The role of Berry phase in the spectrum of order parameter dynamics: a new perspective on Haldane's conjecture on antiferromagnetic spin chains

Details The role of Berry phase in the spectrum of order parameter dynamics: a new perspective on Haldane's conjecture on antiferromagnetic spin chains The role of Berry phase in the spectrum of order parameter dynamics: a new perspective on Haldane's conjecture on antiferromagnetic spin chains

2000-03-17

arxiv.org/abs/cond-mat/0003293v1

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages, Revtex

Scientific paper

We formulate the dynamics of local order parameters by extending the recently developed adiabatic spinwave theory involving the Berry curvature, and derive a formula showing explicitly the role of the Berry phase in determining the spectral form of the low-lying collective modes. For antiferromagnetic spin chains, the Berry phase becomes a topological invariant known as the Chern number. Our theory predicts the existence of the Haldane gap for a topologically trivial ground state, and a linear dispersion of low-lying excitations for a non-trivial ground state.

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