On-site Potential Research Articles

Many-body localization in a non-Hermitian quasiperiodic system

In the present study, the interplay among interaction, topology, quasiperiodicity, and non-Hermiticity is studied. The hard-core bosons model on a one-dimensional lattice with asymmetry hoppings and quasiperiodic onsite potentials is selected. This model, which preserves time-reversal symmetry (TRS), will exhibit three types of phase transition: Real-complex transition of eigenenergies, topological phase transition, and many-body localization (MBL) phase transition. For the real-complex transition, it is found that the imaginary parts of the eigenenergies are always suppressed by the MBL. Moreover, by calculating the winding number, a topological phase transition can be revealed with the increase of potential amplitude, and we find that the behavior is quite different from the single-particle systems. Based on our numerical results, we conjecture that these three types of phase transition occur at the same point in the thermodynamic limit, and the MBL transition of quasiperiodic system and disordered system should belong to different universality classes. Finally, we demonstrate that these phase transitions can profoundly affect the dynamics of the non-Hermitian many-body system.

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.

Properties of Normal Modes in a Modified Disordered Klein-Gordon Lattice: From Disorder to Order

We introduce a modified version of the disordered Klein-Gordon lattice model, having two parameters for controlling the disorder strength: D, which determines the range of the coefficients of the on-site potentials, and W, which defines the strength of the nearestneighbor interactions. We fix W = 4 and investigate how the properties of the system's normal modes change as we approach its ordered version, i.e. D → 0. We show that the probability density distribution of the normal mode's frequencies takes a 'U'-shaped profile as D decreases. Furthermore, we use two quantities for estimating the mode's spatial extent, the so-called localization volume V (which is related to the mode's second moment) and the mode's participation number P. We show that both quantities scale as ∝ D−2 when D approaches zero and we numerically verify a proportionality relation between them as V/P ≈ 2.6.

Piecewise Linear Representation of Finance Time Series: Quantum Mechanical Tool

In this work, a piecewise linear representation of economic time series is presented. The representation is based on calculating local maxima and minima in time series. Then, we study the localization properties of the 1D tight-binding equation, where the on-site potential is replaced by a piecewise linear function. The piecewise linear representation is derived from economic time series databases. We carry out numerical work involving direct diagonalization to study eigenvalues of the system. This numerical scheme is applied to different segments of the time series. It is shown that this mathematical tool could be used as a moving indicator to study finance charts.

Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms.

We explore the eigenvalue statistics of a non-Hermitian version of the Su-Schrieffer-Heeger model, with imaginary on-site potentials and randomly distributed hopping terms. We find that owing to the structure of the Hamiltonian, eigenvalues can be purely real in a certain range of parameters, even in the absence of parity and time-reversal symmetry. As it turns out, in this case of purely real spectrum, the level statistics is that of the Gaussian orthogonal ensemble. This demonstrates a general feature which we clarify that a non-Hermitian Hamiltonian whose eigenvalues are purely real can be mapped to a Hermitian Hamiltonian which inherits the symmetries of the original Hamiltonian. When the spectrum contains imaginary eigenvalues, we show that the density of states (DOS) vanishes at the origin and diverges at the spectral edges on the imaginary axis. We show that the divergence of the DOS originates from the Dyson singularity in chiral-symmetric one-dimensional Hermitian systems and derive analytically the asymptotes of the DOS which is different from that in Hermitian systems.

Thermoelectric power generation efficiency of zigzag monolayer nanoribbon of bismuth

The thermoelectric power generation efficiency of a bismuth monolayer nanoribbon has been studied theoretically. We calculate the conductance of such a structure using the multi-orbital tight-binding model and also recursive Green’s function method, in the presence of a substrate and on-site potential. For the case of the substrate-supported bismuth nanoribbon and by proper selection of on-site potential, a boxcar shape conductance in terms of energy has been obtained. Using the Landauer–Büttiker formalism in the non-linear response regime, we calculate heat and charge currents at low temperatures. By calculation of the electrical output power and power conversion thermoelectric efficiency, we have illustrated that such a structure can operate at high thermoelectric efficiency and also a considerable power generation rate.

