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

Abstract

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.

9 pages (8 figures included)

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• Frustration Induced Quantum Phases in Mixed Spin Chain with Frustrated Side Chains
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• Fermionic versus bosonic descriptions of one-dimensional spin-gapped antiferromagnets
• Disordered ground states in a quantum frustrated spin chain with side chains
• Finite Size Scaling, Fisher Zeroes and N=4 Super Yang-Mills
• Spin-Gap States of a Periodic Mixed Spin Chain
• On effects of regular S=1 dilution of S=1/2 antiferromagnetic Heisenberg chains by a quantum Monte Carlo simulation