Tight-binding Systems Research Articles

Upper bound on the energy gap in terms of the localization in tight-binding systems

We present an upper bound on the energy gap above the ground energy in terms of the variance of the particle position in one-particle tight-binding systems. Our inequality gives a complementary relationship between the energy gap and the localization of the particle; that is, the energy gap narrows as the ground state spreads spatially, while the energy gap can broaden as the ground state becomes localized. We first consider the ground state in one-dimensional tight-binding systems and relate the energy gap to the variance of the particle position in the ground state. We then extend the result to higher-dimensional systems. We compare our upper bound with the exact energy gap as calculated numerically in one and two dimensions; this comparison confirms that our upper bound places a tight restriction on the energy gap.

Production of minimally entangled typical thermal states with the Krylov-space approach

The minimally entangled typical thermal states algorithm is applied to fermionic systems using the Krylov-space approach to evolve the system in imaginary time. The convergence of local observables is studied in a tight-binding system with a site-dependent potential. The temperature dependence of the superconducting correlations of the attractive Hubbard model is analyzed on chains, showing an exponential decay with distance and exponents proportional to the temperature at low temperatures, as expected. In addition, the nonlocal parity correlator is calculated at finite temperature. Other possible applications of the minimally entangled typical thermal states algorithm to fermionic systems are also discussed.

Influence of Dimehylsulfoxide on Protein–Ligand Binding Affinities

Because of its favorable physicochemical properties, DMSO is the standard solvent for sample storage and handling of compounds in drug discovery. To date, little attention was given to how DMSO influences protein-ligand binding strengths. In this study we investigated the effects of DMSO on different noncovalent protein-ligand complexes, in particular in terms of the binding affinities, which we determined using nanoESI-MS. For the investigation, three different protein-ligand complexes were chosen: trypsin-Pefabloc, lysozyme-tri-N-acetylchitotriose (NAG3), and carbonic anhydrase-chlorothiazide. The DMSO content in the nanoESI buffer was increased systematically from 0.5 to 8%. For all three model systems, it was shown that the binding affinity decreases upon addition of DMSO. Even 0.5-1% DMSO alters the KD values, in particular for the tight binding system carbonic anhydrase-chlorothiazide. The determined dissociation constant (KD) is up to 10 times higher than for a DMSO-free sample in the case of carbonic anhydrase-chlorothiazide binding. For the trypsin-Pefabloc and lysozyme-NAG3 complexes, the dissociation constants are 7 and 3 times larger, respectively, in the presence of DMSO. This work emphasizes the importance of effects of DMSO as a co-solvent for quantification of protein-ligand binding strengths in the early stages of drug discovery.

LUTTINGER MODEL AND LUTTINGER LIQUIDS

The Luttinger model owes its solvability to a number of peculiar features, like its linear relativistic dispersion relation, which are absent in more realistic fermionic systems. Nevertheless according to the Luttinger liquid conjecture a number of relations between exponents and other physical quantities, which are valid in the Luttinger model, are believed to be true in a wide class of systems, including tight binding or jellium one-dimensional fermionic systems. Recently a rigorous proof of several Luttinger liquid relations in nonsolvable models has been achieved; it is based on exact Renormalization Group methods coming from Constructive Quantum Field Theory and its main steps will be reviewed below.

Environment-assisted quantum transport in ordered systems

Noise-assisted transport in quantum systems occurs when quantum time evolution and decoherence conspire to produce a transport efficiency that is higher than what would be seen in either the purely quantum or purely classical cases. In disordered systems, it has been understood as the suppression of coherent quantum localization through noise, which brings detuned quantum levels into resonance and thus facilitates transport. We report several new mechanisms of environment-assisted transport in ordered systems, in which there is no localization to overcome and where one would naively expect that coherent transport is the fastest possible. Although we are particularly motivated by the need to understand excitonic energy transfer in photosynthetic light-harvesting complexes, our model is general—transport in a tight-binding system with dephasing, a source and a trap—and can be expected to have wider application.

The role of power-law correlated disorder in the Anderson metal-insulator transition

We study the influence of scale-free correlated disorder on the metal-insulator transition in the Anderson model of localization. We use standard transfer matrix calculations and perform finite-size scaling of the largest inverse Lyapunov exponent to obtain the localization length for respective 3D tight-binding systems. The density of states is obtained from the full spectrum of eigenenergies of the Anderson Hamiltonian. We discuss the phase diagram of the metal-insulator transition and the influence of the correlated disorder on the critical exponents.

Effects of the Rashba spin–orbit coupling on Hofstadter’s butterfly

We study the effect of Rashba spin–orbit coupling on the Hofstadter spectrum of a two-dimensional tight-binding electron system in a perpendicular magnetic field. We obtain the generalized coupled Harper spin-dependent equations which include the Rashba spin–orbit interaction and solve for the energy spectrum and spin polarization. We investigate the effect of spin–orbit coupling on the fractal energy spectrum and the spin polarization for some characteristic states as a function of the magnetic flux α and the spin–orbit coupling parameter. We characterize the complexity of the fractal geometry of the spin-dependent Hofstadter butterfly with the correlation dimension and show that it grows quadratically with the amplitude of the spin–orbit coupling. We study some ground state properties and the spin polarization shows a fractal-like behavior as a function of α, which is demonstrated with the exponent close to unity of the decaying power spectrum of the spin polarization. Some degree of spin localization or distribution around + 1 or − 1, for small spin–orbit coupling, is found with the determination of the entropy function as a function of the spin–orbit coupling. The excited states show a more extended (uniform) distribution of spin states.

