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Register a new userOptical conductivity of the Frohlich polaron
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Added by
Andrei Mishchenko S.
Publication date
2003
fields
Physics
and research's language is
English
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We present accurate results for optical conductivity of the three dimensional Frohlich polaron in all coupling regimes. The systematic-error free diagrammatic quantum Monte Carlo method is employed where the Feynman graphs for the momentum-momentum correlation function in imaginary time are summed up. The real-frequency optical conductivity is obtained by the analytic continuation with stochastic optimization. We compare numerical data with available perturbative and non-perturbative approaches to the optical conductivity and show that the picture of sharp resonances due to relaxed excited states in the strong coupling regime is ``washed outby large broadening of these states. As a result, the spectrum contains only a single-maximum broad peak with peculiar shape and a shoulder.
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The polaron optical conductivity is derived within the strong-coupling expansion, which is asymptotically exact in the strong-coupling limit. The polaron optical conductivity band is provided by the multiphonon optical transitions. The polaron optical conductivity spectra calculated within our analytic strong-coupling approach and the numerically accurate Diagrammatic Quantum Monte Carlo (DQMC) data are in a good agreement with each other at large $alpha gtrapprox 9$.
We study the frequency dependence of the optical conductivity $text{Re} , sigma(omega)$ of the Heisenberg spin-$1/2$ chain in the thermal and near the transition to the many-body localized phase induced by the strength of a random $z$-directed magnetic field. Using the method of dynamical quantum typicality, we calculate the real-time dynamics of the spin-current autocorrelation function and obtain the Fourier transform $text{Re} , sigma(omega)$ for system sizes much larger than accessible to standard exact-diagonalization approaches. We find that the low-frequency behavior of $text{Re} , sigma(omega)$ is well described by $text{Re} , sigma(omega) approx sigma_text{dc} + a , |omega|^alpha$, with $alpha approx 1$ in a wide range within the thermal phase and close to the transition. We particularly detail the decrease of $sigma_text{dc}$ in the thermal phase as a function of increasing disorder for strong exchange anisotropies. We further find that the temperature dependence of $sigma_text{dc}$ is consistent with the existence of a mobility edge.
The charge dynamics in weakly hole doped high temperature superconductors is studied in terms of the accurate numerical solution to a model of a single hole interacting with a quantum lattice in an antiferromagnetic background, and accurate far-infrared ellipsometry measurements. The experimentally observed two electronic bands in the infrared spectrum can be identified in terms of the interplay between the electron correlation and electron-phonon interaction resolving the long standing mystery of the mid-infrared band.
A path-integral representation is constructed for the Jahn-Teller polaron (JTP). It leads to a perturbation series that can be summed exactly by the diagrammatic Quantum Monte Carlo technique. The ground-state energy, effective mass, spectrum and density of states of the three-dimensional JTP are calculated with no systematic errors. The band structure of JTP interacting with dispersionless phonons, is found to be similar to that of the Holstein polaron. The mass of JTP increases exponentially with the coupling constant. At small phonon frequencies, the spectrum of JTP is flat at large momenta, which leads to a strongly distorted density of states with a massive peak at the top of the band.
The eigenstate thermalization hypothesis (ETH) is a successful theory that provides sufficient criteria for ergodicity in quantum many-body systems. Most studies were carried out for Hamiltonians relevant for ultracold quantum gases and single-component systems of spins, fermions, or bosons. The paradigmatic example for thermalization in solid-state physics are phonons serving as a bath for electrons. This situation is often viewed from an open-quantum system perspective. Here, we ask whether a minimal microscopic model for electron-phonon coupling is quantum chaotic and whether it obeys ETH, if viewed as a closed quantum system. Using exact diagonalization, we address this question in the framework of the Holstein polaron model. Even though the model describes only a single itinerant electron, whose coupling to dispersionless phonons is the only integrability-breaking term, we find that the spectral statistics and the structure of Hamiltonian eigenstates exhibit essential properties of the corresponding random-matrix ensemble. Moreover, we verify the ETH ansatz both for diagonal and offdiagonal matrix elements of typical phonon and electron observables, and show that the ratio of their variances equals the value predicted from random-matrix theory.
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