Hitesh J. Changlani, Shivam Ghosh, Christopher L. Henley, Andreas M. Läuchli
To understand the role of local sublattice imbalance in low energy spectra of s=1/2 quantum antiferromagnets (as observed by [L.Wang and A.W.Sandvik, Phys.Rev.Lett. 97, 117204 (2006); Phys. Rev. B 81, 054417 (2010)]), we study the s=1/2 quantum nearest neighbor Heisenberg antiferromagnet on the coordination 3 Cayley tree. We perform many-body calculations using an implementation of the Density Matrix Renormalization Group (DMRG) technique for generic tree graphs. We discover that the bond-centered Cayley tree has a quasi-degenerate set of low lying tower of states and an "anomalous" singlet-triplet finite size gap scaling. For understanding the construction of the first excited state from the many-body ground state, we consider a wavefunction ansatz given by the single mode approximation (SMA), which yields a high overlap with the DMRG wavefunction. Observing the ground state entanglement spectrum helps us to analytically understand the scaling of the finite size spin gap and leads us to a picture of the low energy degrees of freedom being "giant spins" arising out of sublattice imbalance. The Schwinger Boson mean field theory has been generalized to non uniform lattices and ground states have been found which are spatially inhomogeneous in the mean field parameters.
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http://arxiv.org/abs/1208.1773
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