Path integrals for dimerized quantum spin systems

Details Path integrals for dimerized quantum spin systems Path integrals for dimerized quantum spin systems

2010-03-30

arxiv.org/abs/1003.5833v3

Nuclear Phys. B 842, 225 (2011)

Physics

Condensed Matter

Strongly Correlated Electrons

20 pages, no figures

Scientific paper

Dimerized quantum spin systems may appear under several circumstances, e.g\ by a modulation of the antiferromagnetic exchange coupling in space, or in frustrated quantum antiferromagnets. In general, such systems display a quantum phase transition to a N\'eel state as a function of a suitable coupling constant. We present here two path-integral formulations appropriate for spin $S=1/2$ dimerized systems. The first one deals with a description of the dimers degrees of freedom in an SO(4) manifold, while the second one provides a path-integral for the bond-operators introduced by Sachdev and Bhatt. The path-integral quantization is performed using the Faddeev-Jackiw symplectic formalism for constrained systems, such that the measures and constraints that result from the algebra of the operators is provided in both cases. As an example we consider a spin-Peierls chain, and show how to arrive at the corresponding field-theory, starting with both a SO(4) formulation and bond-operators.

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