Extended projector method: Application to a spin-boson system

Abstract

Symmetrized Trotter approximations to $e^{\mathrm{-}\beta H}$ are employed to compute the low-energy eigenstates of a two-level system linearly coupled to a harmonic oscillator. At high coupling strengths the ground state is nearly doubly degenerate and the projectors become very inefficient. It is demonstrated that the projection technique in combination with the variational principle yields a new efficient method to calculate simultaneously all nearly degenerate eigenvalues and eigenstates. The dynamic properties of the system in the ground state are studied by evaluating the time- and frequency-dependent correlation functions. Depending on the ratio of the tunneling frequency relative to the oscillator frequency, the system behaves differently under increasing coupling strength.