Anyons from bosons

1996

We consider the analog in one spatial dimension of the Bose-Fermi transmutation for planar systems. That is, the construction of a purely bosonic effective local theory starting from a system of bosons and fermions upon integration over the fermionic variables. We consider a quantum mechanical system of a spin 1/2 particle coupled to an abelian gauge field, which is classically invariant under gauge transformations and charge conjugation. It is found that, unless the flux enclosed by the particle orbits is quantized, and the spin takes a value n + 1/2, at least one of the two symmetries would be anomalous. Thus, charge conjugation invariance and the existence of abelian instantons simultaneously avoid the anomaly and force the particles to be

Physics Letters B, 1990

The inequivalent quantizations of a system of n identical particles on a manifold M, dim M > 2, are in 1-1 correspondence with irreducible unitar 3, representations of the braid group B, (M). The notion of the statistics of the particles is made precise. We give various examples where all the possible statistics for the system are determined, and find instances where the particles obey statistics different from the well-studied Bose, Fermi para-and 0-statistics.

1996

We consider the analog in one spatial dimension of the Bose-Fermi transmutation for planar systems. That is, the construction of a purely bosonic effective local theory starting from a system of bosons and fermions upon integration over the fermionic variables. We consider a quantum mechanical system of a spin 1/2 particle coupled to an abelian gauge field, which is classically invariant under gauge transformations and charge conjugation. It is found that, unless the flux enclosed by the particle orbits is quantized, and the spin takes a value n + 1/2, at least one of the two symmetries would be anomalous. Thus, charge conjugation invariance and the existence of abelian instantons simultaneously avoid the anomaly and force the particles to be

2003

Physical Review B, 2016

Anyons exist as point like particles in two dimensions and carry braid statistics which enable interactions that are independent of the distance between the particles. Except for a relatively few number of models which are analytically tractable, much of the physics of anyons remain still unexplored. In this paper, we show how U(1)-symmetry can be combined with the previously proposed anyonic Matrix Product States to simulate ground states and dynamics of anyonic systems on a lattice at any rational particle number density. We provide proof of principle by studying itinerant anyons on a one dimensional chain where no natural notion of braiding arises and also on a two-leg ladder where the anyons hop between sites and possibly braid. We compare the result of the ground state energies of Fibonacci anyons against hardcore bosons and spinless fermions. In addition, we report the entanglement entropies of the ground states of interacting Fibonacci anyons on a fully filled two-leg ladder at different interaction strength, identifying gapped or gapless points in the parameter space. As an outlook, our approach can also prove useful in studying the time dynamics of a finite number of nonabelian anyons on a finite two-dimensional lattice.

Nuclear Physics B, 1993

Physics Letters B, 1995

The possibility of excitations with fractional spin and statististics in 1 + 1 dimensions is explored. The configuration space of a two-particle system is the half-line. This makes the Hamiltonian self-adjoint for a family of boundary conditions parametrized by one real number γ. The limit γ → 0, (∞) reproduces the propagator of non-relativistic particles whose wavefunctions are even (odd) under particle exchange. A relativistic ansatz is also proposed which reproduces the correct Polyakov spin factor for the spinning particle in 1 + 1 dimensions. These checks support validity of the interpretation of γ as a parameter related to the "spin" that interpolates continuously between bosons (γ = 0) and fermions (γ = ∞). Our approach can thus be useful for obtaining the propagator for one-dimensional anyons.

Arxiv preprint cond-mat/0302019, 2003

We review aspects of classical and quantum mechanics of many anyons confined in an oscillator potential. The quantum mechanics of many anyons is complicated due to the occurrence of multivalued wavefunctions. Nevertheless there exists, for arbitrary number of anyons, a subset of exact solutions which may be interpreted as the breathing modes or equivalently collective modes of the full system. Choosing the three-anyon system as an example, we also discuss the anatomy of the so called "missing" states which are in fact known numerically and are set apart from the known exact states by their nonlinear dependence on the statistical parameter in the spectrum. Though classically the equations of motion remains unchanged in the presence of the statistical interaction, the system is non-integrable because the configuration space is now multiply connected. In fact we show that even though the number of constants of motion is the same as the number of degrees of freedom the system is in general not integrable via action-angle variables. This is probably the first known example of a many body pseudo-integrable system. We discuss the classification of the orbits and the symmetry reduction due to the interaction. We also sketch the application of periodic orbit theory (POT) to many anyon systems and show the presence of eigenvalues that are potentially non-linear as a function of the statistical parameter. Finally we perform the semiclassical analysis of the ground state by minimizing the Hamiltonian with fixed angular momentum and further minimization over the quantized values of the angular momentum.

Physics Letters B, 1997

We consider the analog in one spatial dimension of the Bose-Fermi transmutation for planar systems. A quantum mechanical system of a spin 1/2 particle coupled to an abelian gauge field, which is classically invariant under gauge transformations and charge conjugation is studied. It is found that unless the flux enclosed by the particle orbits is quantized, and the spin takes a value n + 1/2, at least one of the two symmetries would be anomalous. Thus, charge conjugation invariance and the existence of abelian instantons simultaneously force the particles to be either bosons or fermions, but not anyons.

Physical Review B, 2013

Topological degeneracy is the degeneracy of the ground states in a many-body system in the large-system-size limit. Topological degeneracy cannot be lifted by any local perturbation of the Hamiltonian. The topological degeneracies on closed manifolds have been used to discover/define topological order in many-body systems, which contain excitations with fractional statistics. In this paper, we study a new type of topological degeneracy induced by condensing anyons along a line in two-dimensional topological ordered states. Such topological degeneracy can be viewed as carried by each end of the line defect, which is a generalization of Majorana zero modes. The topological degeneracy can be used as a quantum memory. The ends of line defects carry projective non-Abelian statistics even though they are produced by the condensation of Abelian anyons, and braiding them allows us to perform fault tolerant quantum computations.