Anyon condensation and tensor categories

Kong, Liang

doi:10.1016/j.nuclphysb.2014.07.003

Cited by 197 publications

(279 citation statements)

References 66 publications

Supporting

Mentioning

276

Contrasting

Order By: Relevance

“…We remark that the simple-current reductions that we study here correspond to the condensation of bosonic topological excitations [39][40][41][42][43].…”

Section: -10mentioning

confidence: 62%

See 1 more Smart Citation

Simple-current algebra constructions of 2+1-dimensional topological orders

Schoutens

Wen

2016

Phys. Rev. B

View full text Add to dashboard Cite

Self-consistent (non-)Abelian statistics in 2+1 dimensions (2+1D) are classified by modular tensor categories (MTCs). In recent works, a simplified axiomatic approach to MTCs, based on fusion coefficients N ij k and spins s i , was proposed. A numerical search based on these axioms led to a list of possible (non-)Abelian statistics, with rank up to N = 7. However, there is no guarantee that all solutions to the simplified axioms are consistent and can be realized by bosonic physical systems. In this paper, we use simple-current algebra to address this issue. We explicitly construct many-body wave functions, aiming to realize the entries in the list (i.e., realize their fusion coefficients N ij k and spins s i ). We find that all entries can be constructed by simple-current algebra plus conjugation under time-reversal symmetry. This supports the conjecture that simple-current algebra is a general approach that allows us to construct all (non-)Abelian statistics in 2+1D. It also suggests that the simplified theory based on (N ij k ,s i ) is a classifying theory at least for simple bosonic 2+1D topological orders (up to invertible topological orders).

show abstract

“…We remark that the simple-current reductions that we study here correspond to the condensation of bosonic topological excitations [39][40][41][42][43].…”

Section: -10mentioning

confidence: 62%

“…Such reductions correspond to the condensation of bosonic topological excitations [39][40][41][42][43]. So the simplecurrent reduction is also a tool to study the condensation of bosonic topological excitations and the induced topological phase transition between the original topological order and the reduced topological order.…”

Section: Discussionmentioning

confidence: 99%

Simple-current algebra constructions of 2+1-dimensional topological orders

Schoutens

Wen

2016

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…After their condensation, the condensed self-bosons result in a new vacuum, and the original bTO undergoes a phase transition to a new bTO. It was later found [16,17] that mathematically, the set of condensed self-bosons corresponds to a special type of Frobenius algebras [18][19][20][21][22], which are objects in the unitary modular tensor categories (UMTCs) that describe the bTO.…”

Section: Jhep03(2017)172mentioning

confidence: 99%

Fermion condensation and gapped domain walls in topological orders

Wan¹,

Wang²

2017

J. High Energ. Phys.

View full text Add to dashboard Cite

Abstract:We study fermion condensation in bosonic topological orders in two spatial dimensions. Fermion condensation may be realized as gapped domain walls between bosonic and fermionic topological orders, which may be thought of as real-space phase transitions from bosonic to fermionic topological orders. This picture generalizes the previous idea of understanding boson condensation as gapped domain walls between bosonic topological orders. While simple-current fermion condensation was considered before, we systematically study general fermion condensation and show that it obeys a Hierarchy Principle: a general fermion condensation can always be decomposed into a boson condensation followed by a minimal fermion condensation. The latter involves only a single self-fermion that is its own anti-particle and that has unit quantum dimension. We develop the rules of minimal fermion condensation, which together with the known rules of boson condensation, provides a full set of rules for general fermion condensation.

show abstract

“…Yet, any boundary massless modes that often appear must be gapped to have a well defined GSD. The gapping conditions of Abelian topological orders have recently been understood in terms of the concept of Lagrangian subsets [17][18][19][20][21][22][23][24], and subsequently the GSD of these Abelian phases on open surfaces with multiple boundaries were computed [23,25], based on the idea of anyon transport across boundaries. Experiments detecting and utilizing the topological degeneracy with gapped boundaries were proposed in [26,27].…”

Section: Jhep01(2018)134 1 Introduction and Summarymentioning

confidence: 99%

Boundary Hamiltonian theory for gapped topological phases on an open surface

Luo

Pankovich

et al. 2018

J. High Energ. Phys.

View full text Add to dashboard Cite

In this paper we propose a Hamiltonian approach to gapped topological phases on open surfaces. Our setting is an extension of the Levin-Wen model to a 2d graph on an open surface, whose boundary is part of the graph. We systematically construct a series of boundary Hamiltonians such that each of them, when combined with the usual Levin-Wen bulk Hamiltonian, gives rise to a gapped energy spectrum which is topologically protected. It is shown that the corresponding wave functions are robust under changes of the underlying graph that maintain the spatial topology of the system. We derive explicit ground-state wavefunctions of the system on a disk as well as on a cylinder. For boundary quasiparticle excitations, we are able to construct their creation, annihilation, measuring and hopping operators etc. Given a bulk string-net theory, our approach provides a classification scheme of possible types of gapped boundary conditions by Frobenius algebras (modulo Morita equivalence) of the bulk fusion category; the boundary quasiparticles are characterized by bimodules of the pertinent Frobenius algebras. Our approach also offers a set of concrete tools for computations. We illustrate our approach by a few examples.

show abstract

Anyon condensation and tensor categories

Cited by 197 publications

References 66 publications

Simple-current algebra constructions of 2+1-dimensional topological orders

Simple-current algebra constructions of 2+1-dimensional topological orders

Fermion condensation and gapped domain walls in topological orders

Boundary Hamiltonian theory for gapped topological phases on an open surface

Contact Info

Product

Resources

About