Holstein Polaron Model Research Articles

Modeling Of Charge Dynamics in Synthetic DNA under the Influence of an External Electric Field

Based on the Holstein polaron model, the problem of modeling Bloch oscillations of a quantum charged particle in a chain of classical sites placed in a uniform electric field is considered. As is known, in a rigid lattice, Bloch oscillations describe charge oscillations under the influence of a constant electric field. Biopolymers are considered as non-rigid lattice, and movement of lattice sites have significant effect on the charge dynamics. Most of the computational experiments were carried out with the parameters values of homogeneous polyguanine fragments of DNA. At the initial moment, the charge “arises” at one site of the chain placed in a field with constant intensity, so charge have no time to form a polaron. The dynamics of charge in an unperturbed chain (at zero temperature) is simulated. Minimum chain length is estimated, for which end effects have not influence on the charge dynamics during Bloch oscillations. For the center of mass motion of the charge, a comparative analysis was carried out with the dynamics of the polaron, previously studied by Korshunova and Lakhno. A simulation of Bloch charge oscillations at a finite temperature was performed. To determine the frequency of charge oscillations, in addition to visual control, a Fourier series expansion was used. It is shown that averaging over realizations leads to smoothing of oscillations, which complicates the study of the influence of temperature on Bloch oscillations. Based on the simulation results, we assume that it is necessary to study the dynamics of individual implementations in more detail, in order to determine the temperature at which Bloch oscillations are disrupted.

Global sampling of Feynman's diagrams through normalizing flow

Normalizing flows (NF) are powerful generative models with increasing applications in augmenting Monte Carlo algorithms due to their high flexibility and expressiveness. In this work we explore the integration of NF in the diagrammatic Monte Carlo (DMC) method, presenting an architecture designed to sample the intricate multidimensional space of Feynman's diagrams through dimensionality reduction. By decoupling the sampling of diagram order and interaction times, the flow focuses on one interaction at a time. This enables one to construct a general diagram by employing the same unsupervised model iteratively, dressing a zero-order diagram with interactions determined by the previously sampled order. The resulting NF-augmented DMC method is tested on the widely used single-site Holstein polaron model in the entire electron-phonon coupling regime. The obtained data show that the model accurately reproduces the diagram distribution by reducing sample correlation and observables' statistical error, constituting the first example of global sampling strategy for connected Feynman's diagrams in the DMC method. Published by the American Physical Society 2024

Method for obtaining polaron mobility using real and imaginary time path-integral quantum Monte Carlo

We developed a path-integral quantum Monte Carlo-based methodology for calculation of polaron mobility in systems with electron-phonon interaction. Within the method, the current-current correlation function in both the imaginary and real time is calculated in a numerically exact way. The choice of basis for representation of the path integral enabled us to reduce the sign problem and perform real-time calculations for longer times. The DC polaron mobility was extracted by performing analytic continuation that makes use of both the real and imaginary-time data. The method was applied to the Holstein polaron model in one dimension. We obtained reliable results for the temperature dependence of the Holstein polaron mobility for interactions ranging from weak to strong and temperatures that are not too low.

Polaron dynamics of Bloch–Zener oscillations in an extended Holstein model

Recent developments in qubit engineering make circuit quantum electrodynamics devices promising candidates for the study of Bloch oscillations (BOs) and Landau–Zener (LZ) transitions. In this work, a hybrid circuit chain with alternating site energies under external electric fields is employed to study Bloch–Zener oscillations (BZOs), i.e. coherent superpositions of BOs and LZ transitions. We couple each of the tunable qubits in the chain to dispersionless optical phonons and build an extended Holstein polaron model with the purpose of investigating vibronic effects in the BZOs. We employ an extension of the Davydov ansatz in combination with the Dirac–Frenkel time-dependent variational principle to simulate the dynamics of the qubit chain under the influence of high-frequency quantum harmonic oscillators. Band gaps emerge due to energy differences in site energies at alternating qubit sites, and are shown to play key roles in tuning band structures and time periodic reconstructions of the wave patterns. In the absence of qubit–phonon interactions, the qubits undergo either standard BZOs or breathing modes, depending on whether the initial wave packet is formed by a broad or narrow Gaussian wave packet, respectively. The BZOs can get localized in space if the band gaps are sufficiently large. In the presence of qubit–phonon coupling, the periodic behavior of BZOs can be washed out and undergo dynamic localization. The influence of an ohmic bath on the dynamics of BZOs is investigated by means of a Markovian master equation approach. Finally, we calculate the von Neumann entropy as a measure of the entanglement between qubits and phonons.

