We describe a variational method to solve the Holstein model for an electron coupled to dynamical, quantum phonons on an infinite lattice. The variational space can be systematically expanded to achieve high accuracy with modest computational resources (12-digit accuracy for the 1d polaron energy at intermediate coupling). We compute ground and low-lying excited state properties of the model at continuous values of the wavevector k in essentially all parameter regimes. Our results for the polaron energy band, effective mass and correlation functions compare favorably with those of other numerical techniques including DMRG, Global Local and exact diagonalization. We find a phase transition for the first excited state between a bound and unbound system of a polaron and an additional phonon excitation. The phase transition is also treated in strong coupling perturbation theory.

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Mustre de Leon et al. Reply: Koval et al. [1] appear to agree with the physical results obtained in Ref. [2], but assert that our exact results for the coupled electron-phonon model can also be calculated accurately in an adiabatic approximation.We partially agree with this conclusion for some properties, but note that it can be reached only by comparison with a (numerically) exact calculation. In addition, we show that while an adiabatic approximation explains several of the exact results, it fails for at least two important properties in the intermediate and strong coupling regimes: the tunnel splitting and the strength of the optical absorption. In view of rapidly improving experimental probes for polarons and polarization, controlled quantitative calculations are necessary.There are several versions of the adiabatic approximation used in the literature: (a) The ionic coordinates are treated as parameters, and the total energy is minimized as a function of these parameters. (b) The total energy is expanded to quadratic order about a minimum, and the zero-point and harmonic phonon excitations are included.(c) The total energy is calculated for all relevant ionic coordinates, resulting in a multivariable nonlinear potential coupling all of the ionic degrees of freedom. This nonlinear problem is then solved "exactly. " It is clear that versions (a) and (b) of the adiabatic approximation fail qualitatively for intermediate and strong coupling, because they neglect tunneling between degenerate minima. Koval et al. consider the more sophisticated version (c), which results in a difficult calculation.The electronic energy must be obtained for all relevant phonon coordinates, and used to calculate a large, nonsparse Hamiltonian in the basis of infrared and Raman phonons~ntR, n~). The Hamiltonian matrix must then be diagonalized numerically.To calculate absorption spectra, one must take into account that the dipole operator has an electronic as well as a phonon contribution, and thus in the adiabatic approximation is a nontrivial function of the phonon coordinates that must be numerically tabulated and used to obtain matrix elements. In contrast, for the exact method used in Ref.[2], the Hamiltonian matrix is sparse and trivial to calculate, and the dipole operator is also trivial. (Our Hamiltonian matrix is, however, somewhat larger. ) The adiabatic calculation is thus significantly more difficult to program than the exact one, and may not even save computer resources or allow calculations for larger systems, as compared to our exact numerical approach.It is, nonetheless, of interest to know whether one will obtain accurate results if one goes to the trouble of calculating in the adiabatic approximation.We have quantitatively compared energies and eigenstates by diagonalizing the Hamiltonian in the exact and in the adiabatic approximation version (c), with the coupling to Raman phonons Az set to zero for simplicity. We find that for strong electron-IR phonon coupling, AiR, the adiabatic approximation yields ground an...

Layered transition metal dichalcogenides (TMDs) are commonly classified as quasi-two-dimensional materials, meaning that their electronic structure closely resembles that of an individual layer, which results in resistivity anisotropies reaching thousands. Here, we show that this rule does not hold for 1T-TaS 2-a compound with the richest phase diagram among TMDs. Although the onset of charge density wave order makes the in-plane conduction non-metallic, we reveal that the out-of-plane charge transport is metallic and the resistivity anisotropy is close to one. We support our findings with ab initio calculations predicting a pronounced quasi-onedimensional character of the electronic structure. Consequently, we interpret the highly debated metal-insulator transition in 1T-TaS 2 as a quasi-one-dimensional instability, contrary to the long-standing Mott localisation picture. In a broader context, these findings are relevant for the newly born field of van der Waals heterostructures, where tuning interlayer interactions (e.g., by twist, strain, intercalation, etc.) leads to new emergent phenomena.

We develop a new three-dimensional multiparticle Monte Carlo (3DmpMC) approach in order to study the hopping charge transport in disordered organic molecular media. The approach is applied here to study the charge transport across an energetically disordered organic molecular heterojunction, known to strongly influence the characteristics of the multilayer devices based on thin organic films. The role of energetic disorder and its spatial correlations, known to govern the transport in the bulk, are examined here for the bilayer homopolar system where the heterojunction represents the bottleneck for the transport. We study the effects of disorder on both sides of the heterojunction, the effects of the spatial correlation within each material and among the layers. Most importantly, the 3DmpMC approach permits us to treat correctly the effects of the Coulomb interaction among carriers in the region where the charge accumulation in the device is particularly important and the Coulomb interaction most pronounced. The Coulomb interaction enhances the current by increasing the electric field at the heterojunction as well as by affecting the thermalization of the carriers in front of the barrier. Our MC simulations are supplemented by the master equation (ME) calculations in order to build a rather comprehensive picture of the hopping transport over the homopolar heterojunction.