Physics of integer spin antiferromagnetic chains : Haldane gaps and edge states

Abstract

The antiferromagnetic Heisenberg spin chain with integer spin has short-range magnetic order and an excitation energy gap above the ground state. This so-called Haldane gap is proportional to the exchange coupling $J$ of the Heisenberg chain. We discuss recent results about the spin dependence of the Haldane gap and conjecture an analytical formula valid asymptotically for large spin values. We next study the robustness of the edge states of the spin one chain by studying by the DMRG algorithm a spin one ladder. We show that the peculiar hidden topological order of the spin one chain disappears smoothly by increasing the ladder rung coupling without any intervening phase transition. This is evidence for the fragile character of the topological order of the spin one chain.

arXiv comment11 pages, 10 figures. Article published in a special issue of Comptes Rendus de l'Academie des Sciences : Chimie in honor of Michel Verdaguer

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• Comparison of encoding schemes for quantum computing of $S>1/2$ spin chains
• Imperfect Many-Body Localization in Exchange-Disordered Isotropic Spin Chains
• Feynman path integrals for discrete-variable systems: Walks on Hamiltonian graphs
• Topological excitations in quasi two-dimensional quantum magnets with weak interlayer interactions
• Magnetic excitations and exchange parameters of a nickel chain compound PbMn${}_2$Ni${}_6$Te${}_3$O${}_{18}$: Neutron scattering and density functional theory studies