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Non-perturbative flow equations from continuous unitary transformations

J. N. Kriel·A. Y. Morozov·F. G. Scholtz
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Abstract

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.

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J. N. Kriel, A. Y. Morozov, F. G. Scholtz. 2004-08-19. Non-perturbative flow equations from continuous unitary transformations. https://doi.org/10.1088/0305-4470%2F38%2F1%2F015

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