Path integrals for dimerized quantum spin systems

Abstract

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 Néel 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.

20 pages, no figures

References in corpus (4)

• "Deconfined" quantum critical points
• Evidence of Unconventional Universality Class in a Two-Dimensional Dimerized Quantum Heisenberg Model
• Néel-Dimer Transition in Antiferromagnetic Heisenberg Model and Deconfinement of Spinons at the Critical Point
• Massive CP${}^1$ theory from a microscopic model for doped antiferromagnets

Cited by in corpus (2)

• Two-particle decay and quantum criticality in dimerized antiferromagnets
• Translation-Invariant Parent Hamiltonians of Valence Bond Crystals