Classical and quantum spin liquids

Abstract

When considering magnetic systems in the thermodynamic limit and at low enough temperature, one finds typically magnetically ordered phases. In contrast, in the high-temperature regime, the interactions between the spin degrees of freedom become less relevant and the system loses its order: this is a paramagnet. This phenomenon of phase transition has been well understood using statistical mechanics and simple modelling. In these short lecture notes, we will review the possibility that a many-body magnetic system may remain magnetically disordered down to zero-temperature, both for classical or quantum spins. These exotic phases of matter are known, respectively, as classical and quantum spin liquids. We will address in particular the question of classification of these classical or quantum disordered phases. Indeed, while they have no local order parameter by definition, they can still possess different qualitative features related e.g. to the nature of their correlations or elementary excitations, which could be probed experimentally.

lecture notes from a talk given at the IHP workshop about "Open questions in the quantum many-body problem" organized by Yvan Castin and Carlos Sá de Melo

References in corpus (11)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• An exact chiral spin liquid with non-Abelian anyons
• On the stability of U(1) spin liquids in two dimensions
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagomé Lattice
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Fractionalization, topological order, and quasiparticle statistics
• Time-reversal-symmetry-breaking chiral spin liquids: a projective symmetry group approach of bosonic mean-field theories
• Critical Correlations for Short-Range Valence-Bond Wave Functions on the Square Lattice
• A fractionalised "${\mathbb{Z}}_2$" classical Heisenberg spin liquid