Equilibrium Charge Distribution in a Finite Chain with a Trapping Site

The paper considers the problem of the distribution of a quantum particle in a classical one-dimensional lattice with a potential well. The cases of a rigid chain, a Holstein polaron model, and a polaron in a chain with temperature are investigated by direct modeling at fixed parameters. As is known, in the one-dimensional case, a particle is captured by an arbitrarily shallow potential well with an increase of the box size. In the case of a finite chain and finite temperatures, we have quite the opposite result, when a particle, being captured in a well in a short chain, turns into delocalized state with an increase in the chain length. These results may be helpful for further understanding of charge transfer in DNA, where oxoguanine can be considered as a potential well in the case of hole transfer when for excess electron transfer it is thymine dimer.

Strong polaronic effect in a superatomic two-dimensional semiconductor.

Crystalline solids assembled from superatomic building blocks are attractive functional materials due to their hierarchical structure, multifunctionality, and tunability. An interesting example is Re6Se8Cl2, in which the Re6Se8 building blocks are covalently linked into two-dimensional (2D) sheets that are stacked into a layered van der Waals solid. It is an indirect gap semiconductor that, when heavily doped, becomes a superconductor at low temperatures. Given the finite electronic bandwidths (300-400 meV), carrier properties in this material are expected to be strongly influenced by coupling to phonons. Here, we apply angle-resolved photoemission spectroscopy to probe the valence band edge (VBE) of Re6Se8Cl2. We find that dispersion of the VBE is a strong function of temperature. The bandwidth is W = 120 ± 30 meV at 70 K and decreases by one order of magnitude to W ∼ 10 ± 20 meV as temperature is increased to 300 K. This observation reveals the dominant polaronic effects in Re6Se8Cl2, consistent with the Holstein polaron model commonly used to describe molecular solids.

Eigenstate thermalization and quantum chaos in the Holstein polaron model

The eigenstate thermalization hypothesis (ETH) is a successful theory that provides sufficient criteria for ergodicity in quantum many-body systems. Most studies were carried out for Hamiltonians relevant for ultracold quantum gases and single-component systems of spins, fermions, or bosons. The paradigmatic example for thermalization in solid-state physics are phonons serving as a bath for electrons. This situation is often viewed from an open-quantum system perspective. Here, we ask whether a minimal microscopic model for electron-phonon coupling is quantum chaotic and whether it obeys ETH, if viewed as a closed quantum system. Using exact diagonalization, we address this question in the framework of the Holstein polaron model. Even though the model describes only a single itinerant electron, whose coupling to dispersionless phonons is the only integrability-breaking term, we find that the spectral statistics and the structure of Hamiltonian eigenstates exhibit essential properties of the corresponding random-matrix ensemble. Moreover, we verify the ETH ansatz both for diagonal and offdiagonal matrix elements of typical phonon and electron observables, and show that the ratio of their variances equals the value predicted from random-matrix theory.

Vibron properties in quasi 1D molecular structures: the case of two parallel unshifted macromolecuar chains

We study the hopping mechanism of the vibron excitation transport in the system of two parallel unshifted 1D macromolecuar chains in the framework of non-adiabatic polaron theory. We suppose that the vibron interaction with thermal oscillations of the macromolecular structural elements will result in vibron self-trapping and the formation of the partial dressed vibron state. We also suppose that quasiparticle motion takes place via a sequence of random sitejumps, in each of which the quasiparticle can migrate either to the first neighbor site of the macromolecular chain. With use of the modified Holstein polaron model, we calculate the vibron effective mass in dependence of the basic system parameters and temperature. Special attention is paid to the influence of interchain coupling on vibron dressing. We find that for certain values of the system parameters the quasiparticle mass abruptly changes.