Beyond universal behavior in the one-dimensional chain with random nearest-neighbor hopping

We study the one-dimensional nearest neighbor tight binding model of electrons with independently distributed random hopping and no on-site potential (i.e. off-diagonal disorder with particle-hole symmetry, leading to sub-lattice symmetry, for each realization). For non-singular distributions of the hopping, it is known that the model exhibits a universal, singular behavior of the density of states $\rho(E) \sim 1/|E \ln^3|E||$ and of the localization length $\xi(E) \sim |\ln|E||$, near the band center $E = 0$. (This singular behavior is also applicable to random XY and Heisenberg spin chains; it was first obtained by Dyson for a specific random harmonic oscillator chain). Simultaneously, the state at $E = 0$ shows a universal, sub-exponential decay at large distances $\sim \exp [ -\sqrt{r/r_0} ]$. In this study, we consider singular, but normalizable, distributions of hopping, whose behavior at small $t$ is of the form $\sim 1/ [t \ln^{\lambda+1}(1/t) ]$, characterized by a single, continuously tunable parameter $\lambda > 0$. We find, using a combination of analytic and numerical methods, that while the universal result applies for $\lambda > 2$, it no longer holds in the interval $0 < \lambda < 2$. In particular, we find that the form of the density of states singularity is enhanced (relative to the Dyson result) in a continuous manner depending on the non-universal parameter $\lambda$; simultaneously, the localization length shows a less divergent form at low energies, and ceases to diverge below $\lambda = 1$. For $\lambda < 2$, the fall-off of the $E = 0$ state at large distances also deviates from the universal result, and is of the form $\sim \exp [-(r/r_0)^{1/\lambda}]$, which decays faster than an exponential for $\lambda < 1$.

Numerical study of the transverse localization of waves in one-dimensional lattices with randomly distributed gain and loss: effect of disorder correlations

We study numerically the effects of short- and long-range correlations on the localization properties of the eigenstates in a one-dimensional disordered lattice characterized by a random non-Hermitian Hamiltonian, where the imaginary part of the on-site potential is random. We calculate the participation number versus strengths of disorder and correlation. In the short-ranged case and when the correlation length is sufficiently small, we find that there exists a critical value of the disorder strength, below which enhancement and above which suppression of localization occurs as the correlation length increases. In the region where the correlation length is larger, localization is suppressed in all cases. Similar behavior is obtained for long-range correlations as the disorder strength and the correlation exponent are varied. Unlike in the case of a long-range correlated real random potential, no signature of the localization transition is found in a long-range correlated imaginary random potential. In the region where localization is enhanced in the presence of long-range correlations, we find that the enhancement occurs in the whole energy band, but is strongest near the band center. In addition, we find that the anomalous localization enhancement effect occurs near the band center in the long-range correlated case.

Topological characterization of non-Hermitian multiband systems using Majorana's stellar representation

For topological characterization of non-Hermitian multiband systems, Majorana's stellar representation (MSR) is applied to 1D multiband models consisting of asymmetric nearest-neighbor hopping and imaginary on-site potentials. The number of edge states isolated from the continuous bulk bands in the complex energy plane is successfully linked with a topological invariant constructed from MSR. Specifically, the number of isolated edge states can be obtained from a winding number defined for the Majorana stars, which also allows for a geometric visualization of the topology related to the isolated edge modes. A remarkable success of our approach is that our winding number characterization remains valid even in the presence of exceptional points of the continuous bulk bands, where the Hamiltonian becomes non-diagonalizable and hence conventional topological invariants such as the Zak phase and the Chern number cannot be properly defined. Furthermore, cases with the so-called non-Hermitian skin effect are also studied, showing that the bulk-boundary correspondence between our defined winding numbers and isolated edge states can be restored. Of particular interest is a four-band example with an odd number of isolated edge states, where the Zak phase approach necessarily fails upon removing the skin effect, but our MSR-based characterization works equally well. For these reasons, our study is expected to be widely useful in topological studies of non-Hermitian multiband systems, regardless of the skin effect or the presence of the exceptional points in non-Hermitian systems.

Pressure Effects on the Magnetic Phase Diagram of the CeNMSb2 (NM: Au and Ag): A DFT Study.

