Spin liquids in frustrated magnets

Fragile Mott insulators

We prove that there exists a class of crystalline insulators, which we call "fragile Mott insulators," which are not adiabatically connected to any sort of band insulator provided time-reversal and certain point-group symmetries are respected, but which are otherwise unspectacular in that they exhibit no topological order nor any form of fractionalized quasiparticles. Different fragile Mott insulators are characterized by different nontrivial one-dimensional representations of the crystal point group. We illustrate this new type of insulators with two examples: the d Mott insulator discovered in the checkerboard Hubbard model at half-filling and the Affleck-Kennedy-Lieb-Tasaki insulator on the square lattice.

The paired-electron crystal in the two-dimensional frustrated quarter-filled band

The competition between antiferromagnetic and spin-singlet ground states within quantum spin models and the ½-filled band Hubbard model has received intense scrutiny. Here we demonstrate a frustration-induced transition from Néel antiferromagnetism to a spin-singlet state in the interacting ¼-filled band on an anisotropic triangular lattice. While the antiferromagnetic state has equal charge densities, 0.5, on all sites, the spin-singlet state is a paired-electron crystal, with pairs of charge-rich sites separated by pairs of charge-poor sites. The paired-electron crystal provides a natural description of the spin-gapped state proximate to superconductivity in many organic charge transfer solids. Pressure-induced superconductivity in these correlated-electron systems is likely a result of a transition from the ¼-filled band valence bond solid to a valence bond liquid.

Kitaev-Heisenberg model on a honeycomb lattice: possible exotic phases in iridium oxides A2IrO3

We derive and study a spin one-half Hamiltonian on a honeycomb lattice describing the exchange interactions between Ir4+ ions in a family of layered iridates A2IrO3 (A=Li,Na). Depending on the microscopic parameters, the Hamiltonian interpolates between the Heisenberg and exactly solvable Kitaev models. Exact diagonalization and a complementary spin-wave analysis reveal the presence of an extended spin-liquid phase near the Kitaev limit and a conventional Néel state close to the Heisenberg limit. The two phases are separated by an unusual stripy antiferromagnetic state, which is the exact ground state of the model at the midpoint between two limits.

Probing quantum frustrated systems via factorization of the ground state

The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure of frustration: strongly frustrated systems are those that cannot accommodate for classical-like solutions. The exact form of the factorized ground states and the critical frustration are determined for various classes of nonexactly solvable spin models with different spatial ranges of the interactions. For weak frustration, the existence of disentangling transitions determines the range of applicability of mean-field descriptions in biological and physical problems such as stochastic gene expression and the stability of long-period modulated structures.