Non-Abelian Chern-Simons particles in an external magnetic field (original) (raw)
Related papers
Statistical Mechanics of an Ideal Gas of Non-Abelian Anyons
2012
We study the thermodynamical properties of an ideal gas of non-Abelian Chern-Simons particles and we compute the second virial coefficient, considering the effect of general soft-core boundary conditions for the two-body wavefunction at zero distance. The behaviour of the second virial coefficient is studied as a function of the Chern-Simons coupling, the isospin quantum number and the hard-coreness parameters. Expressions for the main thermodynamical quantities at the lower order of the virial expansion are also obtained: we find that at this order the relation between the internal energy and the pressure is the same found (exactly) for 2D Bose and Fermi ideal gases. A discussion of the comparison of obtained findings with available results in literature for systems of hard-core non-Abelian Chern-Simons particles is also supplied.
Statistical interparticle potential of an ideal gas of non-Abelian anyons
2013
We determine and study the statistical interparticle potential of an ideal system of non-Abelian Chern-Simons (NACS) particles, comparing our results with the corresponding results of an ideal gas of Abelian anyons. In the Abelian case, the statistical potential depends on the statistical parameter α and it has a "quasi-bosonic" behaviour for 0 < α < 1/2 (non-monotonic with a minimum) and a "quasi-fermionic" behaviour for 1/2 < α < 1 (monotonically decreasing without a minimum). In the non-Abelian case the behavior of the statistical potential depends on the Chern-Simons coupling and the isospin quantum number: as a function of these two parameters, a phase diagram with quasi-bosonic, quasi-fermionic and bosonic-like regions is obtained and investigated. Finally, using the obtained expression for the statistical potential, we compute the second virial coefficient of the NACS gas, which correctly reproduces the results available in literature.
2012
We study a 2+1 dimensional theory of bosons and fermions with an ω ∝ k 2 dispersion relation. The most general interactions consistent with specific symmetries impart fractional statistics to the fermions. Unlike examples involving Chern-Simons gauge theories, our statistical phases derive from the exchange of gapless propagating bosons with marginal interactions. Even though no gap exists, we show that the anyonic statistics are precisely defined. Symmetries combine with the vacuum structure to guarantee the non-renormalization of our anyonic phases. arXiv:1205.6816v1 [hep-th] 30 May 2012 1 Despite the absence of a gap, the anyonic phase is well-defined, as we show in section 3.1
Synthetic non-Abelian statistics by Abelian anyon condensation
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.
Kohn-Sham density functional theory of Abelian anyons
Physical Review B, 2021
We develop a density functional treatment of non-interacting abelian anyons, which is capable, in principle, of dealing with a system of a large number of anyons in an external potential. Comparison with exact results for few particles shows that the model captures the behavior qualitatively and semi-quantitatively, especially in the vicinity of the fermionic statistics. We then study anyons with statistics parameter 1 + 1/n, which are thought to condense into a superconducting state. An indication of the superconducting behavior is the mean-field result that, for uniform density systems, the ground state energy increases under the application of an external magnetic field independent of its direction. Our density-functional-theory based analysis does not find that to be the case for finite systems of anyons, which can accommodate a weak external magnetic field through density transfer between the bulk and the boundary rather than through transitions across effective Landau levels, but the "Meissner repulsion" of the external magnetic field is recovered in the thermodynamic limit as the effect of the boundary becomes negligible. We also consider the quantum Hall effect of anyons, and show that its topological properties, such as the charge and statistics of the excitations and the quantized Hall conductance, arise in a self-consistent fashion.
A Chern-Simons effective field theory for the Pfaffian quantum Hall state
Nuclear Physics B, 1998
We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state. To arrive at this theory, we observe that the edge theory of the Pfaffian state of bosons at ν = 1 is an SU (2)2 Kac-Moody algebra. It follows that the corresponding bulk effective field theory is an SU (2) Chern-Simons theory with coupling constant k = 2. The effective field theories for other Pfaffian states, such as the fermionic one at ν = 1/2 are obtained by a fluxattachment procedure. We discuss the non-Abelian statistics of quasiparticles in the context of this effective field theory.
Statistical mechanics of anyons
Nuclear Physics B, 1985
We study the statistical mechanics of a two-dimensional gas of free anyons -particles which interpolate between Bose-Einstein and Fermi-Dirac character. Thermodynamic quantities are discussed in the low-density regime. In particular, the second virial coefficient is evaluated by two different methods and is found to exhibit a simple, periodic, but nonanalytic behavior as a function of the statistics determining parameter.
Anyons and the quantum Hall effect—A pedagogical review
Annals of Physics, 2008
The dichotomy between fermions and bosons is at the root of many physical phenomena, from metallic conduction of electricity to super-fluidity, and from the periodic table to coherent propagation of light. The dichotomy originates from the symmetry of the quantum mechanical wave function to the interchange of two identical particles. In systems that are confined to two spatial dimensions particles that are neither fermions nor bosons, coined ''anyons'', may exist. The fractional quantum Hall effect offers an experimental system where this possibility is realized. In this paper we present the concept of anyons, we explain why the observation of the fractional quantum Hall effect almost forces the notion of anyons upon us, and we review several possible ways for a direct observation of the physics of anyons. Furthermore, we devote a large part of the paper to non-abelian anyons, motivating their existence from the point of view of trial wave functions, giving a simple exposition of their relation to conformal field theories, and reviewing several proposals for their direct observation.
Two-dimensional quantum liquids from interacting non-Abelian anyons
New Journal of Physics, 2011
A set of localized, non-Abelian anyons -such as vortices in a px +ipy superconductor or quasiholes in certain quantum Hall states -gives rise to a macroscopic degeneracy. Such a degeneracy is split in the presence of interactions between the anyons. Here we show that in two spatial dimensions this splitting selects a unique collective state as ground state of the interacting many-body system. This collective state can be a novel gapped quantum liquid nucleated inside the original parent liquid (of which the anyons are excitations). This physics is of relevance for any quantum Hall plateau realizing a non-Abelian quantum Hall state when moving off the center of the plateau.
Nuclear Physics B, 2001
We present a pure Chern-Simons formulation of families of interesting Conformal Field Theories describing edge states of non-Abelian Quantum Hall states. These theories contain two Abelian Chern-Simons fields describing the electromagnetically charged and neutral sectors of these models, respectively. The charged sector is the usual Abelian Chern-Simons theory that successfully describes Laughlin-type incompressible fluids. The neutral sector is a 2 + 1-dimensional theory analogous to the 1 + 1-dimensional orbifold conformal field theories. It is based on the gauge group O(2) which contains a Z 2 disconnected group manifold, which is the salient feature of this theory. At level q, the Abelian theory of the neutral sector gives rise to a Z 2q symmetry, which is further reduced by imposing the Z 2 symmetry of charge-conjugation invariance. The remaining Z q symmetry of the neutral sector is the origin of the non-Abelian statistics of the (fermionic) q-Pfaffian states.