Creation and manipulation of anyons in the Kitaev model

We analyze the effect of local spin operators in the Kitaev model on the honeycomb lattice. We show, in perturbation around the isolated-dimer limit, that they create Abelian anyons together with fermionic excitations which are likely to play a role in experiments. We derive the explicit form of the operators creating and moving Abelian anyons without creating fermions and show that it involves multispin operations. Finally, the important experimental constraints stemming from our results are discussed.     

Emergent geometry experienced by fermions in graphene in the presence of dislocations

In graphene in the presence of strain the elasticity theory metric naturally appears. However, this is not the one experienced by fermionic quasiparticles. Fermions propagate in curved space, whose metric is defined by expansion of the effective Hamiltonian near the topologically protected Fermi point. We discuss relation between both types of metric for different parametrizations of graphene surface. Next, we extend our consideration to the case, when the dislocations are present. We consider the situation, when the deformation is described by elasticity theory and calculate both torsion and emergent magnetic field carried by the dislocation. The dislocation carries singular torsion in addition to the quantized flux of emergent magnetic field. Both may be observed in the scattering of quasiparticles on the dislocation. Emergent magnetic field flux manifests itself in the Aharonov–Bohm effect while the torsion singularity results in Stodolsky effect.     

The Higgs model for anyons and Liouville action

We connect Liouville theory, anyons and Higgs model in a purely geometrical way.     

Wilson fermions in a two-dimensional model

Wilson's action for fermions on a lattice is compared to the continuum action in a model obtained from the chiral Gross-Neveu model by performing a chiral transformation. The local definition of the axial current leads to two anomalies unrelated by the constraint of Lorentz invariance. In the large-N limit, the mass counterterm of the action is determined; this term is unnecessary in the Osterwalder-Seiler regularization. An expansion in the fermion propagator and in the axial current coupling may be formulated and summed to all orders for large N.     

Composite fermions in Suzuki's preon model

We consider fermions in the preon model invented by Suzuki to describe electroweak vector bosons as composite objects. It turns out that composite fermions are in this model very heavy and cannot be interpreted as the ordinary quarks and leptons. This is the case both in Suzuki's original theory and in a modified theory introduced in this paper.     

Slave anyons in the t-J model at the supersymmetric point

We discuss the properties of the supersymmetric t-J model in the formalism of the slave operators. In particular we introduce a generalized abelian bosonization for the model in two dimensions, and show that holons and spinons can be anyons of arbitrary complementary statistics (slave-anyon representation). The braiding properties of these anyonic operators are thoroughly analyzed, and are used to provide an explicit linear realization of the superalgebra SU(1|2). Finally, we prove that the hamiltonian of the t-J model in the slave-anyon representation is invariant under SU(1|2) for J = 2t.     

Cluster states of fermions in the single l-shell model

The paper deals with the ground state structure of the partly filled l-shell of a fermionic gas of atoms of spin s in a spherically symmetric spin independent trap potential. At particle numbers N=n(2s+1), n=1,2,...,2l+1 the basic building blocks are clusters consisting of (2s+1) atoms, whose wave functions are completely symmetric and antisymmetric in space and spin variables, respectively. The creation operator of a cluster is constructed and applied also to create multi cluster states. Ground state energy expressions are derived for the n-cluster states at different l, s values and interpreted in simple terms.     

Hopping-parameter expansion and the Schwinger model with Wilson fermions

The hopping-parameter expansion method is used to study the Euclidean lattice Schwinger model with Wilson fermions. The effect of virtual fermion loops is also analyzed. The relation between the \(\bar \psi \psi\) operators in the continuum and on the lattice is constructed. Our result shows satisfactory scaling behavior and reproduces well the exactly calculable value for the fermion condensate in the continuum.     

Chiral Schwinger model with massive fermions

We study the chiral Schwinger model with massive fermions. By bosonizing it within the path integral framework, we find an equivalent bosonic lagrangian with an interaction term of the sine-Gordon type. The consistency of the theory is discussed.