Projectorbased renormalization method (PRM) for manyparticle systems
Abstract
Here we present a recently developed renormalization approach to manyparticle systems. By starting from a bare Hamiltonian l H=l H_0+l H_{1} with an unperturbed part l H_{0} and a perturbation l H_1, we define an effective Hamiltonian which has a banddiagonal shape with respect to the eigenbasis 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 elctronphonon coupling in manyelectron systems. By starting from an Hamiltonian which includes a small gauge symmetry breaking field, we directly derive a BCSlike equation for the energy gap from the PRM where the effective electronelectron interaction for Cooper pairs does not contain any singularities.
 Publication:

APS March Meeting Abstracts
 Pub Date:
 March 2004
 Bibcode:
 2004APS..MARB38010H