‘‘Θ physics’’ and quantum spin chains (abstract)

The one-dimensional quantum Heisenberg antiferromagnet with exchange alternation is related to the nonlinear 0(3) sigma model with a topological ‘‘θ term’’ in the Langrangian. The models with parity symmetry (θ=0 or π) are respectively related to the integer and half-integer spin models without exchange alternation. The nonlinear quantum physics of Heisenberg antiferromagnets is placed in a wider context of topologically nontrivial field theories and the spin-Peierls effect in half-integer spin systems (and its absence in integer spin systems) explained.