We explore the influence of pressure on the magnetic ground state of the heavy-fermion antiferromagnet (ferromagnet) CeAuSb (CeAgSb) using first-principles calculations. The total-energy differences obtained by including the spin-orbit interactions and the on-site Coulomb potential for the Ce-derived 4f-orbitals are necessary to realize the accurate magnetic ground state of CeNMSb (NM: Au and Ag). According to our results, the appearance of a new magnetic phase of CeAuSb (CeAgSb) at the pressure of 2.1 GPa (3.5 GPa) is due to the rotation of the magnetic easy axis from the <001> to the <100> direction. Additionally, our data confirm that CeAgSb is antiferromagnetic (AFM) above a critical pressure , and such a tendency is expected for CeAuSb and remains to be seen. Through the spin-orbit-coupling Hamiltonian and detailed information on the occupation of individual 4f-orbitals of the Ce atom obtained by the electronic-structure calculations, we can deduce the rotation of the magnetic easy axis upon the application of pressure. According to the present and previous studies, the differences among the magnetic properties of CeNMSb (NM: Cu, Ag and Au) compounds are not due to the different noble metals, but due to the subtle differences in the relative position of Ce atoms and, in turn, different occupations of Ce 4f-orbitals.

Prethermalization in a classical phonon field: Slow relaxation of the number of phonons

We investigate the emergence of an astonishingly long pre-thermal plateau in a classical phonon field, here a harmonic chain with on-site pinning. Integrability is broken by a weak anharmonic on-site potential with strength $\lambda$. In the small $\lambda$ limit, the approach to equilibrium of a translation invariant initial state is described by kinetic theory. However, when the phonon band becomes narrow, we find that the (non-conserved) number of phonons relaxes on much longer time scales than kinetic. We establish rigorous bounds on the relaxation time, and develop a theory that yields exact predictions for the dissipation rate in the limit $\lambda \to 0$. We compare the theoretical predictions with data from molecular dynamics simulations and find good agreement. Our work shows how classical systems may exhibit phenomena which at the first glance appear to require quantization.

Survival of current in a periodically driven hard-core bosonic system

We study the survival of the current induced initially by applying a twist at the boundary of a chain of hard-core bosons (HCBs), subject to a periodic double $\delta$-function kicks in the staggered on-site potential. We study the current flow and the work-done on the system at the long-time limit as a function of the driving frequency. Like a recent observation in the HCB chain with single $\delta$-function kick in the staggered on-site potential, here we also observe many dips in the current flow and concurrently many peaks in the work-done on the system at some specific values of the driving frequency. However, unlike the single kicked case, here we do not observe a complete disappearance of the current in the limit of a high driving frequency, which shows the absence of any dynamical localization in the double $\delta$-functions kicked HCB chain. Our analytical estimations of the saturated current and the saturated work-done, defined at the limit of a large time together with a high driving frequency, match very well with the exact numerics. In the case of the very small initial current, induced by a very small twist $\nu$, we observe that the saturated current is proportional to $\nu$. Finally, we study the time-evolution of the half-filled HCB chain where the particles are localized in the central part of the chain. We observe that the particles spread linearly in a light-cone like region at the rate determined by the maximum value of the group velocity. Except for a very trivial case, the maximum group velocity never vanishes, and therefore we do not observe any dynamical localization in the system.

Surface charge theorem and topological constraints for edge states: Analytical study of one-dimensional nearest-neighbor tight-binding models

