Related papers: Nonabelian Anyon Condensation in 2+1d topological …
The coset construction of two-dimensional conformal field theory (2D CFT) defines a 2D CFT by taking the quotient of two previously known chiral algebras. In this work, we use the methods of non-abelian (non-invertible) anyon condensation…
The string-net approach by Levin and Wen, and the local unitary transformation approach by Chen, Gu, and Wen, provide ways to classify topological orders with gappable edge in 2D bosonic systems. The two approaches reveal that the…
We generalize the hierarchy construction to generic 2+1D topological orders (which can be non-Abelian) by condensing Abelian anyons in one topological order to construct a new one. We show that such construction is reversible and leads to a…
We discuss the problem of tachyon condensation in the framework of background independent open string field theory. We show, in particular, that the computation of the string field theory action simplifies considerably if one looks at…
We propose a family of order parameters to detect the symmetry fractionalization class of anyons in 2D topological phases. This fractionalization class accounts for the projective, as opposed to linear, representations of the symmetry group…
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…
Symmetry-enriched topological (SET) phases combine intrinsic topological order with global symmetries, giving rise to novel symmetry phenomena. While SET phases with Abelian anyons are relatively well understood, those involving nonabelian…
We introduce a numerical method for identifying topological order in two-dimensional models based on one-dimensional bulk operators. The idea is to identify approximate symmetries supported on thin strips through the bulk that behave as…
We propose a symmetry-based approach to constructing lattice models for chiral topological phases, focusing on non-Abelian anyons. Using a 2+1D version of anyon chains and modular tensor categories(MTCs), we ensure exact MTC symmetry at the…
The remarkable complexity of the vacuum state of a topologically-ordered many-body quantum system encodes the character and intricate braiding interactions of its emergent particles, the anyons.} Quintessential predictions exploiting this…
Topological phase transitions beyond anyon condensation remain poorly understood. A notable example is the transition between the toric code (TC) and double semion (DS) phases, which has two distinct $\mathbb{Z}_2$ topological orders in (2…
In this thesis I develop a formalism whereby a tensor network may be understood in terms of a unitary braided tensor category, and represented in a particularly efficient manner corresponding to the exploitation of this mathematical…
While the topological order in two dimensions has been studied extensively since the discover of the integer and fractional quantum Hall systems, topological states in 3 spatial dimensions are much less understood. In this paper, we propose…
It is well-known that many topological phase transitions of intrinsic Abelian topological phases are accompanied by condensation and confinement of anyons. However, for non-Abelian topological phases, more intricate phenomena can occur at…
We describe a family of phase transitions connecting phases of differing non-trivial topological order by explicitly constructing Hamiltonians of the Levin-Wen[PRB 71, 045110] type which can be tuned between two solvable points, each of…
Identifying experimental signatures of anyons, which exhibit fractional exchange statistics, remains a central challenge in the study of two-dimensional topologically ordered systems. Previous theoretical work has shown that the threshold…
Synthetic anyons can be implemented in a noninteracting many-body system, by using specially tailored localized (physical) probes, which supply the demanded nontrivial topology in the system. We consider the Hamiltonian for noninteracting…
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…
We use a family of critical spin chain models discovered recently by one of us [M. Greiter, Mapping of Parent Hamiltonians, Springer, Berlin/Heidelberg 2011] to propose and elaborate that non-Abelian, SU(2) level $k=2S$ anyon statistics…
Boundary conformal field theory is brought to bear on the study of topological insulating phases of non-abelian anyonic chains. These topologically non-trivial phases display protected anyonic end modes. We consider antiferromagnetically…