Path integrals for dimerized quantum spin systems

ADRIANA FOUSSATS A,∗, ANDRÉS GRECO A, ALEJANDRO MURAMATSU B

NUCLEAR PHYSICS B

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2011 vol. 842 p. 225 - 247

0550-3213

Dimerized quantum spin systems may appear under several circumstances, e.g. by a modulation of theantiferromagnetic exchange coupling in space, or in frustrated quantum antiferromagnets. In general, suchsystems 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 firstone deals with a description of the dimers degrees of freedom in an SO(4) manifold, while the secondone provides a path-integral for the bond-operators introduced by Sachdev and Bhatt. The path-integralquantization is performed using the Faddeev–Jackiw symplectic formalism for constrained systems, suchthat 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 an SO(4) formulation and bond-operators.