Effective field theory with a $θ$-vacua structure for 2d spin systems

Details Effective field theory with a $θ$-vacua structure for 2d spin systems Effective field theory with a $θ$-vacua structure for 2d spin systems

2006-06-13

arxiv.org/abs/cond-mat/0606314v1

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages, 2 figures

Scientific paper

10.1103/PhysRevB.74.140407

We construct a nonlinear sigma (NL$\sigma$) model description of 2+1d spin systems, by coupling together antiferromagnetic spin chains via interchain exchange terms. Our mapping incorporates methods developed recently by ourselves and by Senthil and Fisher, which aim at describing competition between antiferromagnetic and valence-bond-solid orders in quantum magnets. The resulting 2+1d $O$(4) NL$\sigma$ model contains a topological $\theta$-term whose vacuum angle $\theta$ varies continuously with $\delta$, the bond-alternation strength of the interchain interaction. This implies that the $\theta$-vacua structure for this NL$\sigma$ model can be explored by tuning $\delta$ in a suitable 2d spin system, which is strongly reminiscent of the situation for 1+1 AF spin chains with bond-alternation.

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