We report a breakthrough development allowing one to solve a broad class of polaron problems with highly nonlinear electron-phonon coupling that were considered unsolvable without uncontrolled simplifications in the past using a Monte Carlo technique formulated in the coordinate representation for both the particle and the atomic displacements. The only condition is the sign positivity of the hopping amplitude. The technique dramatically simplifies (with the corresponding efficiency gains) for models with dispersionless phonons. Our study sheds important light on the nature and universality of the most striking qualitative and quantitative effects demonstrated by the ``standard'' (Peierls/Su-Schrieffer-Heeger) model based on the linearized displacement-modulated hopping.
We report a breakthrough development allowing one to solve a broad class of polaron problems with highly nonlinear electron-phonon coupling that were considered unsolvable without uncontrolled simplifications in the past using a Monte Carlo technique formulated in the coordinate representation for both the particle and the atomic displacements. The only condition is the sign positivity of the hopping amplitude. The technique dramatically simplifies (with the corresponding efficiency gains) for models with dispersionless phonons. Our study sheds important light on the nature and universality of the most striking qualitative and quantitative effects demonstrated by the ``standard'' (Peierls/Su-Schrieffer-Heeger) model based on the linearized displacement-modulated hopping.
Polarons originating from phonon displacement modulated hopping have relatively light masses and thus are of significant current interest as candidates for the bipolaron mechanism of high-temperature superconductivity [Sous et al., Phys. Rev. Lett. 121, 247001 (2018)]. We observe that the bond model, when the dominant coupling comes from atomic vibrations on lattice bonds, can be solved by efficient sign-free Monte Carlo methods based on the path-integral formulation of the particle sector in combination with either the (real-space) diagrammatic or Fock-path-integral representation of the phonon sector. We introduce the corresponding algorithms and provide illustrative results for singlet bipolarons in two dimensions. The data suggest that the route towards high-temperature superconductivity (if any) in the multiparametric space of the model lies between the Scylla of large size of moderately light bipolarons and the Charybdis of large mass of compact bipolarons. As a result, on-site repulsion is helping s-wave superconductivity in sharp contrast with existing expectations.
We develop an exact computational method based on numerical X propagators for solving polaron models with arbitrary nonlinear couplings of local vibration modes to the electron density and magnitude of the hopping amplitude. Our approach covers various polaron models, some of which were impossible to treat by any existing approximation-free techniques. Moreover, it remains efficient in the most relevant but computationally challenging regime of phonon frequencies much smaller than the electron bandwidth. As a case study, we consider the double-well type nonlinear model with quadratic ( g 2 < 0 ) and quartic ( g 4 > 0 ) interactions describing a broad class of technologically important materials, such as quantum paraelectric compounds and halide perovskites. We observe, depending on the model parameters, three qualitatively different regimes: (1) quantum interplay of quartic and quadratic interactions that suppresses effects of the quadratic coupling, (2) intermediate-coupling regime with exponential ∝ exp ( α g 2 Ω − 1 / 4 ) scaling of the quasiparticle weight and mass renormalization, and (3) strong-coupling asymptotic behavior.
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).]
Many condensed matter problems involve a particle coupled to its environment. The polaron, originally introduced to describe electrons in a polarizable medium, describes a particle coupled to a bosonic field. The Holstein polaron model, although simple, including only optical Einstein phonons and an interaction that couples them to the electron density, captures almost all of the standard polaronic properties. We herein investigate polarons that differ significantly from this behaviour. We study a model with phonon-modulated hopping, and find a radically different behaviour at strong couplings. We report a sharp transition, not a crossover, with a diverging effective mass at the critical coupling. We also look at a model with acoustic phonons, away from the perturbative limit, and again discover unusual polaron properties. Our work relies on the Bold Diagrammatic Monte Carlo (BDMC) method, which samples Feynman diagrammatic expansions efficiently, even those with weak sign problems. Proposed by Prokof'ev and Svistunov, it is extended to lattice polarons for the first time here. We also use the Momentum Average (MA) approximation, an analytical method proposed by Berciu, and find an excellent agreement with the BDMC results. A novel MA approximation able to treat dispersive phonons is also presented, along with a new exact solution for finite systems, inspired by the same formalism.
We study polarons in the one-dimensional Bond-Peierls electron-phonon model in which phonons on bonds of a lattice modulate the hopping of electrons between lattice sites and contrast the results to those known for the breathing-mode Peierls problem. By inspecting the atomic limit, we show that polaronic dressing and mass enhancement of Bond-Peierls polarons depend on the momentum dependence of the phonons. For dispersionless phonons, Bond-Peierls polarons are perfectly localized in the atomic limit, unlike their breathing-mode counterparts because the carrier creates a string of phonon excitations that can only be annihilated via processes that retrace the carrier to its original site. However, inclusion of phonon dispersion leads to a nondivergent polaron mass even in the atomic limit and depending on the form of the phonon dispersion may lead to a transition to a non-zero-momentum ground state akin to that found in the breathing-mode Peierls model.
We study polarons in the one-dimensional Bond-Peierls electron-phonon model, in which phonons on bonds of a lattice modulate the hopping of electrons between lattice sites, and contrast the results to those known for the Breathing-Mode Peierls problem. By inspecting the atomic limit, we show that polaronic dressing and mass enhancement of Bond-Peierls polarons depend on the momentum dependence of the phonons. For dispersionless phonons, Bond-Peierls polarons are perfectly localized in the atomic limit, unlike their Breathing-mode counterparts, because the carrier creates a string of phonon excitations that can only be annihilated via processes that retrace the carrier to its original site. However, inclusion of phonon dispersion leads to a non-divergent polaron mass even in the atomic limit and depending on the form of the phonon dispersion may lead to a transition to a non-zero-momentum ground state akin to that found in the Breathing-mode Peierls model.