# Polynomial basis constructions for the spin-boson model

Andreas Alvermann (Greifswald)

17.06.2011 at 10:15

The spin-boson model, which describes a two-state system coupled to a bath of harmonic oscillators, is a paradigmatic example of a quantum dissipative system. A notable property of this model is the existence of a quantum phase transition at stronger system-bath coupling. The talk will discuss the spin-boson model from the perspective of exact diagonalization techniques. These techniques are standard tools for small quantum systems, but their application to continuous degrees of freedom is complicated by the rapid growth of the Hilbert space. For the case of the spin-boson model, straightforward computations involving discretization of the bath density of states lead only to poor results. The basis of our investigation is a recently developed numerical approach based on polynomial basis constructions. In the talk I will review this approach and show how it may have helped to resolve the controversy about the critical behaviour of the sub-ohmic spin-boson model. Related polynomial techniques for other problems will be sketched briefly.

A 348 Theresienst. 37