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Register a new userSpectral signatures of Holstein polarons
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We review numerical results for ground-state and spectral properties of the single-electron Holstein model.
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The polaron formation is investigated in the intermediate regime of the Holstein model by using an exact diagonalization technique for the one-dimensional infinite lattice. The numerical results for the electron and phonon propagators are compared with the nonadiabatic weak- and strong-coupling perturbation theories, as well as with the harmonic adiabatic approximation. A qualitative explanation of the crossover regime between the self-trapped and free-particle-like behaviors, not well-understood previously, is proposed. It is shown that a fine balance of nonadiabatic and adiabatic contributions determines the motion of small polarons, making them light. A comprehensive analysis of spatially and temporally resolved low-frequency lattice correlations that characterize the translationally invariant polaron states is derived. Various behaviors of the polaronic deformation field, ranging from classical adiabatic for strong couplings to quantum nonadiabatic for weak couplings, are discussed.
We study the Holstein polaron in transverse magnetic field using non-perturbational methods. At strong fields and large coupling, we show that the polaron has a Hofstadter spectrum, however very distorted and of lower symmetry than that of a (heavier) bare particle. For weak magnetic fields, we identify non-perturbational behaviour of the Landau levels not previously known.
We derive a general procedure for evaluating the ${rm n}$th derivative of a time-dependent operator in the Heisenberg representation and employ this approach to calculate the zeroth to third spectral moment sum rules of the retarded electronic Greens function and self-energy for a system described by the Holstein-Hubbard model allowing for arbitrary spatial and time variation of all parameters (including spatially homogeneous electric fields and parameter quenches). For a translationally invariant (but time-dependent) Hamiltonian, we also provide sum rules in momentum space. The sum rules can be applied to various different phenomena like time-resolved angle-resolved photoemission spectroscopy and benchmarking the accuracy of numerical many-body calculations. This work also corrects some errors found in earlier work on simpler models.
Employing the recently developed self-consistent variational basis generation scheme, we have investigated the bipolaron-bipolaron interaction within the purview of Holstein-Hubbard and the extended-Holstein-Hubbard (F2H) model on a discrete one-dimensional lattice. The density-matrix renormalization group (DMRG) method has also been used for the Holstein-Hubbard model. We have shown that there exists no bipolaron-bipolaron attraction in the Holstein-Hubbard model. In contrast, we have obtained clear-cut bipolaron-bipolaron attraction in the F2H model. Composite bipolarons are formed above a critical electron-phonon coupling strength, which can survive the finite Hubbard $U$ effect. We have constructed the phase diagram of F2H polarons and bipolarons, and discussed the phase separation in terms of the formation of composite bipolarons.
We use a recently developed extension of the weak coupling diagrammatic determinantal quantum Monte Carlo method to investigate the spin, charge and single particle spectral functions of the one-dimensional quarter-filled Holstein model with phonon frequency $omega_0 = 0.1 t$. As a function of the dimensionless electron-phonon coupling we observe a transition from a Luttinger to a Luther-Emery liquid with dominant $2k_f$ charge fluctuations. Emphasis is placed on the temperature dependence of the single particle spectral function. At high temperatures and in both phases it is well accounted for within a self-consistent Born approximation. In the low temperature Luttinger liquid phase we observe features which compare favorably with a bosonization approach retaining only forward scattering. In the Luther-Emery phase, the spectral function at low temperatures shows a quasiparticle gap which matches half the spin gap whereas at temperatures above which this quasiparticle gap closes, characteristic features of the Luttinger liquid model are apparent. Our results are based on lattice simulations on chains up to L=20 for two-particle properties and on CDMFT calculations with clusters up to 12 sites for the single-particle spectral function.
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