Symmetry Properties of the k-Body Embedded Unitary Ensemble of Random Matrices

Abstract

We extend the recent study of the k-body embedded Gaussian ensembles by Benet et al. (Phys. Rev. Lett. 87 (2001) 101601-1 and Ann. Phys. 292 (2001) 67) and by Asaga et al. (cond-mat/0107363 and cond-mat/ 0107364). We show that central results of these papers can be derived directly from the symmetry properties of both, the many-particle states and the random k-body interaction. We offer new insight into the structure of the matrix of second moments of the embedded ensemble, and of the supersymmetry approach. We extend the concept of the embedded ensemble and define it purely group-theoretically.

LaTeX2e, 30 pages, 14 references

References in corpus (1)

• Non-Ergodic Behaviour of the k-Body Embedded Gaussian Random Ensembles for Bosons

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• Regularities with random interactions in energy centroids defined by group symmetries
• A smooth transition towards a Tracy-Widom distribution for the largest eigenvalue of interacting $k$-body fermionic Embedded Gaussian Ensembles
• Random matrix ensembles with random interactions: Results for EGUE(2)-SU(4)
• Fold bifurcation entangled surfaces for one-dimensional Kitaev lattice model