Dissipative Driven Single-Band Tight-Binding Dynamics

The dissipative dynamics of a driven single-band tight-binding system is investigated using a Hopfield model of a reservoir. The system is linearly coupled to reservoir and main dynamical variables of the system are obtained in Heisenberg picture by tracing out the reservoir degrees of freedom.

Resonant states and wavepacket super-diffusion in intra-chain correlated ladders withdiluted disorder

In this work, we study a tight-binding Hamiltonian model system of a binary correlated ladder withdiluted disorder. We introduce intra-chain correlations between the on-site potentials by imposing thatϵi, s = − ϵi, − s wheres = ± 1 indexes the two ladder chains. Further, we consider each ladder chain as composed ofinter-penetrating ordered and random sub-chains. We show that the presence of a randomon-site distribution in one of the inter-penetrating chains leads to Anderson localizationexcept at a specific symmetric pair of energy eigenmodes. Further, by integrating thetime-dependent Schroedinger equation, we follow the time-evolution of an initially localizedone-electron wavepacket. We report that the remaining delocalized resonant modes areresponsible for a super-diffusive spread of the wavepacket dispersion while the wavepacketparticipation function remains finite. A scaling analysis of the wavepacket distributionshows that it obeys a universal scaling form with the development of a power-lawtail followed by a super-diffusively evolving cutoff. We obtain three exponentscharacterizing this super-diffusive dynamics and show that they satisfy a simple scalingrelation.

Collective excitations in layered organic conductors

We apply the dielectric formalism within random phase approximation (RPA) and G 0 W 0 approximation to the tight-binding multi-band systems with the three-dimensional long-range Coulomb interaction in order to calculate the one-particle spectral function for TTF–TCNQ, and to investigate dielectric properties of quasi-two-dimensional conductor β ′ ′ ‐ ( BEDT – TTF ) 2 SF 5 CH 2 CF 2 SO 3 . In the model with two one-dimensional electron bands per donor and acceptor chains, appropriate for TTF–TCNQ, the RPA dielectric response comprises a low energy collective mode due to the strong coupling between the plasmon and the dipolar modes, together with the mode at order of magnitude higher energies. The first mode is responsible for the absence of low-energy quasi-particles and the appearance of broad dispersion at low energies in the spectral function. The wide structure at higher energies is due the second mode. These results are in the qualitative agreement with the ARPES data. In the model with two conducting bands, one one-dimensional and the other two-dimensional, which can be applied to β ′ ′ ‐ ( BEDT – TTF ) 2 SF 5 CH 2 CF 2 SO 3 , the coupling between the plasmon and the dipolar mode leads to the appearance of the low energy collective mode perpendicular to the stacks, while the low energy dipolar mode persists along the stacks, as is observed in optical measurements.

Shaping the spatiotemporal dynamics of the electron density in a hybrid metal-semiconductor nanostructure

A one-dimensional semiconductor nanostructure is locally excited through a metal aperture. It is shown that the electron density can be coherently localized at desired spatial and temporal positions by using nontrivially shaped laser pulses. To obtain the optimized laser field, Bloch equations for a tight-binding model system are solved together with a genetic pulse-shaping algorithm. Full three-dimensional finite-difference time-domain (FDTD) simulations of the Maxwell-Bloch equations confirm the predicted coherent spatiotemporal control.

Optimal block-tridiagonalization of matrices for coherent charge transport

Numerical quantum transport calculations are commonly based on a tight-binding formulation. A wide class of quantum transport algorithms require the tight-binding Hamiltonian to be in the form of a block-tridiagonal matrix. Here, we develop a matrix reordering algorithm based on graph partitioning techniques that yields the optimal block-tridiagonal form for quantum transport. The reordered Hamiltonian can lead to significant performance gains in transport calculations, and allows to apply conventional two-terminal algorithms to arbitrarily complex geometries, including multi-terminal structures. The block-tridiagonalization algorithm can thus be the foundation for a generic quantum transport code, applicable to arbitrary tight-binding systems. We demonstrate the power of this approach by applying the block-tridiagonalization algorithm together with the recursive Green’s function algorithm to various examples of mesoscopic transport in two-dimensional electron gases in semiconductors and graphene.

Magnetic Translation Symmetry on the Lattice

Magnetic translation symmetry on a finite periodic square lattice is investigated for an arbitrary uniform magnetic field in arbitrary dimensions. It can be used to classify eigenvectors of the Hamiltonian. The system can be converted to another system of half or lower dimensions. A higher dimensional generalization of Harper equation is obtained for tight-binding systems.

