Uniform Hopping Research Articles

Multichannel coupling induced topological insulating phases with full multimerization

We propose and experimentally realize a class of quasi-one-dimensional topological lattices whose unit cells are constructed by coupled multiple identical resonators, with uniform hopping and inversion symmetry. In the presence of coupling-path-induced effective zero hopping within the unit cells, the systems are characterized by complete multimerization with degenerate −1 energy edge states for open boundary condition. Su–Schrieffer–Heeger subspaces with fully dimerized limits corresponding to pairs of nontrivial flat bands are derived from the Hilbert spaces. In particular, topological bound states in the continuum (BICs) are inherently present in even multimer chains, manifested by embedding the topological bound states into a continuous band assured by bulk-boundary correspondence. Moreover, we experimentally demonstrate the degenerate topological edge states and topological BICs in radio-frequency circuits.

Diffusion of O Atoms on a CO-Covered Ru(0001) Surface─A Combined High-Speed Scanning Tunneling Microscopy and Density Functional Theory Study at an Enhanced CO Coverage

The diffusion of adsorbed O atoms on a CO-covered Ru(0001) surface has recently been explained by a “door-opening” mechanism which is driven by fluctuations in the CO layer. Here, we analyze how this mechanism changes at a higher CO coverage than the 0.33 monolayers applied in the previous study and, therefore, lower concentrations of empty sites. High-speed scanning tunneling microscopy was used to track the O atoms. A statistical model based on nearest-neighbor jumps and uniform hopping probabilities into the six equivalent directions of the Ru(0001) lattice describes the data well. Surprisingly, the hopping rates, which involve site exchanges with CO molecules, are higher than the site exchanges at 0.33 monolayers. Density functional theory calculations were performed to explain these observations. The configurations of the CO molecules around the adsorbed O atoms obtained at the higher CO coverage are disordered. Displacements of CO molecules cost less energy than displacements in the ordered (3×3)R30° structure of the previous study. In addition, the activation energies for the jumps of the O atoms are lowered by enhanced O/CO repulsions. The atomic processes are thus faster at the higher coverage, but the general features of the door-opening mechanism remain valid.

Periodically driven model with quasiperiodic potential and staggered hopping amplitudes: Engineering of mobility gaps and multifractal states

In this study, we examine whether periodic driving of a model with a quasiperiodic potential can generate interesting Floquet phases that have no counterparts in the static model. Specifically, we consider the Aubry-Andr\'e model, which is a one-dimensional time-independent model with an on-site quasiperiodic potential ${V}_{0}$ and a nearest-neighbor hopping amplitude that is taken to have a staggered form. We add a uniform hopping amplitude that varies in time either sinusoidally or as a square pulse with a frequency $\ensuremath{\omega}$. Unlike the static Aubry-Andr\'e model, which has a simple phase diagram with only two phases (only extended or only localized states), we find that the driven model has four possible phases for the Floquet eigenstates: a phase with gapless quasienergy bands and only extended states, a phase with multiple mobility gaps separating different quasienergy bands, a mixed phase with coexisting extended, multifractal, and localized states, and a phase with only localized states. The multifractal states have generalized inverse participation ratios that scale with the system size with exponents that are different from the values for both extended and localized states. In addition, we observe intricate reentrant transitions between the different kinds of states when $\ensuremath{\omega}$ and ${V}_{0}$ are varied. The appearance of such transitions is confirmed by the behavior of the Shannon entropy. Many of our numerical results can be understood from an analytic Floquet Hamiltonian derived using a Floquet perturbation theory that uses the inverse of the driving amplitude as the perturbation parameter. In the limit of high frequency and large driving amplitude, we find that the Floquet quasienergies match the energies of the undriven system, but the Floquet eigenstates are much more extended. We also study the spreading of a one-particle wave packet, and we find that it is always ballistic but the ballistic velocity varies significantly with the system parameters, sometimes showing a nonmonotonic dependence on ${V}_{0}$ that does not occur in the static model. Finally, we compare the results for the driven model, which has a static staggered hopping amplitude, with a model that has a static uniform hopping amplitude, and we find some significant differences between the two cases. All of our results are found to be independent of the driving protocol, either sinusoidal or square pulse. We conclude that the interplay of the quasiperiodic potential and driving produces a rich phase diagram that does not appear in the static model.

