2012/08/31 by Hitesh J. Changlani, Shivam Ghosh, Christopher L. Henley +1 · 3 citations
Mathematics · Physics and Astronomy · #Antiferromagnetism #Condensed matter physics #Energy spectrum #Heisenberg model #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Quantum mechanics #Spectrum (functional analysis) #Theoretical and Computational Physics #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.87.085107
published as Phys. Rev. B 87, 085107 (2013) · 19 pages, 12 figures, 6 tables. Changes made to manuscript after referee suggestions: parts reorganized, clarified discussion on Fibonacci tree, typos corrected
openalex publication_date 2013/02/06 · arxiv created 2013/03/11 · arxiv updated 2013/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
To understand the role of local sublattice imbalance in low-energy spectra of s=(1)/(2) quantum antiferromagnets, 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 quasidegenerate set of a 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 wave function ansatz given by the single-mode approximation, which yields a high overlap with the DMRG wave function. Observing the ground-state entanglement spectrum leads us to a picture of the low-energy degrees of freedom being ``giant spins'' arising out of sublattice imbalance, which helps us analytically understand the scaling of the finite-size spin gap. The Schwinger-boson mean-field theory has been generalized to nonuniform lattices, and ground states have been found which are spatially inhomogeneous in the mean-field parameters.