Path integral approach to order by disorder selection in partially polarized quantum spin systems

C. A. LAMAS; D. C. CABRA; P. PUJOL; G. L. ROSSINI

EUROPEAN PHYSICAL JOURNAL B - CONDENSED MATTER

SPRINGER

Lugar: Berlin; Año: 2015 vol. 88 p. 176 - 185

1434-6028

In this paper we study the frustrated J1 −J2 quantum Heisenberg model on the square lattice forJ 2 > J1/2, in a magnetic field. In this regime the classical system is known to have a degenerate manifoldof lowest energy configurations, where standard thermal order by disorder occurs. In order to study itsquantum version we use a path integral formulation in terms of coherent states. We show that the classicaldegeneracy in the plane transverse to the magnetic field is lifted by quantum fluctuations. Collinear statesare then selected, in a similar pattern to that set by thermal order by disorder, leaving a Z2 degeneracy.A careful analysis reveals a purely quantum mechanical effect given by the tunneling between the twominima selected by fluctuations. The effective description contains two planar (XY -like) fields conjugateto the total magnetization and the difference of the two sublattice magnetizations. Disorder in either orboth of these fields produces the locking of their conjugate observables.