Creation and manipulation of anyons in the Kitaev model

Majorana-Mediated Spin Transport in Kitaev Quantum Spin Liquids

We study the spin transport through the quantum spin liquid (QSL) by investigating the real-time and real-space dynamics of the Kitaev spin system with zigzag edges using the time-dependent Majorana mean-field theory. After the magnetic-field pulse is introduced to one of the edges, spin moments are excited in the opposite edge region although spin moments are never induced in the Kitaev QSL region. This unusual spin transport originates from the fact that the S=1/2 spins are fractionalized into the itinerant and localized Majorana fermions in the Kitaev system. Although both Majorana fermions are excited by the magnetic pulse, only the itinerant ones flow through the bulk regime without spin excitations, resulting in the spin transport in the Kitaev system despite the presence of a nonzero spin gap. We also demonstrate that this phenomenon can be observed in the system with small Heisenberg interactions using the exact diagonalization.

Candidate quantum spin liquid due to dimensional reduction of a two-dimensional honeycomb lattice

As with quantum spin liquids based on two-dimensional triangular and kagome lattices, the two-dimensional honeycomb lattice with either a strong spin-orbital coupling or a frustrating second-nearest-neighbor coupling is expected to be a source of candidate quantum spin liquids. An ammonium salt [(C₃H₇)₃NH]₂[Cu₂(C₂O₄)₃](H₂O)_2.2 containing hexagonal layers of Cu²⁺ was obtained from solution. No structural transition or long-range magnetic ordering was observed from 290 K to 2 K from single crystal X-ray diffraction, specific heat and susceptibility measurements. The anionic layers are separated by sheets of ammonium and H₂O with distance of 3.5 Å and no significant interaction between anionic layers. The two-dimensional honeycomb lattice is constructed from Jahn-Teller distorted Cu²⁺ and oxalate anions, showing a strong antiferromagnetic interaction between S = 1/2 metal atoms with θ = −120 (1) K. Orbital analysis of the Cu²⁺ interactions through the oxalate-bridges suggests a stripe mode pattern of coupling with weak ferromagnetic interaction along the b axis, and strong antiferromagnetic interaction along the a axis. Analysis of the magnetic susceptibility shows that it is dominated by a quasi-one-dimensional contribution with spin chains that are at least as well isolated as those of well-known quasi-one-dimensional spin liquids.

Magnetic impurities in the honeycomb Kitaev model

We study the effect of coupling magnetic impurities to the honeycomb lattice spin-1/2 Kitaev model in its spin-liquid phase. We show that a spin-S impurity coupled to the Kitaev model is associated with an unusual Kondo effect with an intermediate coupling unstable fixed point Kc∼J/S separating topologically distinct sectors of the Kitaev model. We also show that the massless spinons in the spin-liquid mediate an interaction of the form Siα2Sjβ2/Rij3 between distant impurities unlike the usual dipolar RKKY interaction SiαSjα/Rij3 noted in various 2D impurity problems with a pseudogapped density of states of the spin bath. Furthermore, this long-range interaction is possible only if the impurities (a) couple to more than one neighboring spin on the host lattice and (b) the impurity spin S≠1/2.

Topological quantum computation via the quantum tunneling effect

Quantum computers are predicted to utilize quantum states to process tasks far faster than those of conventional classical computers. In this Letter we show an alternative approach towards building topological quantum computers by tuning the quantum tunneling effect of degenerate quantum states in topological order, instead of braiding anyons. Using a designer Hamiltonian-the Wen-Plaquette model as an example, we study its quantum tunneling effect of the toric codes and show how to control the toric codes to realize topological quantum computation. In particular, we give a proposal to the measurement of the toric codes from Aharonov-Bohm interferences of quasiparticles.

Demonstrating anyonic fractional statistics with a six-qubit quantum simulator

Anyons are exotic quasiparticles living in two dimensions that do not fit into the usual categories of fermions and bosons, but obey a new form of fractional statistics. Following a recent proposal [Phys. Rev. Lett. 98, 150404 (2007)], we present an experimental demonstration of the fractional statistics of anyons in the Kitaev spin lattice model using a photonic quantum simulator. We dynamically create the ground state and excited states (which are six-qubit graph states) of the Kitaev model Hamiltonian, and implement the anyonic braiding and fusion operations by single-qubit rotations. A phase shift of pi related to the anyon braiding is observed, confirming the prediction of the fractional statistics of Abelian 1/2 anyons.

Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices

Anyons are particlelike excitations of strongly correlated phases of matter with fractional statistics, characterized by nontrivial changes in the wave function, generalizing Bose and Fermi statistics, when two of them are interchanged. This can be used to perform quantum computations [A. Yu. Kitaev, Ann. Phys. (N.Y.) 303, 2 (2003)]. We show how to simulate the creation and manipulation of Abelian and non-Abelian anyons in topological lattice models using trapped atoms in optical lattices. Our proposal, feasible with present technology, requires an ancilla particle which can undergo single-particle gates, be moved close to each constituent of the lattice and undergo a simple quantum gate, and be detected.

Topological degeneracy and vortex manipulation in Kitaev's honeycomb model

The classification of loop symmetries in Kitaev's honeycomb lattice model provides a natural framework to study the Abelian topological degeneracy. We derive a perturbative low-energy effective Hamiltonian that is valid to all orders of the expansion and for all possible toroidal configurations. Using this form we demonstrate at what order the system's topological degeneracy is lifted by finite size effects and note that in the thermodynamic limit it is robust to all orders. Further, we demonstrate that the loop symmetries themselves correspond to the creation, propagation, and annihilation of fermions. We note that these fermions, made from pairs of vortices, can be moved with no additional energy cost.