For a wide class of noninteracting tight-binding models in one dimension we present an analytical solution for all scattering and edge states on a half-infinite system. Without assuming any symmetry constraints we consider models with nearest-neighbor hoppings and one orbital per site but arbitrary size of the unit cell and generic modulations of on-site potentials and hoppings. The solutions are parametrized by determinants which can be calculated from recursion relations. This representation allows for an elegant analytic continuation to complex quasimomentum consistent with previous treatments for continuum models. Two important analytical results are obtained: (1) An explicit proof of the surface charge theorem is presented including a unique relationship between the boundary charge $Q_B^{(\alpha)}$ of a single band $\alpha$ and the bulk polarization in terms of the Zak-Berry phase with no unknown integer left. This establishes a precise form of a bulk-boundary correspondence relating the {\it boundary charge of a single band} to bulk properties. (2) We derive a topological constraint for the phase-dependence of the edge state energies, where the phase variable describes a continuous shift of the lattice towards the boundary. The topological constraint is shown to be equivalent to the quantization of a topological index $I=\Delta Q_B-\bar{\rho}\in \{-1,0\}$ introduced in an accompanying letter [arXiv:1911.06890]. Here $\Delta Q_B$ is the change of the boundary charge $Q_B$ for a given chemical potential in the insulating regime when the lattice is shifted by one site towards the boundary, and $\bar{\rho}$ is the average charge per site (both in units of the elementary charge $e=1$). This establishes an interesting link between universal properties of the boundary charge and edge state physics discussed within the field of topological insulators.

Topological invariants to characterize universality of boundary charge in one-dimensional insulators beyond symmetry constraints

In the absence of any symmetry constraints we address universal properties of the boundary charge $Q_B$ for a wide class of nearest-neighbor tight-binding models in one dimension with one orbital per site but generic modulations of on-site potentials and hoppings. We provide a precise formulation of the bulk-boundary correspondence relating the boundary charge of a single band uniquely to the Zak phase evaluated in a particular gauge. We reveal the topological nature of $Q_B$ by proving the quantization of a topological index $eI=\Delta Q_B - \bar{\rho}$, where $\Delta Q_B$ is the change of $Q_B$ when shifting the lattice by one site towards a boundary and $\bar{\rho}$ is the average charge per site. For a single band we find this index to be given by the winding number of the fundamental phase difference of the Bloch wave function between the two lattice sites defining the boundary of a half-infinite system. For a given chemical potential we establish a central topological constraint $I\in\{-1,0\}$ related only to charge conservation of particles and holes. Our results are shown to be stable against disorder and we propose generalizations to multi-channel and interacting systems.

Designing pretty good state transfer via isospectral reductions

We present an algorithm to design networks that feature pretty good state transfer (PGST), which is of interest for high-fidelity transfer of information in quantum computing. Realizations of PGST networks have so far mostly relied either on very special network geometries or imposed conditions such as transcendental on-site potentials. However, it was recently shown [Eisenberg et al., arXiv:1804.01645] that PGST generally arises when a network's eigenvectors and the factors $P_{\pm}$ of its characteristic polynomial $P$ fulfill certain conditions, where $P_{\pm}$ correspond to eigenvectors which have $\pm 1$ parity on the input and target sites. We combine this result with the so-called isospectral reduction of a network to obtain $P_{\pm}$ from a dimensionally reduced form of the Hamiltonian. Equipped with the knowledge of the factors $P_{\pm}$, we show how a variety of setups can be equipped with PGST by proper tuning of $P_{\pm}$. Having demonstrated a method of designing networks featuring pretty good state transfer of single site excitations, we further show how the obtained networks can be manipulated such that they allow for robust storage of qubits. We hereby rely on the concept of compact localized states, which are eigenstates of a Hamiltonian localized on a small subdomain, and whose amplitudes completely vanish outside of this domain. Such states are natural candidates for the storage of quantum information, and we show how certain Hamiltonians featuring pretty good state transfer of single site excitation can be equipped with compact localized states such that their transfer is made possible.

Effects of disorder on the transport and thermoelectric properties of silicene superlattices

Abstract Unavoidable structural disorder associated with the variation of the widths of barriers and wells as well as the heights of barriers in superlattices of 2D materials can affect considerably electronic transport and related phenomena. In this work, we study the impact of structural disorder on the electronic transport and thermoelectric properties of gated silicene superlattices (GSSLs). A low-energy effective Hamiltonian has been used to describe electrons in silicene. The transfer matrix approach, the Landauer–Buttiker formalism and the Cutler–Mott formula have been implemented to obtain the transport and thermoelectric properties. In particular, the conductance, Seebeck coefficient and power factor are investigated in ordered and disordered GSSLs. The results show that disorder related to the width of barriers-wells is not equivalent to the one associated to the height of barriers. The former barely changes the transport and thermoelectric coefficients at low energy, while the latter greatly affects them in the whole energy range. We also assess the disorder associated to the on-site potential of silicene layers, finding that its influence is limited. So, our results indicate that in the design and fabrication of GSSLs a precise control of the height of the barriers is required in order to have and preserve good thermoelectric properties.