Steady states and phase transitions in heterogeneous asymmetric exclusion processes

We study nonequilibrium steady states in totally asymmetric exclusion processes (TASEPs) with open boundary conditions having spatially inhomogeneous hopping rates. Considering smoothly varying hopping rates, we show that the steady states are in general classified by the steady state currents in direct analogy with open TASEPs having uniform hopping rates. We calculate the steady state bulk density profiles, which are now spatially nonuniform. We also obtain the phase diagrams in the plane of the control parameters, which, despite having phase boundaries that are in general curved lines, have the same topology as their counterparts for conventional open TASEPs, independent of the form of the hopping rate functions. This reveals a type of universality, not encountered in critical phenomena. Surprisingly and in contrast to the phase transitions in an open TASEP with uniform hopping, our studies on the phase transitions in the model reveal that all three transitions are first order in nature. We also demonstrate that this model admits delocalised domain walls (DDWs) on the phase boundaries, demarcating the generalised low and high density phases in this model. However, in contrast to the DDWs observed in an open TASEP with uniform hopping, the envelopes of the DDWs in the present model are generally curved lines.

Edge States in 1D Rhombus Lattices

AbstractThe band structure and topological properties of a 1D rhombus lattice are studied by defining three models according to the manners of intracell hopping amplitudes. Results show that in the presence of uniform intracell hopping amplitudes, degenerate topological edge states appear at the ends of the lattice. When the intracell hopping amplitudes change, the edge states change in different ways, but they are robust to a small amount of disorder. The inversion symmetry breaking modifies the degeneracy of the edge states and makes the edge states localized at one end of the lattice. Next, when local magnetic flux is introduced, the band structures of the three models are further modulated. New gaps can be opened and edge states can be induced with their different topological properties. This rhombus lattice can be a promising candidate for studying the edge states and their dependence on structural parameters and magnetic flux in 1D systems.

Role of density-dependent magnon hopping and magnon-magnon repulsion in ferrimagnetic spin-(1/2, S ) chains in a magnetic field

We compare the ground-state features of alternating ferrimagnetic chains $(1/2,\phantom{\rule{0.28em}{0ex}}S)$ with $S=1,\phantom{\rule{0.28em}{0ex}}3/2,\phantom{\rule{0.28em}{0ex}}2,\phantom{\rule{0.28em}{0ex}}5/2$ in a magnetic field and the corresponding Holstein-Primakoff bosonic models up to order $\sqrt{s/S}$, with $s=1/2$, considering the fully polarized magnetization as the boson vacuum. The single-particle Hamiltonian is a Rice-Mele model with uniform hopping and modified boundaries, while the interactions have a correlated (density-dependent) hopping term and magnon-magnon repulsion. The magnon-magnon repulsion increases the many-magnon energy and the density-dependent hopping decreases the kinetic energy. We use density matrix renormalization group calculations to investigate the effects of these two interaction terms in the bosonic model and display the quantitative agreement between the results from the spin model and the full bosonic approximation. In particular, we verify the good accordance in the behavior of the edge states, associated with the ferrimagnetic plateau, from the spin and from the bosonic models. Furthermore, we show that the boundary magnon density strongly depends on the interactions and particle statistics.

Charge density waves on a half-filled decorated honeycomb lattice

Tight binding models like the Hubbard Hamiltonian are most often explored in the context of uniform intersite hopping $t$. The electron-electron interactions, if sufficiently large compared to this translationally invariant $t$, can give rise to ordered magnetic phases and Mott insulator transitions, especially at commensurate filling. The more complex situation of non-uniform $t$ has been studied within a number of situations, perhaps most prominently in multi-band geometries where there is a natural distinction of hopping between orbitals of different degree of overlap. In this paper we explore related questions arising from the interplay of multiple kinetic energy scales and electron-phonon interactions. Specifically, we use Determinant Quantum Monte Carlo (DQMC) to solve the half-filled Holstein Hamiltonian on a `decorated honeycomb lattice', consisting of hexagons with internal hopping $t$ coupled together by $t^{\,\prime}$. This modulation of the hopping introduces a gap in the Dirac spectrum and affects the nature of the topological phases. We determine the range of $t/t^{\,\prime}$ values which support a charge density wave (CDW) phase about the Dirac point of uniform hopping $t=t^{\,\prime}$, as well as the critical transition temperature $T_c$. The QMC simulations are compared with the results of Mean Field Theory (MFT).

