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Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields

Is the Heisenberg picture better than the Schrödinger picture?

A. Katz

Published Aug 1, 1966• 3 citations
Publisher
DOI
10.1007/bf02719334

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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.

•Jan 1, 2011•0 citations
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.