The Flow Equation Approach to Many-Particle Systems by Stefan Kehrein

By Stefan Kehrein

This self-contained creation addresses the radical circulation equation method for lots of particle structures and offers an up to date evaluate of the topic. The textual content first discusses the final principles and ideas of the circulate equation procedure, after which in a moment half illustrates them with a number of purposes in condensed topic concept. The 3rd and final a part of the booklet includes an outlook with present views for destiny research.

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Extra resources for The Flow Equation Approach to Many-Particle Systems (Springer Tracts in Modern Physics, 217)

Example text

It is interesting to see how the flow equation approach fares in this situation. As a cautionary remark one should mention that while the weak-coupling observations in the previous section can be carried over rather generally to interacting many-body systems, the flow equation analysis of the strong-coupling potential scattering model seems not to be generalizable to strong-coupling interacting many-body systems. We will later see this explicitly for the case of the Kondo model. However, the flow equation analysis of the attractive potential scattering model provides some interesting insights into the method.

Also, the full unitary transformation U (B = ∞) completely hides the fact that it can be expressed as such an B-ordered exponential, and hence that is generated by infinitesimal 7 We will discuss an example for this in Sect. 3. Notice that the complexity of such calculations typically grows considerably with every order. 9 A generator that does not respect energy scale separation does not automatically make the approach uncontrolled. Energy scale separation is not important in all interactions as one knows from the many successful applications of conventional perturbation theory.

Of course, the potential scattering model is trivial from a many-particle point of view. Still, it is nontrivial from the scaling point of view as we have seen before. In Chap. 4 we will then discuss applications of the flow equation method to models that are both non-trivial from the scaling and the manyparticle point of view. 1 Setting up the Flow Equations The basic idea of the flow equation approach is to make the interaction increasingly energy-diagonal. The ansatz for the flowing Hamiltonian should reflect this.

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