Exact Solution of a Model of Localization
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Physics
Quantum Physics
Quantum Physics
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The exact solution is presented for the "susceptibility," χ (the number of sites covered by the maximally extended eigenfunction), for the zero-energy solutions of a hopping model on a randomly dilute Cayley tree. If p is the concentration, then χ~(p−p)−1 with p~pce1/ξ1, where pc is the critical percolation concentration and ξ1 the one-dimensional localization length. This result is argued to hold for the dilute quantum Heisenberg antiferromagnet at zero temperature.
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1982-07-26
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Physical Review Letters