Non-perturbative flow equations from continuous unitary transformations

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.

24 pages, 13 figures

References in corpus (1)

• Large N Scaling Behavior of the Lipkin-Meshkov-Glick Model

Cited by in corpus (8)

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• On the Thermodynamic Limit of the Lipkin Model
• Flow equation approach to the linear response theory of superconductors
• Strong-coupling expansion and effective hamiltonians
• Eigenvalue distributions from a star product approach