The Determination of Listeria monocytogenes in Foods with Optical Biosensors

Listeria monocytogenes is a food-borne intracellular pathogen that is resistant to adverse conditions of food processing and is a causative agent of high mortality listeriosis disease. Analysis of large food lots is limited by culture methods. Nowadays, although the conventional culture methods have been adopted as the gold standard method, they can be insufficient to control food parties that reach very large quantities. Biosensors with on-site detection potential and their characterizing with high accuracy and precision offers many opportunities for real-time estimation of industrial contamination. As the most promising technique for rapid detection of L.monocytogenes, ones based on surface plasmon resonance (SPR) and fiber optic biosensors (FOBs) where direct or indirect detections can be made by detecting the interaction of the biomarker element with the optical field without marking or labeling, have come to the fore. SPR and FOBs can be detected directly in the range of 102-106 cfu/ml and ≤101-103 cfu/ml, respectively.

Nagaoka ferromagnetism observed in a quantum dot plaquette.

Engineered, highly controllable quantum systems are promising simulators of emergent physics beyond the simulation capabilities of classical computers1. An important problem in many-body physics is itinerant magnetism, which originates purely from long-range interactions of free electrons and whose existence in real systems has been debated for decades2,3. Here we use a quantum simulator consisting of a four-electron-site square plaquette of quantum dots4 to demonstrate Nagaoka ferromagnetism5. This form of itinerant magnetism has been rigorously studied theoretically6-9 but has remained unattainable in experiments. We load the plaquette with three electrons and demonstrate the predicted emergence of spontaneous ferromagnetic correlations through pairwise measurements of spin. We find that the ferromagnetic ground state is remarkably robust to engineered disorder in the on-site potentials and we can induce a transition to the low-spin state by changing the plaquette topology to an open chain. This demonstration of Nagaoka ferromagnetism highlights that quantum simulators can be used to study physical phenomena that have not yet been observed in any experimental system. The work also constitutes an important step towards large-scale quantum dot simulators of correlated electron systems.

Anomalous energy diffusion in two-dimensional nonlinear lattices.

Heat transport in one-dimensional (1D) momentum-conserved lattices is generally assumed to be anomalous, thus yielding a power-law divergence of thermal conductivity with system length. However, whether heat transport in a two-dimensional (2D) system is anomalous or not is still up for debate because of the difficulties involved in experimental measurements or due to the insufficiently large simulation cell size. Here we simulate energy and momentum diffusion in the 2D nonlinear lattices using the method of fluctuation correlation functions. Our simulations confirm that energy diffusion in the 2D momentum-conserved lattices is anomalous and can be well described by the Lévy-stable distribution. As is expected, we verify that 2D nonlinear lattices with on-site potentials exhibit normal energy diffusion, independent of the dimension. Contrary to the hypothesis of a 1D system, we further clarify that anomalous heat transport in the 2D momentum-conserved system cannot be corroborated by the momentum superdiffusion any longer. Our findings offer some valuable insights into mechanisms of thermal transport in 2D system.

Anomalous localization enhancement in one-dimensional non-Hermitian disordered lattices

We study numerically the localization properties of eigenstates in a one-dimensional random lattice described by a non-Hermitian disordered Hamiltonian, where both the disorder and the non-Hermiticity are inserted simultaneously in the on-site potential. We calculate the averaged participation number, the Shannon entropy and the structural entropy as a function of other parameters. We show that, in the presence of an imaginary random potential, all eigenstates are localized in the thermodynamic limit and strong anomalous Anderson localization occurs at the band center. In contrast to the usual localization anomalies where a weaker localization is observed, the localization of the eigenstates near the band center is strongly enhanced in the present non-Hermitian model. This phenomenon is associated with the occurrence of a large number of strongly-localized states with pure imaginary energy eigenvalues.