Quantum computational supremacy in the sampling of bosonic random walkers on a one-dimensional lattice

We study the sampling complexity of a probability distribution associated with an ensemble of identical noninteracting bosons undergoing a quantum random walk on a one-dimensional lattice. With uniform nearest-neighbor hopping we show that one can efficiently sample the distribution for times logarithmic in the size of the system, while for longer times there is no known efficient sampling algorithm. With time-dependent hopping and optimal control, we design the time evolution to approximate an arbitrary Haar-random unitary map analogous to that designed for photons in a linear optical network. This approach highlights a route to generating quantum complexity by optimal control only of a single-body unitary matrix. We study this in the context of two potential experimental realizations: a spinor optical lattice of ultracold atoms and a quantum gas microscope.

Variational study of the interacting, spinless Su–Schrieffer–Heeger model

We study the phase diagram and the total polarization distribution of the Su–Schrieffer–Heeger model with nearest neighbor interaction in one dimension at half-filling. To obtain the ground state wave-function, we extend the Baeriswyl variational wave function to account for alternating hopping parameters. The ground state energies of the variational wave functions compare well to exact diagonalization results. For the case of uniform hopping for all bonds, where it is known that an ideal conductor to insulator transition takes place at finite interaction, we also find a transition at an interaction strength somewhat lower than the known value. The ideal conductor phase is a Fermi sea. The phase diagram in the whole parameter range shows a resemblance to the phase diagram of the Kane–Mele–Hubbard model. We also calculate the gauge invariant cumulants corresponding to the polarization (Zak phase) and use these to reconstruct the distribution of the polarization. We calculate the reconstructed polarization distribution along a path in parameter space which connects two points with opposite polarization in two ways. In one case we cross the metallic phase line, in the other, we go through only insulating states. In the former case, the average polarization changes discontinuously after passing through the metallic phase line, while in the latter the distribution ‘walks across’ smoothly from one polarization to its opposite. This state of affairs suggests that the correlation acts to break the chiral symmetry of the Su–Schrieffer–Heeger model, in the same way as it happens when a Rice–Mele onsite potential is turned on.

Effect of the anisotropy of long-range hopping on localization in three-dimensional lattices

It has become widely accepted that particles with long-range hopping do not undergo Anderson localization. However, several recent studies demonstrated localization of particles with long-range hopping. In particular, it was recently shown that the effect of long-range hopping in 1D lattices can be mitigated by cooperative shielding, which makes the system behave effectively as one with short-range hopping. Here, we show that cooperative shielding, demonstrated previously for 1D lattices, extends to 3D lattices with isotropic long-range $r^{-\alpha}$ hopping, but not to 3D lattices with dipolar-like anisotropic long-range hopping. We demonstrate the presence of localization in 3D lattices with uniform ($\alpha=0$) isotropic long-range hopping and the absence of localization with uniform anisotropic long-range hopping by using the scaling behaviour of eigenstate participation ratios. We use the scaling behaviour of participation ratios and energy level statistics to show that the existence of delocalized, non-ergodic extended, or localized states in the presence of disorder depends on both the exponents $\alpha$ and the isotropy of the long-range hopping amplitudes.

Asymmetric simple exclusion process with position-dependent hopping rates: Phase diagram from boundary-layer analysis.

