The Renormalized Field Operator in the Heisenberg Picture

Brian P. Anderson

Alexander D. Sukhanov

Jarno N. van der Kolk

Using the Density Matrix Renormalization Group (DMRG) one can simulate spin systems without the computation time growing as 2 , making it feasible to simulate large systems. In this paper, the impact of using the DMRG in the Schrodinger picture and in the Heisenberg picture is investigated for three different models, a spin1 2 XX chain, a spin1 2 XXZ chain and a Bose-Hubbard model. Simulations in the Heisenberg model will turn out to perform better only in the XX chain for certain operators. For all the other tested models, the Schrodinger picture is to be preferred. We will also try to shed some light on why the simulations in the Heisenberg picture fail so quickly.

B. R. Mollow

Resonant light scattering is considered in the Heisenberg picture by making use of operator radiation reaction theory. A crucial commutator between matter and free-field variables is shown to vanish, and the validity of the quantum fluctuation-regression theorem, like that of the optical Bloch equations which govern the reduced atomic density matrix, is firmly established, apart from renormalization difficulties, within the rotating wave approximation.

I. Golhirsch, Evgeny Levich, Victor Yakhot