Similarity renormalization of the electron--phonon coupling

Abstract

We study the problem of the phonon-induced electron-electron interaction in a solid. Starting with a Hamiltonian that contains an electron-phonon interaction, we perform a similarity renormalization transformation to calculate an effective Hamiltonian. Using this transformation singularities due to degeneracies are avoided explicitely. The effective interactions are calculated to second order in the electron-phonon coupling. It is shown that the effective interaction between two electrons forming a Cooper pair is attractive in the whole parameter space. For a simple Einstein model we calculate the renormalization of the electronic energies and the critical temperature of superconductivity.

17 pages, LaTeX2e, uses AMS-fonts, 5 ps-figures included. Replaced by a completely revised version that contains several new results on the renormalization of single particle energies, on the superconducting gap, and on the critical temperature

References in corpus (4)

• Nonperturbative Light-Front QCD
• Flow Equations for Electron-Phonon Interactions
• Theory of the Anderson impurity model: The Schrieffer--Wolff transformation re--examined
• Low temperature equilibrium correlation functions in dissipative quantum systems

Cited by in corpus (19)

• Non-linear feedback effects in coupled Boson-Fermion systems
• Flow Equations and Normal Ordering. A Survey
• Enhanced Perturbative Continuous Unitary Transformations
• Flow equation approach to the sine-Gordon model
• Calculating critical temperatures of superconductivity from a renormalized Hamiltonian
• Flow equations for QED in the light front dynamics
• Microscopic model for Bose-Einstein condensation and quasiparticle decay
• Derivation of the t-J model for finite doping
• Possibility of Electron Pairing in Small Metallic Nanoparticles
• Assisted hopping in the Anderson impurity model: A flow equation study
• Dissipative flow equations
• Assisted hopping and interaction effects in impurity models
• Efficient flow equations for dissipative systems
• Truncation errors in self-similar continuous unitary transformations
• Quantum melting of long-range ordered quantum antiferromagnets investigated by momentum-space continuous similarity transformations
• Response Theory of the Electron-Phonon Coupling
• Hole Dispersions for Antiferromagnetic Spin-1/2 Two-Leg Ladders by Self-Similar Continuous Unitary Transformations
• Collective modes in superconductors including Coulomb repulsion
• Flow equation approach to diagonal representation of an unbounded Hamiltonian with complex eigenvalues