| Description |
We study the spin 1/2 quantum Heisenberg antiferromagnet on a Bethe
lattice diluted to the percolation threshold. Dilution creates areas
of even/odd sublattice imbalance resulting in "dangling spins'' :
spins which can not be paired up into dimers with their nearest
neighbors (L. Wang and A. W. Sandvik, Phys. Rev. Lett. 97, 117204
(2006); Phys. Rev. B 81, 054417 (2010)). These spins are found to
significantly affect the low energy spectrum: the lowest energy gaps
are found to scale “anomalously†with system size (N), being much
smaller than the expected 1/N scaling. By computing multiple excited
states in the low energy spectrum (using a version of the Density
Matrix Renormalization Group (DMRG) algorithm for generic tree
graphs), and studying their correspondence with the geometry of the
percolation cluster, we provide evidence that the dangling spins
collectively act as "emergent'' spin 1/2 (or in some cases spin-1)
degrees of freedom. By evaluating inter-site correlation and
susceptibility matrices, we detect the presence and location of these
emergent spins. We process our numerical data to compute an effective
Hamiltonian in terms of the emergent spins, and find them to have
pairwise Heisenberg interactions that decay exponentially with
distance.
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