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Calculation of multi-fractal dimensions in spin chains. (English) Zbl 1322.81047
Summary: It was demonstrated in [the authors, “Calculation of multi-fractal dimensions in spin chains”, Phys. Rev. E 86, No. 2, Article ID 021104 (2012; doi:10.1103/PhysRevE.86.021104)] that the ground-state wave functions for a large variety of one-dimensional spin-\(\frac12\) models are multi-fractals in the natural spin-\(z\) basis. We present here the details of analytical derivations and numerical confirmations of this statement.

MSC:
81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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