Frustrated Quantum Magnets

TL;DR

This paper reviews various quantum phases in two-dimensional magnetic insulators, including symmetry-breaking Neel phases, valence bond crystals, and spin liquids, highlighting their properties, excitations, and the effects of lattice geometry.

Contribution

It provides a comprehensive overview of quantum phases in 2D magnets, emphasizing the distinctions between gapless and gapful phases and exploring effects of lattice degeneracy.

Findings

Neel phases exhibit symmetry breaking and magnon excitations.

Valence Bond Crystals have long-range order in local singlet objects.

Resonating Valence Bond Spin Liquids lack local order and host deconfined spin-1/2 excitations.

Abstract

A description of different phases of two dimensional magnetic insulators is given. The first chapters are devoted to the understanding of the symmetry breaking mechanism in the semi-classical Neel phases. Order by disorder selection is illustrated. All these phases break SU(2) symmetry and are gapless phases with magnon excitations. Different gapful quantum phases exist in two dimensions: the Valence Bond Crystal phases (VBC) which have long range order in local S=0 objects (either dimers in the usual Valence Bond acception or quadrumers..), but also Resonating Valence Bond Spin Liquids (RVBSL), which have no long range order in any local order parameter and an absence of susceptibility to any local probe. VBC have gapful S = 0, or 1 excitations, RVBSL on the contrary have deconfined spin-1/2 excitations. Examples of these two kinds of quantum phases are given in chapters 4 and 5. A special class of magnets (on the kagome or pyrochlore lattices) has an infinite local degeneracy in the classical limit: they give birth in the quantum limit to different behaviors which are illustrated and questionned in the last lecture.