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Showing 1 to 17 of 17 for “"Anyons"”.
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Interacting Anyons in One and Two Dimensions: Strong Zero Modes in Anyon Chains and Non-Abelian Anyons on a Torus
… the zero mode in the diagrammatic formalism of anyons. In the second part, we construct a hopping model of non-abelian anyons on a torus. We demonstrate that that the model possesses a translational symmetry around each non-trivial torus loop. By calculating the level spacing statistics of the …
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Non-Abelian Anyons in the Kitaev Honeycomb Model
… phase is an essential feature of non-Abelian anyons for the realization of topological quantum computation. This thesis is primarily a study about the numerical calculation of the Berry phase of non-Abelian anyons in the Kitaev honeycomb lattice model. It is also a guide for experimental the …
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Interacting non-Abelian anyons in an exactly solvable lattice model
In this thesis, we study the non-Abelian anyons that emerge as vortices in Ki-taev's honeycomb spin lattice model. By generalizing the solution of the model, we explicity demonstrate the non-Abelian fusion rules and the braid statistics that charaterize the anyons. This is based on showing the …
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BPS Approaches to Anyons, Quantum Hall States and Quantum Gravity
… of various bound states of non-Abelian anyons, analyse some interesting unitarity bound violations, and test some recently proposed bosonization dualities. Secondly, we turn on a chemical potential and break conformal invariance, putting the theory into the regime of the Fractional …
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Dissecting topological quantum computation
Anyons are quasiparticles that may be realized in two dimensional systems. They come in two types, the simpler Abelian anyons and the more complex non-Abelian anyons. Both of these have been considered as a means for quantum computation, but non-Abelian anyons are usually assumed to be better …
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Quasiparticles in Quantum Many-Body Systems
… that direction. Also such lattice models hosting anyons are particularly important to control the movement of anyons while experimentally implemented with ultra-cold atoms in optical lattices. We construct lattice models by implementing analytical states and parent Hamiltonians on two-dimensional …
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Topological phases of matter
… there are particle-like excitations called anyons. In contrast, in (3+1)D topologically ordered phases, there are both particle-like and loop-like excitations. These excitations exhibit braiding statistics, meaning that carrying one excitation adiabatically around another transform the …
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Optimising Qubit Designs for Topological Quantum Computation
… qudits where logic gates are imposed by braiding anyons in 2+1 dimensions. We also study qudits designed from ring-shaped, anyon-like excitations in 3+1 dimensions, where logic gates are implemented by elements of the loop braid group. We introduce the concept of local representations, where the …
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Topological phases in narrow-band systems
… Hall state, excitations of this state are anyons when there is an incommensurate filling. The underlying lattice allows access to a new regime in which the anyon gas can form a charged superfluid, including states with intrinsic topological order or that similar to a BCS-type state. The …
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The Death of Quasiparticles: Strongly Interacting Gapless Phases with Fermi Surfaces and Fractional Statistics
… to close the anyon energy gaps, the original anyons lose their coherence and a variety of novel phases emerge. A highlight in this direction is a new mechanism for topological superconductivity in itinerant abelian and non-abelian anyon fluids, which could make contact with experiments on …
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Anyonic symmetry and twist defects
… called twist defects, which permute orbiting anyons by their symmetries. We see how to realize these defects at domain walls on the gapped edges of non-chiral fractional quantum Hall states. We have distinct gapped edge phases in one to one correspondence with the anyonic symmetries. …
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An algebro-geometric study of two models of quantum computaiton
… the TQFT resulting from the presence of abelian anyons with exchange statistics a q-th root of unity. Such a resource is a topologically fault-tolerant quantum memory. The abelian character of the emergent particle statistics leads us to answer the second question via an algebraic realization of …
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Defects, topology, and the geometric phase in condensed matter physics
… a general notion of a group defect that permutes anyons and use the toric code as well as a new honeycomb model \cite{roytwist}, as examples. I discuss fusion of these defects as well as ground state degeneracy. The latter is treated geometrically using covering spaces. A common theme running …
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Aspects of highly-entangled quantum matter : from exotic phases, to quantum computation, and dynamics
… which provides a generalization of non-Abelian anyons in three spatial dimensions. In Part III, we investigate the dynamics of operator spreading and entanglement growth in quantum circuits composed of random, local unitary operators. We relate quantities averaged over realizations of the …
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Linear and nonlinear edge dynamics and quasiparticle excitations in fractional quantum Hall systems
… relation and is in agreement with the theory of anyons, so that it is a good anti-anyon for the Laughlin's quasihole. On the other hand, even though we find that the Laughlin’s quasielectron satisfies the spin-statistics relation, it carries the wrong spin to be the anti-anyon of Laughlin’s …
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Solitons and dualities in 2+1 dimensions
… as composite objects, bound states of (dual) anyons. We comment on potential links with three-dimensional mirror symmetry. We also compute the equivariant expected degeneracy of local Abelian vortices on the $\Omega$-deformed sphere, finding it to be a $q$-analog of the undeformed version. By …
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The curious case of the inverted oscillator: On the dynamics and symmetries of quadratic potentials in the lowest Landau level
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms