Hamiltonian Flow Equations for the Lipkin Model

Abstract

We derive Hamiltonian flow equations giving the evolution of the Lipkin Hamiltonian to a diagonal form using continuous unitary transformations. To close the system of flow equations, we present two different schemes. First we linearize an operator with three pairs of creation and destruction operators by reducing it to the $z$ component of the quasi spin. We obtain the well known RPA-result in the limit of large particle number. In the second scheme we introduce a new operator which improves the resulting spectrum considerably especially for few particles.

10 pages, 2 eps figures, uses article.sty, epsfig.sty

References in corpus (1)

• Calculating critical temperatures of superconductivity from a renormalized Hamiltonian

Cited by in corpus (6)

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• Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
• Flow Equations and Normal Ordering. A Survey
• IMSRG with flowing 3 body operators, and approximations thereof
• Non-perturbative flow equations from continuous unitary transformations
• Non-perturbative flow equations from continuous unitary transformations