-flip and non-spin-flip scattering. In addition, the conductance can be increased by increasing the next-nearest neighbor hopping energy in the ferromagnetic material.

From frustrated to unfrustrated: Coupling two triangular-lattice itinerant quantum magnets

Motivated by systems that can be seen as composed of two frustrated sublattices combined into a less frustrated total lattice, we study the double-exchange model with nearest-neighbor (NN) and next--nearest-neighbor (NNN) couplings on the honeycomb lattice. When adding NN hopping and its resulting double exchange to the antiferromagnetic (AFM) Heisenberg coupling, the resulting phase diagram is quite different from that of purely Heisenberg-like magnetic models and strongly depends on electron filling. For half filling, patterns of AFM dimers dominate, where the effective electronic bands remain graphene-like with Dirac cones in all phases, from the FM to the $120^\circ$ limit. When the density of states at the Fermi level is sizable, we find non-coplanar incommensurate states as well as a small-vortex phase. Finally, a non-coplanar commensurate pattern realizes a Chern insulator at quarter filling. In the case of both NN and NNN hopping, the noncoplanar spin pattern inducing Chern insulators in triangular lattices is found to be quite stable under coupling into a honeycomb system. The resulting total phases are topologically nontrivial and either a Chern insulator with $C=2$ or a magnetic topological crystalline insulator protected by a combination or mirror-reflection and time-reversal symmetries arise.

Bosonic self-energy functional theory

We derive the self-energy functional theory for bosonic lattice systems with broken $U(1)$ symmetry by parametrizing the bosonic Baym-Kadanoff effective action in terms of one- and two-point self-energies. The formalism goes beyond other approximate methods such as the pseudoparticle variational cluster approximation, the cluster composite boson mapping, and the Bogoliubov+U theory. It simplifies to bosonic dynamical-mean field theory when constraining to local fields, whereas when neglecting kinetic contributions of non-condensed bosons it reduces to the static mean-field approximation. To benchmark the theory we study the Bose-Hubbard model on the two- and three-dimensional cubic lattice, comparing with exact results from path integral quantum Monte Carlo. We also study the frustrated square lattice with next-nearest neighbor hopping, which is beyond the reach of Monte Carlo simulations. A reference system comprising a single bosonic state, corresponding to three variational parameters, is sufficient to quantitatively describe phase-boundaries, and thermodynamical observables, while qualitatively capturing the spectral functions, as well as the enhancement of kinetic fluctuations in the frustrated case. On the basis of these findings we propose self-energy functional theory as the omnibus framework for treating bosonic lattice models, in particular, in cases where path integral quantum Monte Carlo methods suffer from severe sign problems (e.g. in the presence of non-trivial gauge fields or frustration). Self-energy functional theory enables the construction of diagrammatically sound approximations that are quantitatively precise and controlled in the number of optimization parameters, but nevertheless remain computable by modest means.

Superconducting Phase Diagram of the Paramagnetic One-Band Hubbard Model

We study spin-fluctuation-mediated superconductivity in the one-band Hubbard model. Higher-order effective interactions in U give rise to a superconducting instability which is very sensitive to changes in the Fermi surface topology arising as a function of doping and changes in the band structure. We show the superconducting phase diagram as a function of doping and next-nearest neighbor hopping in the limit of very small Coulomb interaction strength and discuss peculiarities arising at the phase boundaries separating different superconducting domains.

The Effect of Next-Nearest Neighbour Hopping in the One, Two, and Three Dimensional Holstein Model.

Allowing a single electron to hop to next-nearest neighbours (NNN) in addition to the closest atomic sites in the Holstein model, a modified Trugman method is applied to exactly calculate the effect on the polaronic effective mass in one, two, and three dimensions, building on the previous study of the one-dimensional NNN Holstein model. We also present perturbative calculations and a heuristic scaling factor for the coupling strength and ion frequency to nearly map the NNN Holstein model back onto the original Holstein model. When account is taken of the modified electronic bandwidth near the electron energy, we find that including NNN hopping effectively increases the polaron effective mass.

Bosonic integer quantum Hall states in topological bands with Chern number two

We study the interacting bosons in topological Hofstadter bands with Chern number two. Using exact diagonalization, we demonstrate that bosonic integer quantum Hall (BIQH) state emerges at integer boson filling factor $\nu=1$ of the lowest Chern band with evidences including a robust spectrum gap and quantized topological Hall conductance two. Moreover, the robustness of BIQH state against different interactions and next-nearest neighbor hopping is investigated. The strong nearest neighbor interaction would favor a charge density wave. When the onsite interaction decreases, BIQH state undergoes a continuous transition into a superfluid state. Without next-nearest neighbor hopping, the ground state is possibly in a metallic Fermi-liquid-like phase.

Charge instabilities of the two-dimensional Hubbard model with attractive nearest neighbour interaction

Attractive non-local interactions jointly with repulsive local interaction in a microscopic modelling of electronic Fermi liquids generate a competition between an enhancement of the static charge susceptibility–ultimately signalling charge instability and phase separation–and its correlation induced suppression. We analyse this scenario through the investigation of the extended Hubbard model on a two-dimensional square lattice, using the spin rotation invariant slave-boson representation of Kotliar and Ruckenstein. The quasiparticle density of states, the renormalised effective mass and the Landau parameter F s0 are presented, whereby the positivity of F s0 – 1 constitutes a criterion for stability. Van Hove singularities in the density of states support possible charge instabilities. A (negative) next-nearest neighbour hopping parameter t' shifts their positions and produces a tendency towards charge instability even for low filling whereas the t'-controlled particle-hole asymmetry of the correlation driven effective mass is small. A region of instability on account of the attractive interaction V is identified, either at half filling in the absence of strong electronic correlations or, in the case of large on-site interaction U, at densities far from half filling.

Variational identification of a fractional Chern insulator in an extended Bose-Hubbard model

We study the extended Bose-Hubbard model on the square lattice at half filling as a function of next-nearest neighbor hopping amplitude and interaction strength. To variationally map out the phase diagram of this model, we develop a two-parameter family of wave-functions based on the parton construction which can describe both topological and broken symmetry phases on equal footing. In addition, our wave-functions resolve long standing issues with more conventional short-range Jastrow wave-functions. Using this variational ansatz, we show that a spontaneous time-reversal symmetry breaking fractional Chern insulator is energetically favored over a critical region between two superfluid phases. In verifying the properties of these parton wave-functions we exemplify a more robust way to identify topology through the Hall conductance.

Kohn's localization in disordered fermionic systems with and without interactions

Understanding the metal-insulator transition in disordered many-fermion systems, both with and without interactions, is one of the most challenging and consequential problems in condensed matter physics. In this paper we address this issue from the perspective of the modern theory of the insulating state (MTIS), which has already proven to be effective for band and Mott insulators in clean systems. First we consider noninteracting systems with different types of aperiodic external potentials: uncorrelated disorder (one-dimensional Anderson model), deterministic disorder (Aubry-Andr\'e Hamiltonian and its modification including next-nearest neighbour hopping), and disorder with long-range correlations (self-affine potential). We show how the many-body localisation tensor defined within the MTIS may be used as a powerful probe to discriminate the insulating and the metallic phases, and to locate the transition point. Then we investigate the effect of weak repulsive interactions in the Aubry-Andr\'{e} Hamiltonian, a model which describes a recent cold-atoms experiment. By treating the weak interactions within a mean-field approximation we obtain a linear shift of the transition point towards stronger disorder, providing evidence for delocalisation induced by interactions.