Phase Diagrams of Mixed Spin Chains with Period 4 by the Nonlinear $σ$ Model

Details Phase Diagrams of Mixed Spin Chains with Period 4 by the Nonlinear $σ$ Model Phase Diagrams of Mixed Spin Chains with Period 4 by the Nonlinear $σ$ Model

1999-11-07

arxiv.org/abs/cond-mat/9911098v1

Physics

Condensed Matter

Strongly Correlated Electrons

9 pages (8 figures included)

Scientific paper

10.1103/PhysRevB.61.8863

We study mixed quantum spin chains consisting of two kinds of spins with magnitudes, s_a and s_b. The spins are arrayed as s_a-s_a-s_b-s_b in a unit cell and the exchange couplings are accordingly periodic with period 4. The spin Hamiltonian is mapped onto a nonlinear $\sigma$ model based on the general formula for periodic inhomogeneous spin chains. The gapless condition given by the nonlinear $\sigma$ model determines boundaries between disordered phases in the space of the exchange parameters. The phase diagram has a rich phase structure characterized by the values of s_a and s_b. We explain all phases in the singlet-cluster-solid picture which is an extension of the valence-bond-solid picture.

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