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

Abstract

In this paper we study the frustrated J1−J2quantum Heisenberg model on the square lattice for J2>J1/2, in a magnetic field. In this regime the classical system is known tohave a degenerate manifold of lowest energy configurations, where standard thermal orderby disorder occurs. In order to study its quantum version we use a path integralformulation in terms of coherent states. We show that the classical degeneracy in theplane 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, leavinga Z2 degeneracy. A careful analysis revealsa purely quantum mechanical effect given by the tunneling between the two minima selectedby 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 or both of these fields produces the locking of their conjugateobservables.