This study of the one-dimensional (1D) Su-Schrieffer-Heeger model in a weak-coupling perturbative regime points out the effective-mass behavior as a function of the adiabatic parameter ${\ensuremath{\omega}}_{\ensuremath{\pi}}/J,$ where ${\ensuremath{\omega}}_{\ensuremath{\pi}}$ is the zone-boundary phonon energy and J is the electron band hopping integral. Computation of low order diagrams shows that two-phonon scattering processes become appreciable in the intermediate regime in which zone-boundary phonons energetically compete with band electrons. Consistently, in the intermediate (and also moderately antiadiabatic) range the relevant mass renormalization signals the onset of a polaronic crossover whereas the electrons are essentially undressed in the fully adiabatic and antiadiabatic systems. The effective mass is roughly twice as much the bare band value in the intermediate regime while an abrupt increase (mainly related to the peculiar 1D dispersion relations) is obtained at ${\ensuremath{\omega}}_{\ensuremath{\pi}}\ensuremath{\sim}\sqrt{2}J.$
This study of the one-dimensional (1D) Su-Schrieffer-Heeger model in a weak-coupling perturbative regime points out the effective-mass behavior as a function of the adiabatic parameter \ensuremathω\ensuremathπ/J, where \ensuremathω\ensuremathπ is the zone-boundary phonon energy and J is the electron band hopping integral. Computation of low order diagrams shows that two-phonon scattering processes become appreciable in the intermediate regime in which zone-boundary phonons energetically compete with band electrons. Consistently, in the intermediate (and also moderately antiadiabatic) range the relevant mass renormalization signals the onset of a polaronic crossover whereas the electrons are essentially undressed in the fully adiabatic and antiadiabatic systems. The effective mass is roughly twice as much the bare band value in the intermediate regime while an abrupt increase (mainly related to the peculiar 1D dispersion relations) is obtained at \ensuremathω\ensuremathπ\ensuremath∼2J.
Polarons with different types of electron-phonon coupling have fundamentally different properties. When the dominant interaction is between the electron density and lattice displacement, the momentum of the ground state does not change and the polaron gets exponentially heavy at strong coupling. In contrast, one-dimensional Peierls/Su-Schrieffer-Heeger (PSSH) polarons with interaction originating from displacement-modulated hopping feature a shift of the ground-state momentum to finite values and moderate values of effective mass as coupling is increased [D. J. J. Marchand et al., Phys. Rev. Lett. 105, 266605 (2010)]. Based on Diagrammatic Monte Carlo method, we investigate whether unusual properties of PSSH polarons depend on the type of the displacement-modulated hopping and to what degree they survive in higher dimension. We study two different PSSH models: with bosonic degrees of freedom residing on sites (model A) and bonds (model B) of the two-dimensional square lattice. For model A, we find that in both adiabatic and intermediate regimes, the momentum of the ground state experiences a continuous transition from zero to a finite value as a function of coupling strength. The transition is driven by quadratic instability of the dispersion function, implying that effective mass diverges at the critical point, and then decreases in an anisotropic fashion with increasing coupling. Unexpectedly, for model B, the momentum of the ground state always stays at zero and the effective mass increases monotonously with coupling. The increase is far from exponential and tends to level off at strong interaction, resulting in relatively light polarons. Having light polarons in the strong coupling regime is crucial for the bipolaron mechanism of high-temperature superconductivity [J. Sous, M. Chakraborty, R. V. Krems, and M. Berciu, Phys. Rev. Lett. 121, 247001 (2018).]
We study the nature of the ground state of the Su-Schrieffer-Heeger model for electron-phonon interactions in one dimension in the half-filled-band case. We consider the cases of spinless electrons (n=1) and spin-\textonehalf{} electrons (n=2), and discuss the stability of the Peierls-dimerized ground state as a function of the ionic mass and electron-phonon coupling constant. We first consider the zero-mass limit of the theory and extend our results to finite mass using renormalization-group arguments. For spinless electrons, it is found that quantum fluctuations destroy the long-range dimerization order for the small electron-phonon coupling constant if the ionic mass is finite. For spin-\textonehalf{} electrons, the system is dimerized for an arbitrary coupling constant and phonon frequency. Renormalization-group trajectories show that the low-energy behavior of the system is governed by the zero-mass limit of the theory, an n-component Gross-Neveu model. Monte Carlo simulations are performed for the model at finite phonon frequencies, and the results are compared with the static limit result. We study in particular the set of parameters appropriate for polyacetylene and find a 15% reduction in the phonon order parameter due to fluctuations of the phonon field. A finite-size scaling analysis of the numerical data for the cases n=1and2 is performed, which confirms the results obtained from the renormalization-group analysis.
Nondiagonal couplings to a bosonic bath completely change polaronic dynamics, from the usual diagonally coupled paradigm of smoothly varying properties. We study, using analytic and numerical methods, a model having both diagonal Holstein and nondiagonal Su-Schrieffer-Heeger (SSH) couplings. The critical coupling found previously in the pure SSH model, at which the k=0 effective mass diverges, now becomes a transition line in the coupling constant plane---the form of the line depends on the adiabaticity parameter. Detailed results are given for the quasiparticle and ground-state properties, over a wide range of couplings and adiabaticity ratios. The new paradigm involves a destabilization, at the transition line, of the simple Holstein polaron to one with a finite ground-state momentum, but with everywhere a continuously evolving band shape. No ``self-trapping transition'' exists in any of these models. The physics may be understood entirely in terms of competition between different hopping terms in a simple renormalized effective band theory. The possibility of further transitions is suggested by the results.
We use a newly developed quantum Monte Carlo method to investigate the impact of finite dispersion of the optical phonon mode on the properties of the bond Su-Schrieffer-Heeger polaron in two dimensions. We compare the properties of the bond polaron, such as effective mass, ground state energy, and Z factor, with and without positive phonon bandwidth. Our findings reveal that when we exclude phonon dispersion, at the same electron-phonon coupling strength, the effective mass increases as the phonon frequency decreases, indicating a heavier polaron in the deep adiabatic regime. However, in the dispersive case, we observe that the effective mass increases as the phonon bandwidth increases. Moreover, we notice a crossover from a light polaron state to a heavy polaron state in the deep adiabatic regime for both the dispersionless and dispersive cases.
Nonadiabatic effects in the electron-phonon coupling are important whenever the ratio between the phononic and the electronic energy scales---the adiabatic ratio---is non-negligible. For superconducting systems, this gives rise to additional diagrams in the superconducting self-energy, the vertex, and cross-corrections. In this work, we explore these corrections in a two-dimensional single-band system through the crossover between the weak-coupling Bardeen-Cooper-Schrieffer (BCS) and strong-coupling Bose-Einstein regimes. By focusing on the pseudogap phase, we identify the parameter range in which the pairing amplitude is amplified by nonadiabatic effects and, due to controlled approximations, we map them throughout the BCS-BEC crossover. These effects become stronger as the system is driven deeply in the crossover regime, for phonon frequencies of the order of the hopping energy and for large enough electron-phonon coupling. Finally, we provide the phase space regions in which the effects of nonadiabaticity are more relevant for unconventional superconductors.
Electron-phonon coupling is typically not associated with magnetic order but with either charge density waves (patterns of high and low electron density) or valence-bond solids (patterns of strong and weak electronic bonds). Using quantum Monte Carlo simulations, the authors demonstrate that, within the paradigmatic two-dimensional Su-Schrieffer-Heeger model, the electron-phonon interaction favors antiferromagnetic order in large regions of the phase diagram. A valence-bond solid is observed in the adiabatic regime, while the two phases are connected by an apparently direct phase transition.