Polaron tunneling dynamics of a linear polymer of nucleotides

The formation of polaron and its migration in a DNA chain are studied within asemiclassical Peyrard–Bishop–Holstein polaron model. Comparing the energetics of thepolaron system found from the quantum-chemical and semiclassical calculations,we extract the charge–phonon coupling constant for poly-DNA sequences. Thecoupling constant is found to be larger for G–C than for the A–T pairs. With thiscoupling constant we study tunneling in DNA. The rates and the nature of tunnelinghave strong dependence on the DNA sequence. By changing the trap positions inthe molecular bridge the tunneling rate can be varied by up to seven orders ofmagnitude.

Dynamics of a self‐trapped quasiparticle in a one‐dimensional molecular lattice with two phonon modes

AbstractIn this work we study numerically the dynamics of a self‐trapped quasiparticle (electron, hole or excitation) in a one‐dimensional molecular chain with two phonon modes, one acoustical and one optical. This model generalizes the model of Davydov solitons and Holstein polaron model: Davydov solitons are formed by a quasiparticle interacting with acoustical phonons, and Holstein polarons are formed due the interaction with optical phonons. Our model describes soliton‐like (large polaron) states in soft quasi‐one‐dimensional systems, such as conducting polymers, alpha‐helical polypeptide macromolecules, DNA etc. For the purpose of modelling self‐trapping of quasiparticles without any influence of chain boundaries, we consider a molecular chain with periodic boundary conditions. Then, to study the dynamics of quasiparticles in such states, we use the adiabatic acceleration method. We show that soliton velocity is an oscillating function of time. These oscillations are caused by the presence of optical vibrations and by the Peierls–Nabarro barrier formed by discrete lattice. We also show that self‐trapping of a quasiparticle takes place at random dynamical lattice potential induced by some random initial conditions for acoustical and optical phonons, provided the random range constant, i.e., the amplitude of random field, is not too big. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Extended Holstein polaron model for charge transfer in dry DNA

The variational method is applied to the study of charge transfer in dry DNA by using an extended Holstein small polaron model in two cases: the site-dependent finite-chain discrete case and the site-independent continuous one. The treatments in the two cases are proven to be consistent in theory and calculation. Discrete and continuous treatments of Holstein model both can yield a nonlinear equation to describe the charge migration in an actual long-range DNA chain. Our theoretical results of binding energy Eb, probability amplitude of charge carrier and the relation between energy and charge–lattice coupling strength are in accordance with the available experimental results and recent theoretical calculations.

Extrinsic Semiconductor Character of a Double Strand of DNA: Holstein's Polarons as Donors and Acceptors

We study the electrical conductivity problem of DNA, applying the Holstein's polaron model to a double strand of DNA. We show that the Holstein's polarons act as donors and acceptors in DNA and that the existence of such donors and acceptors provides us the extrinsic semiconductor character of DNA. This character of DNA may explain with a unified point of view almost all the known results recently obtained by experiments in the study of conductivity problems of DNA, which seem so controversial so far.

Small polarons in dense lattice systems

There is considerable evidence for the persistence of small polaron like entities in colossal magnetoresistance oxides, which are dense electronic systems with electron density n≲1 per site. This has brought up again the question of whether and how small (narrow band) polaronic states survive in a dense electronic system. We investigate this question in a simple one band Holstein polaron model, in which spinless electrons on a tight binding lattice cause an on-site lattice distortion x0. In the small polaron limit, each electron is localized, and the electron hopping tij is neglected. We develop a systematic approach in powers of tij, identify classical t0, quantum mean field t1, and quantum fluctuation t2 terms, and show that the last two terms are relatively small, even for dense systems, so long as the narrowed polaron bandwidth t*=t exp(−u) is much smaller than the Einstein phonon energy ħω0. (Here u=(x20/2x2zp) with xzp being the zero point phonon displacement.) The relevance of these results for CMR oxides is briefly discussed.

