The structure of edge states in general finite antiferromagnetic quantum spin chains with arbitrary spin value S is discussed within the framework of the nonlinear-sigma model (NL\ensuremath{\sigma}M) plus a topological \ensuremath{\theta} term. Based on a large-N theory of SU(N) quantum antiferromagnets and strong-coupling expansion, we argue that edge states with fractionalized spin quantum number S' exist in all spin chains with S\ensuremath{\ge}1, with S'=S/2 for integer spin chains and S'=(S-1/2)/2 for half-integer spin chains.The structure of edge states in general finite antiferromagnetic quantum spin chains with arbitrary spin value S is discussed within the framework of the nonlinear-sigma model (NL\ensuremath{\sigma}M) plus a topological \ensuremath{\theta} term. Based on a large-N theory of SU(N) quantum antiferromagnets and strong-coupling expansion, we argue that edge states with fractionalized spin quantum number S' exist in all spin chains with S\ensuremath{\ge}1, with S'=S/2 for integer spin chains and S'=(S-1/2)/2 for half-integer spin chains.

Physical review. B, Condensed matterJul 1, 199494 citations

Edge states in open antiferromagnetic Heisenberg chains

Shaojin Qin, Tai Kai Ng, Zhao-Bin Su

We report our results in investigating edge effects of open antiferromagnetic Heisenberg spin chains with spin magnitudes S=1/2,1,3/2,2 using the density-matrix renormalization-group method initiated by White. For integer spin chains, we find that edge states with spin magnitude ${\mathit{S}}_{\mathrm{edge}}$ =S/2 exist, in agreement with the valence-bond-solid model picture. For half-integer spin chains, we find that no edge states exist for the S=1/2 spin chain, but an edge state exists in the S=3/2 spin chain with a ${\mathit{S}}_{\mathrm{edge}}$ =1/2, in agreement with a previous conjecture by Ng. The properties of the edge state in the S=3/2 chain is studied in detail. Strong finite-size effects associated with spin dimerization in half-integer spin chains are also discussed.We report our results in investigating edge effects of open antiferromagnetic Heisenberg spin chains with spin magnitudes S=1/2,1,3/2,2 using the density-matrix renormalization-group method initiated by White. For integer spin chains, we find that edge states with spin magnitude ${\mathit{S}}_{\mathrm{edge}}$=S/2 exist, in agreement with the valence-bond-solid model picture. For half-integer spin chains, we find that no edge states exist for the S=1/2 spin chain, but an edge state exists in the S=3/2 spin chain with a ${\mathit{S}}_{\mathrm{edge}}$=1/2, in agreement with a previous conjecture by Ng. The properties of the edge state in the S=3/2 chain is studied in detail. Strong finite-size effects associated with spin dimerization in half-integer spin chains are also discussed.

arXiv:cond-mat/9502047Physical review. B, Condensed matterNov 1, 199553 citations

{\mathit{S}}_{\mathrm{edge}}

=S/2 exist, in agreement with the valence-bond-solid model picture. For half-integer spin chains, we find that no edge states exist for the S=1/2 spin chain, but an edge state exists in the S=3/2 spin chain with a

{\mathit{S}}_{\mathrm{edge}}

=1/2, in agreement with a previous conjecture by Ng. The properties of the edge state in the S=3/2 chain is studied in detail. Strong finite-size effects associated with spin dimerization in half-integer spin chains are also discussed.