Physics – Quantum Physics
Scientific paper
2010-12-22
Physics
Quantum Physics
51 pages, 27 figures, 8 tables
Scientific paper
The method of "Isotropic Entanglement" (IE), inspired by Free Probability Theory and Random Matrix Theory, predicts the eigenvalue distribution of quantum many-body (spin) systems with generic interactions. At the heart is a "Slider", which interpolates between two extrema by matching fourth moments. The first extreme treats the non-commuting terms classically and the second treats them isotropically. Isotropic means that the eigenvectors are in generic positions. We prove Matching Three Moments and Slider Theorems and further prove that the interpolation is universal, i.e., independent of the choice of local terms. Our examples show that IE provides an accurate picture well beyond what one expects from the first four moments alone.
Edelman Alan
Movassagh Ramis
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