Projector-based renormalization method (PRM) for many-particle systems
Abstract
Here we present a recently developed renormalization approach to many-particle systems. By starting from a bare Hamiltonian l H=l H_0+l H1 with an unperturbed part l H0 and a perturbation l H_1, we define an effective Hamiltonian which has a band-diagonal shape with respect to the eigen-basis of l H_0. This means that all transition matrix elements are suppressed which have energy differences larger than a given cutoff λ that is smaller than the cutoff Λ of the original Hamiltonian. This property is used to derive a renormalization procedure which resembles a recent flow equation approach on the basis of unitary transformations. For demonstration of the method we discuss the elctron-phonon coupling in many-electron systems. By starting from an Hamiltonian which includes a small gauge symmetry breaking field, we directly derive a BCS-like equation for the energy gap from the PRM where the effective electron-electron interaction for Cooper pairs does not contain any singularities.
- Publication:
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APS March Meeting Abstracts
- Pub Date:
- March 2004
- Bibcode:
- 2004APS..MARB38010H