We present the first unbiased results for the mobility μ of a one-dimensional Holstein polaron obtained by numerical analytic continuation combined with diagrammatic and worldline Monte Carlo methods in the thermodynamic limit. We have identified for the first time several distinct regimes in the λ-T plane including a band conduction region, incoherent metallic region, an activated hopping region, and a high-temperature saturation region. We observe that although mobilities and mean free paths at different values of λ differ by many orders of magnitude at small temperatures, their values at T larger than the bandwidth become very close to each other.
We present the first unbiased results for the mobility μ of a one-dimensional Holstein polaron obtained by numerical analytic continuation combined with diagrammatic and worldline Monte Carlo methods in the thermodynamic limit. We have identified for the first time several distinct regimes in the λ-T plane including a band conduction region, incoherent metallic region, an activated hopping region, and a high-temperature saturation region. We observe that although mobilities and mean free paths at different values of λ differ by many orders of magnitude at small temperatures, their values at T larger than the bandwidth become very close to each other.
The Holstein model is a benchmark model of systems with electron-phonon interaction. However, its electrical transport properties are not yet fully understood. In this work, we performed numerically exact calculations of the imaginary-time current-current correlation function of the Holstein Hamiltonian for a broad range of model parameters. These calculations were performed using a path-integral-based quantum Monte Carlo method. We compared these results with the results obtained under the assumption of conventional band transport, small polaron hopping, and polaron band transport. From this comparison, we identified the regions in parameter space where each of these transport regimes is valid. In some cases when an imaginary-time comparison of current-current correlation functions could not give conclusive results, we complemented it with real-time comparisons or a comparison with the literature data on numerically exact dc mobilities. Overall, we found that the parameter space is almost completely covered by the three mentioned transport regimes.
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.
We compute the Holstein polaron spectral function on a one-dimensional ring using the finite-temperature T Lanczos method. With increasing T additional features in the spectral function emerge even at temperatures below the phonon frequency. We observe a substantial spread of the spectral weight towards lower frequencies and the broadening of the quasiparticle (QP) peak. In the weak-coupling regime the QP peak merges with the continuum in the high-T limit. In the strong-coupling regime the main features of the low-T spectral function remain detectable up to the highest T used in our calculations. The effective polaron mass shows a nonmonotonic behavior as a function of T at small phonon frequency but increases with T at larger frequencies. The self-energy remains k independent even at elevated T in the frequency range corresponding to the polaron band, while at higher frequencies it develops a distinguishable k dependence. Analytical expressions for the first few frequency moments are derived, and they agree well with those extracted from numerical calculations in a wide-T regime.
We introduce the first bold diagrammatic Monte Carlo approach to deal with polaron problems at a finite electron density nonperturbatively, i.e., by including vertex corrections to high orders. Using the Holstein model on a square lattice as a prototypical example, we demonstrate that our method is capable of providing accurate results in the thermodynamic limit in all regimes from a renormalized Fermi liquid to a single polaron, across the nonadiabatic region where Fermi and Debye energies are of the same order of magnitude. By accounting for vertex corrections, the accuracy of the theoretical description is increased by orders of magnitude relative to the lowest-order self-consistent Born approximation employed in most studies. We also find that for the electron-phonon coupling typical for real materials, the quasiparticle effective mass increases and the quasiparticle residue decreases with increasing the electron density at constant electron-phonon coupling strength.
The optical-conductivity profile carries information on electronic dynamics in interacting quantum many-body systems. Its computation is a formidable task that is usually approached by invoking the single-particle (bubble) approximation and neglecting vertex corrections, the importance of which remains elusive even in model Hamiltonian calculations. Here, we combine analytical arguments with our recent breakthroughs in numerically exact and approximate calculations of finite-temperature real-time correlation functions to thoroughly assess the importance of vertex corrections in the one-dimensional Holstein polaron model. We find, both analytically and numerically, vanishing vertex corrections to optical conductivity in the limits of zero electron-phonon interaction, zero electronic bandwidth, and infinite temperature. Furthermore, our numerical results show that vertex corrections to the electron mobility also vanish in many parameter regimes between these limits. In some of these cases, the vertex corrections still introduce important qualitative changes to the optical-conductivity profile in comparison to the bubble approximation even though the self-energy remains approximately local. We trace these changes back to the bubble approximation not fully capturing a time-limited slowdown of the electron on intermediate timescales between ballistic and diffusive transport. We find that the vertex corrections are overall most pronounced for intermediate electron-phonon interaction and may increase or decrease the bubble-approximation mobility depending on the values of the model parameters.
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.