A bosonized-field-theory representation of spin operators in the uniform-field-induced Tomonaga-Luttinger-liquid (TLL) phase in spin-1 Haldane chains is formulated by means of the non-Abelian (Tsvelik’s Majorana fermion theory) and the Abelian bosonizations and Furusaki-Zhang technique [Phys. Rev. B 60, 1175 (1999)]. It contains massive magnon fields as well as massless boson fields. From it, a...

The Italian physicist Ettore Majorana, who disappeared in 1938, is now widely recognized for inventing the notion of a fermionic particle, the Majorana fermion, which has the strange property of being its own antiparticle [1]. What is perhaps less well known is that he also developed a natural and exact representation of a quantum spin [2], which inspired Julian Schwinger to create the bosonic ...

We investigate the electronic transport through a single-level quantum-dot which is capacitively coupled to a charge-qubit. By employing the method of nonequilibrium Green's functions, we calculate the electric current through quantum dot at finite bias voltages. The Green's functions and self-energies of the system are calculated perturbatively and self-consistently to the second order of inte...

Majorana fermions are long-sought exotic particles that are their own antiparticles. Here we propose to utilize superconducting circuits to construct two superconducting-qubit arrays where Majorana modes can occur. A so-called Majorana qubit is encoded by using the unpaired Majorana modes, which emerge at the left and right ends of the chain in the Majorana-fermion representation. We also show ...

When a topological order is realized in a certain class of superconductors, it supports Majorana fermions on the edge or in the vortex core. Vortices with Majorana fermion modes are neither fermions nor bosons but non-Abelian anyons, obeying the non-Abelian statistics for which the exchange operations of particles are not commutative. Because of this remarkable feature, Majorana fermions plays ...

In the Majorana representation of a spin 1/2 we find an identity which relates spin-spin correlators to one-particle fermionic correlators. This should be contrasted with the straightforward approach in which two-particle (four-fermion) correlators need to be calculated. We discuss applications to the analysis of the dynamics of a spin coupled to a dissipative environment and of a quantum detec...

Field-theoretic methods are applied to a number of two-dimensional lattice models with Abelian symmetry groups. It is shown, using a vortex + spin-wave decomposition. that the Z, Villain models are related to a class of continuum field theories with analogous duality properties. Fermion operators for these field theories are discussed. In the case of the Ising model, the vortices and spin-waves...

Topological superconductors, which support Majorana fermion excitations, have been the subject of intense studies due to their novel transport properties and their potential applications in fault-tolerant quantum computations. Here we propose a new type of topological superconductors that can be used as a novel source of correlated spin currents. We show that inducing superconductivity on a AII...

In various dimensional euclidean lattice gauge theories, we examine a compatibility of the Majorana decomposition and the charge conjugation property of lattice Dirac operators. In 8n and 1+8n dimensions, we find a difficulty to decompose a classical lattice action of the Dirac fermion into a system of the Majorana fermion and thus to obtain a factrized form of the Dirac determinant. Similarly,...