Irrational Versus Rational Charge and Statistics in Two-Dimensional Quantum Systems

We show that quasiparticle excitations with irrational charge and irrational exchange statistics exist in tight-binding systems described, in the continuum approximation, by the Dirac equation in (2+1)-dimensional space and time. These excitations can be deconfined at zero temperature, but when they are, the charge rerationalizes to the value 1/2 and the exchange statistics to that of "quartons" (half-semions).

Entanglement in disordered systems at criticality

AbstractEntanglement is a physical resource of a quantum system just like mass, charge or energy. Moreover it is an essential tool for many purposes of nowadays quantum information processing, e.g. quantum teleportation, quantum cryptography or quantum computation. In this work we investigate an extended system of N qubits. In our system a qubit is the absence or presence of an electron at a site of a tight‐binding system. Several measures of entanglement between a given qubit and the rest of the system and also the entanglement between two qubits and the rest of the system are calculated in a one‐electron picture in the presence of disorder. We invoke the power law band random matrix model which even in one dimension is able to produce multifractal states that fluctuate at all length scales. The concurrence, the tangle and the entanglement entropy all show interesting scaling properties. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Treatment of laser-field effects on a molecular wire and its coupling to the leads

The influence of strong laser pulses on molecular wires is studied within different theoretical approaches. The wire is modeled by a tight-binding system coupled to two fermionic reservoirs mimicking the electronic leads. In the present model the effect of the laser field is two-fold: it directly influences the site energies but also modulates the coupling between wire and leads. In this investigation we study the effects of two approximations on treating the indirect field effect. The results from the approximative treatment are compared to a theory which takes fully into account the laser-field effect on the coupling term.

Electron capture and transport mediated by lattice solitons

We study electron transport in a one-dimensional molecular lattice chain. The molecules are linked by Morse interaction potentials. The electronic degree of freedom, expressed in terms of a tight binding system, is coupled to the longitudinal displacements of the molecules from their equilibrium positions along the axis of the lattice. More specifically, the distance between two sites influences in an exponential fashion the corresponding electronic transfer matrix element. We demonstrate that when an electron is injected in the undistorted lattice it causes a local deformation such that a compression results leading to a lowering of the electron's energy below the lower edge of the band of linear states. This corresponds to self-localization of the electron due to a polaronlike effect. Then, if a traveling soliton lattice deformation is launched a distance apart from the electron's position, upon encountering the polaronlike state it captures the latter dragging it afterwards along its path. Strikingly, even when the electron is initially uniformly distributed over the lattice sites a traveling soliton lattice deformation gathers the electronic amplitudes during its traversing of the lattice. Eventually, the electron state is strongly localized and moves coherently in unison with the soliton lattice deformation. This shows that for the achievement of coherent electron transport we need not start with the polaronic effect.

Perfect Transfer of Many-Particle Quantum State viaHigh-Dimensional Systems with Spectrum-MatchedSymmetry

The quantum state transmission through the medium ofhigh-dimensional many-particle system (boson or spinless fermion) is generallystudied with a symmetry analysis. We discover that, if the spectrum of a Hamiltonianmatches the symmetry of a fermion or boson system in a certain fashion, aperfect quantum state transfer can be implemented without any operation onthe medium with pre-engineered nearest neighbor (NN). We also study a simplebut realistic near half-filled tight-binding fermion system with uniform NNhopping integral. We show that an arbitrary many-particle state near thefermi surface can be perfectly transferred to its translational counterpart.

Rashba quantum wire: exact solution and ballistic transport

The effect of Rashba spin–orbit interaction in quantum wires with hard-wall boundaries isdiscussed. The exact wavefunction and eigenvalue equation are worked out, pointing outthe mixing between the spin and spatial parts. The spectral properties are also studiedwithin perturbation theory with respect to the strength of the spin–orbit interaction anddiagonalization procedure. A comparison is made with the results of a simple model,the two-band model, that takes account only of the first two sub-bands of thewire. Finally, the transport properties within the ballistic regime are analyticallycalculated for the two-band model and through a tight-binding Green function forthe entire system. Single and double interfaces separating regions with differentstrengths of spin–orbit interaction are analysed by injecting carriers into the first andthe second sub-band. It is shown that in the case of a single interface the spinpolarization in the Rashba region is different from zero, and in the case of twointerfaces the spin polarization shows oscillations due to spin-selective bound states.

Transmission, reflection and localization in a random medium with absorption or gain

We study reflection and transmission of waves in a random tight-binding system withabsorption or gain for weak disorder, using a scattering matrix formalism. Our aim is todiscuss analytically the effects of absorption or gain on the statistics of wave transport.Treating the effects of absorption or gain exactly in the limit of no disorder allows us toidentify short- and long-length regimes relative to absorption or gain lengths, where theeffects of absorption/gain on statistical properties are essentially different. Inthe long-length regime, we find that a weak absorption or a weak gain induceidentical statistical corrections in the inverse localization length, but lead to differentcorrections in the mean reflection coefficient. In contrast, a strong absorptionor a strong gain strongly suppress the effect of disorder in identical ways (toleading order), both in the localization length and in the mean reflection coefficient.