On Algebraic Integrability of the Deformed Elliptic Calogero-Moser Problem

We discuss stationary solutions of the discrete nonlinear Schrödinger equation (DNSE) with a potential of the ϕ 4 type which is generically applicable to several quantum spin, electron and classical lattice systems. We show that there may arise chaotic spatial structures in the form of incommensurate or irregular quantum states. As a first (typical) example we consider a single electron which is strongly coupled with phonons on a 1D chain of atoms — the (Rashba)–Holstein polaron model. In the adiabatic approximation this system is conventionally described by the DNSE. Another relevant example is that of superconducting states in layered superconductors described by the same DNSE. Amongst many other applications the typical example for a classical lattice is a system of coupled nonlinear oscillators. We present the exact energy spectrum of this model in the strong coupling limit and the corresponding wave function. Using this as a starting point we go on to calculate the wave function for moderate coupling and find that the energy eigenvalue of these structures of the wave function is in exquisite agreement with the exact strong coupling result. This procedure allows us to obtain (numerically) exact solutions of the DNSE directly. When applied to our typical example we find that the wave function of an electron on a deformable lattice (and other quantum or classical discrete systems) may exhibit incommensurate and irregular structures. These states are analogous to the periodic, quasiperiodic and chaotic structures found in classical chaotic dynamics.

Fractal and Chaotic Solutions of the Discrete Nonlinear Schrödinger Equation in Classical and Quantum Systems

We discuss stationary solutions of the discrete nonlinear Schrödinger equation (DNSE) with a potential of the ϕ 4 type which is generically applicable to several quantum spin, electron and classical lattice systems. We show that there may arise chaotic spatial structures in the form of incommensurate or irregular quantum states. As a first (typical) example we consider a single electron which is strongly coupled with phonons on a 1D chain of atoms — the (Rashba)–Holstein polaron model. In the adiabatic approximation this system is conventionally described by the DNSE. Another relevant example is that of superconducting states in layered superconductors described by the same DNSE. Amongst many other applications the typical example for a classical lattice is a system of coupled nonlinear oscillators. We present the exact energy spectrum of this model in the strong coupling limit and the corresponding wave function. Using this as a starting point we go on to calculate the wave function for moderate coupling and find that the energy eigenvalue of these structures of the wave function is in exquisite agreement with the exact strong coupling result. This procedure allows us to obtain (numerically) exact solutions of the DNSE directly. When applied to our typical example we find that the wave function of an electron on a deformable lattice (and other quantum or classical discrete systems) may exhibit incommensurate and irregular structures. These states are analogous to the periodic, quasiperiodic and chaotic structures found in classical chaotic dynamics.

The polaron: Ground state, excited states, and far from equilibrium

The authors describe a variational approach for solving the Holstein polaron model with dynamical quantum phonons on an infinite lattice. The method is simple, fast, extremely accurate, and gives ground and excited state energies and wavefunctions at any momentum k. The method can also be used to calculate coherent quantum dynamics for inelastic tunneling and for strongly driven polarons far from equilibrium.

Localized excitations in hydrogen-bonded molecular crystals.

Localized excitations analogous to the small Holstein polaron, to localized modes in alkali halides, and to localized excitonic states, are postulated for a set of internal vibrational modes in crystalline acetanilide. The theoretical framework in which one can describe the characteristics of the ir and Raman spectroscopy peaks associated with these localized states is adequately provided by the Davydov model (formally equivalent to the Holstein polaron model). The possible low-lying excitations arising from this model are determined using a variational approach. Hence, the contribution to the spectral function due to each type of excitation can be calculated. The internal modes of chief concern here are the amide-I (C?O stretch) and the N---H stretch modes for which we demonstrate consistency of the theoretical model with the available ir data. Past theoretical approaches will be discussed and reasons why one should prefer one description over another will be examined.

Polaron Lattices

AbstractThe Holstein polaron model in a linear chain is extended to several electrons. A filled polaron band results, which is stable for any number of electrons (in the continuum limit).