Non-perturbative flow equations from continuous unitary transformations
摘要
We use a novel parameterization of the flowing Hamiltonian to show that the flow equations based on continuous unitary transformations, as proposed by Wegner, can be implemented through a nonlinear partial differential equation involving one flow parameter and two system specific auxiliary variables. The implementation is non-perturbative as the partial differential equation involves a systematic expansion in fluctuations, controlled by the size of the system, rather than the coupling constant. The method is applied to the Lipkin model to construct a mapping which maps the non-interacting spectrum onto the interacting spectrum to a very high accuracy. This function is universal in the sense that the full spectrum for any (large) number of particles can be obtained from it. In a similar way expectation values for a large class of operators can be obtained, which also makes it possible to probe the stucture of the eigenstates.
引用
@article{arxiv.cond-mat/0408420,
title = {Non-perturbative flow equations from continuous unitary transformations},
author = {J. N. Kriel and A. Y. Morozov and F. G. Scholtz},
journal= {arXiv preprint arXiv:cond-mat/0408420},
year = {2015}
}
备注
24 pages, 13 figures