Microscopic Models of 2D Magnets with Fractionalized Excitations

Abstract

We demonstrate that spin-charge separation can occur in two dimensions and note its confluence with superconductivity, topology, gauge theory, and fault-tolerant quantum computation. We construct a microscopic Ising-like model and, at a special coupling constant value, find its exact ground state as well as neutral spin 1/2 (spinon), spinless charge e (holon), and $Z_2$ vortex (vison) states and energies. The fractionalized excitations reflect the topological order of the ground state which is evinced by its fourfold degeneracy on the torus -- a degeneracy which is unrelated to translational or rotational symmetry -- and is described by a $Z_2$ gauge theory. Our model is related to the quantum dimer model and is a member of a family of topologically-ordered models, one of which is integrable and realizes the toric quantum error correction code.

Final version accepted for publication in Phys. Rev. B. Two new figures and several clarifications have been added

References in corpus (3)

• Large N expansion for frustrated and doped quantum antiferromagnets
• Two-dimensional periodic frustrated Ising models in a transverse field
• Dual Vortex Theory of Strongly Interacting Electrons: Non-Fermi Liquid to the (Hard) Core

Cited by in corpus (32)

• Non-Abelian Anyons and Topological Quantum Computation
• Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
• Fractionalization in an Easy-axis Kagome Antiferromagnet
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Quantum dimer model on the kagome lattice: solvable dimer liquid and Ising gauge theory
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Spin-exchange interactions of spin-one bosons in optical lattices: singlet, nematic and dimerized Phases
• A Class of $P,T$-Invariant Topological Phases of Interacting Electrons
• Resonating valence bond states in the PEPS formalism
• From classical to quantum dynamics at Rokhsar-Kivelson points
• Phase diagram of spin-1/2 J1-J2 Heisenberg model on honeycomb lattice
• Microscopic models for fractionalized phases in strongly correlated systems
• Frustrated quantum magnets
• Parent Hamiltonian for the Chiral Spin Liquid
• Exactly soluble models for fractional topological insulators in 2 and 3 dimensions
• Exotic quantum phases and phase transitions in correlated matter
• Theory of d-density wave viewed from a vertex model and its implications
• Quantum phase diagram of the spin-$1$ $J_1-J_2$ Heisenberg model on the honeycomb lattice
• Numerical study of fractionalization in an Easy-axis Kagome antiferromagnet
• Statistics of spinons in the spin-liquid phase of Cs2CuCl4
• Correlated Fermions on a Checkerboard Lattice
• Spin Structure Factor of the Frustrated Quantum Magnet Cs_2CuCl_4
• The planar pyrochlore antiferromagnet: A large-N analysis
• Quantum Disordered Ground States in Frustrated Antiferromagnets with Multiple Ring Exchange Interactions
• Quantum three-coloring dimer model and the disruptive effect of quantum glassiness on its line of critical points
• The types of Mott insulator
• The Roton Fermi Liquid
• Fermionic quantum dimer and fully-packed loop models on the square lattice
• U(1) spin liquids and valence bond solids in a large-N three-dimensional Heisenberg model
• A magnetic model with a possible Chern-Simons phase
• Response to defects in multi- and bipartite entanglement of isotropic quantum spin networks
• Evolution of the single-hole spectral function across a quantum phase transition in the anisotropic-triangular-lattice antiferromagnet