Related papers: The Quantum Double Model with Boundary: Condensati…
The macroscopic theory of anyon condensation, rooted in the categorical structure of topological excitations, provides a complete classification of gapped boundaries in topologically ordered systems, where distinct boundaries correspond to…
We provide explicit constant-depth local unitary circuits that realize general anyon permutations in Kitaev's quantum double models. This construction can be naturally understood through a correspondence between anyon permutation symmetries…
We analyze phase transitions induced by forbidding charges and fluxes in $\mathcal{D}(S_3)$, the simplest non-Abelian model among quantum doubles, a class of 2D spin lattice topological models introduced by Kitaev. Contrary to a topological…
The theory of topological quantum computation is underpinned by two important classes of models. One is based on non-abelian Chern-Simons theory, which yields the so-called $\rm{SU}(2)_k$ anyon models that often appear in the context of…
Transitions between different topologically ordered phases have been studied by artificially creating boundaries between these gapped phases and thus studying their effects relating to condensation and tunneling of particles from one phase…
The algebraic tools used to study topological phases of matter are not clearly suited to studying processes in which the bulk energy gap closes, such as phase transitions. We describe an elementary two edge thought experiment which reveals…
We study effectively one-dimensional systems that emerge at the edge of a two-dimensional topologically ordered state, or at the boundary between two topologically ordered states. We argue that anyons of the bulk are associated with…
We investigate transitions between topologically ordered phases in two spatial dimensions induced by the condensation of a bosonic quasiparticle. To this end, we formulate an extension of the theory of symmetry breaking phase transitions…
The recent article [arXiv:2307.12552] gave local topological order (LTO) axioms for a quantum spin system, showed they held in Kitaev's Toric Code and in Levin-Wen string net models, and gave a bulk boundary correspondence to describe bulk…
We derive new dualities of topological quantum field theories in three spacetime dimensions that generalize the familiar level-rank dualities of Chern-Simons gauge theories. The key ingredient in these dualities is non-abelian anyon…
We generalize the twisted quantum double model of topological orders in two dimensions to the case with boundaries by systematically constructing the boundary Hamiltonians. Given the bulk Hamiltonian defined by a gauge group $G$ and a…
Models for topological quantum computation are based on braiding and fusing anyons (quasiparticles of fractional statistics) in (2+1)-D. The anyons that can exist in a physical theory are determined by the symmetry group of the Hamiltonian.…
We generalize the Electric-magnetic (EM) duality in the quantum double (QD) models to the case of topological orders with gapped boundaries. We also map the QD models with boundaries to the Levin-Wen (LW) models with boundaries. To this…
Topological quantum error correction based on the manipulation of the anyonic defects constitutes one of the most promising frameworks towards realizing fault-tolerant quantum devices. Hence, it is crucial to understand how these defects…
We compute the spectra of anyon quasiparticles in all three super-selection sectors of the Kitaev model (i.e., visons, fermions and bosons), perturbed by a Zeeman field away from its exactly solvable limit, to gain insights on the…
We give a complete classification of the anyon sectors of Kitaev's quantum double model on the infinite triangular lattice and for finite gauge group $G$, including the non-abelian case. As conjectured, the anyon sectors of the model…
Bose condensation is central to our understanding of quantum phases of matter. Here we review Bose condensation in topologically ordered phases (also called topological symmetry breaking), where the condensing bosons have non-trivial mutual…
Transitions between quantum spin liquids (QSLs) are fundamental problems lying beyond the Landau paradigm and requiring a deep understanding of the entanglement structures of QSLs called topological orders. The novel concept of anyon…
This paper studies fault-tolerant quantum computation with gapped boundaries. We first introduce gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories using their Hamiltonian realizations. We classify the…
Anyons exhibit a non-trivial interplay between local exclusion rules and non-local braiding and exchange phases, making a consistent commutation algebra and second-quantized formulation challenging. We develop an algebraic framework for…