In this paper, we study a one-dimensional totally asymmetric simple exclusion process with position-dependent hopping rates. Under open boundary conditions, this system exhibits boundary-induced phase transitions in the steady state. Similarly to totally asymmetric simple exclusion processes with uniform hopping, the phase diagram consists of low-density, high-density, and maximal-current phases. In various phases, the shape of the average particle density profile across the lattice including its boundary-layer parts changes significantly. Using the tools of boundary-layer analysis, we obtain explicit solutions for the density profile in different phases. A detailed analysis of these solutions under different boundary conditions helps us obtain the equations for various phase boundaries. Next, we show how the shape of the entire density profile including the location of the boundary layers can be predicted from the fixed points of the differential equation describing the boundary layers. We discuss this in detail through several examples of density profiles in various phases. The maximal-current phase appears to be an especially interesting phase where the boundary layer flows to a bifurcation point on the fixed-point diagram.

Tight-binding approximation for bulk and edge electronic states in graphene

The tight-binding approximation is employed here to investigate electronic bulk and edge (“surface”) states in semi-infinite graphene sheets and graphene monolayer ribbons with various edge terminations (zigzag, horseshoe, and armchair edges). It is shown that edge states do not exist for a uniform hopping (transfer) matrix. The problem is generalized to include edge elements of the hopping matrix distinct from the infinite-sheet (“bulk”) ones. In this case, semi-infinite graphene sheets with zigzag or horseshoe edges exhibit edge states, while semi-infinite graphene sheets with armchair edges do not. The energy of the edge states lies above the (zero) Fermi level. Similarly, symmetric graphene ribbons with zigzag or horseshoe edges exhibit edge states, while ribbons with asymmetric edges (zigzag and horseshoe) do not. It is also shown how to construct the “reflected” solutions (bulk states) for the intervening equations with finite differences both for semi-infinite sheets and ribbons.

Charge carrier transport mechanisms in nanocrystalline indium oxide

The charge transport properties of nanocrystalline indium oxide (In2O3) are studied. A number of nanostructured In2O3 samples with various nanocrystal sizes are prepared by sol–gel method and characterized using various techniques. The mean nanocrystals size varies from 7–8nm to 18–20nm depending on the conditions of their preparation. Structural characterizations of the In2O3 samples are performed by means of transmission electron microscopy and X-ray diffraction. The analysis of dc and ac conductivity in a wide temperature range (T=50–300K) shows that at high temperatures charge carrier transport takes place over conduction band and at low temperatures a variable range hopping transport mechanism can be observed. We find out that the temperature of transition from one mechanism to another depends on nanocrystal size: the transition temperature rises when nanocrystals are bigger in size. The average hopping distance between two sites and the activation energy are calculated basing on the analysis of dc conductivity at low temperature. Using random barrier model we show a uniform hopping mechanism taking place in our samples and conclude that nanocrystalline In2O3 can be regarded as a disordered system.

Resonant atom-field interaction in large-size coupled-cavity arrays

We consider an array of coupled cavities with staggered intercavity couplings, where each cavity mode interacts with an atom. In contrast to large-size arrays with uniform hopping rates where the atomic dynamics is known to be frozen in the strong-hopping regime, we show that resonant atom-field dynamics with significant energy exchange can occur in the case of staggered hopping rates even in the thermodynamic limit. This effect arises from the joint emergence of an energy gap in the free photonic dispersion relation and a discrete frequency at the gap's center. The latter corresponds to a bound normal mode stemming solely from the finiteness of the array length. Depending on which cavity is excited, either the atomic dynamics is frozen or a Jaynes-Cummings-like energy exchange is triggered between the bound photonic mode and its atomic analog. As these phenomena are effective with any number of cavities, they are prone to be experimentally observed even in small-size arrays.

Transport properties of normal metal–graphene nanoribbon–normal metal junctions

Transport properties are investigated theoretically for the junctions consisting of two normal metals and a graphene nanoribbon which has zigzag shaped edges with the electron hopping weaker than that in the other region. We find that the conductance of the present model has the same asymptotic behavior for N L ⪢ 1 as that with the spatially uniform hopping in the N ≥ 3 case, where N L and N are integers corresponding to length and width, respectively. The result seems to indicate that the zigzag edges do not contribute to the transport properties in the case with N L ⪢ 1 .

Exact results for spatial decay of correlations in low-dimensional insulators

We study decay rates of one-body reduced density matrices in insulators, described by a tight-binding model, where not only an external potential but also hoppings are spatially modulated. We determine analytically the power in the power law and the correlation length in $D=1$ case and in several lattice directions in $D=2$ case. Unlike the uniform hopping case, in the $D=1$ system and in some directions of the $D=2$ system the correlation length is not determined uniquely by the gap. Moreover, a crossover from $D=2$ decay rates to $D=1$ ones is investigated.

Magnetic polarons in the one-dimensional ferromagnetic Kondo model

The ferromagnetic Kondo model with classical corespins is studied via unbiased Monte Carlo simulations. We show that with realistic parameters for the manganites and at low temperatures, the double-exchange mechanism does not lead to phase separation in one-dimensional chains but rather stabilizes individual ferromagnetic polarons. Within the ferromagnetic polaron picture, the pseudogap in the one-particle spectral function ${A}_{k}(\ensuremath{\omega})$ can easily be explained. Ferromagnetic polarons also clear up a seeming failure of the double-exchange mechanism in explaining the comparable bandwidths in the ferromagnetic and paramagnetic phase. For our analysis, we extend a simplified model, the finite-temperature uniform hopping approach (UHA), to include polarons. It can easily be evaluated numerically and provides a simple quantitative understanding of the physical features of the ferromagnetic Kondo model.

Uniform hopping approach to the ferromagnetic Kondo model at finite temperature

We study the ferromagnetic Kondo model with classical corespins via unbiased Monte-Carlo simulations and derive a simplified model for the treatment of the corespins at any temperature. Our simplified model captures the main aspects of the Kondo model and can easily be evaluated both numerically and analytically. It provides a better qualitative understanding of the physical features of the Kondo model and rationalizes the Monte-Carlo results, including the spectral density A_k(omega) of a 1D chain with nearest neighbor Coulomb repulsion. By calculating the specific heat and the susceptibility of systems up to size 16^3, we determine the Curie temperature of the 3D one-orbital double-exchange model, which agrees with experimental values.

Effective spinless fermions in the strong-coupling Kondo model

Starting from the two-orbital Kondo-lattice model with classical ${t}_{2g}$ spins, an effective spinless fermion model is derived for strong Hund coupling ${J}_{H}$ with a projection technique. The model is studied by Monte Carlo simulations and analytically using a uniform hopping approximation. The results for the spinless fermion model are in remarkable agreement with those of the original Kondo-lattice model, independent of the carrier concentration, and even for moderate Hund coupling ${J}_{H}.$ Phase separation, the phase diagram in uniform hopping approximation, as well as spectral properties including the formation of a pseudogap are discussed for both the Kondo-lattice and the effective spinless fermion model in one and three dimensions.

IPM approach to Hubbard model. Applications and limitations of restricted CI calculations to ground states of some ? networks containing fused 5- and 6-membered rings

The validity of the independent particle model (IPM) approach in treating the Hubbard model with uniform hopping parameter t and uniform on-site repulsion term U is investigated for several |U/t| ratios on the ground states of some π networks containing fused 5- and 6-membered rings with up to N=32 π electrons. It is shown that single and double excitation configuration interaction (SD-CI) based on a closed-shell Hückel-type reference determinant plus a correction added for the size consistency error using appropriate known correction terms leads to sensible estimates of the ground-state energy for up to |U/t|≤4. The IPM approach is hence well suited for treating the chemically relevant region of |U/t|≈1.5−2 for π systems. The systems studied in this work involve several fullerene-type fragments with up to N=16, for which a full configuration interaction (FCI) calculation is possible, and three larger systems, namely Corannulene (N=20), the C26 fullerene (N=26) and the C fullerene anion of Td symmetry (N=32), for which only a limited CI involving single, double, triple, and quadruple excitations (SDTQ-CI) could be performed as a guide. SD-CI calculations on these latter systems further reproduced qualitatively correct charge densities and nearest-neighbor bond orders. Wherever possible, the obtained results were compared with those obtained by different methods present in the literature, based on Monte Carlo approaches. Further we indicated a strategy as to how to perform optimum FCI Hubbard/Pariser–Parr–Pople (PPP) calculations as far as computation time is concerned. © 1999 John Wiley & Sons, Inc. Int J Quant Chem 76: 83–98, 2000