Quantum phases and phase transitions of Mott insulators

Abstract

This article contains a theoretical overview of the physical properties of antiferromagnetic Mott insulators in spatial dimensions greater than one. Many such materials have been experimentally studied in the past decade and a half, and we make contact with these studies. The simplest class of Mott insulators have an even number of S=1/2 spins per unit cell, and these can be described with quantitative accuracy by the bond operator method: we discuss their spin gap and magnetically ordered states, and the transitions between them driven by pressure or an applied magnetic field. The case of an odd number of S=1/2 spins per unit cell is more subtle: here the spin gap state can spontaneously develop bond order (so the ground state again has an even number of S=1/2 spins per unit cell), and/or acquire topological order and fractionalized excitations. We describe the conditions under which such spin gap states can form, and survey recent theories (T. Senthil et al., cond-mat/0312617) of the quantum phase transitions among these states and magnetically ordered states. We describe the breakdown of the Landau-Ginzburg-Wilson paradigm at these quantum critical points, accompanied by the appearance of emergent gauge excitations.

51 pages, 13 figures

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• Quantum critical transport, duality, and M-theory
• Topological order, emergent gauge fields, and Fermi surface reconstruction
• Modified kagome physics in the natural spin-1/2 kagome lattice systems - kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2
• High-Order Coupled Cluster Method Study of Frustrated and Unfrustrated Quantum Magnets in External Magnetic Fields
• Emergent gauge fields and the high temperature superconductors
• Quantum electrodynamics in 2+1 dimensions, confinement, and the stability of U(1) spin liquids
• Quantum phase transitions beyond the Landau-Ginzburg paradigm and supersymmetry
• Effect of anisotropy on the ground-state magnetic ordering of the spin-one quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice
• Quantum phases and phase transitions of Mott insulators
• Frustrated Quantum Antiferromagnets: Application of High-Order Coupled Cluster Method
• Influence of the spin quantum number $s$ on the zero-temperature phase transition in the square lattice $J$-$J^{\prime }$ model
• Analytical recursive method to ascertain multisite entanglement in doped quantum spin ladders
• Centipede ladder at quarter filling
• The two dimensional Antiferromagnetic Heisenberg model with next nearest neighbour Ising exchange