Related papers: Fusion Structure from Exchange Symmetry in (2+1)-D…
Abstract spin chains axiomatize the structure of local observables on the 1D lattice which are invariant under a global symmetry, and arise at the physical boundary of 2+1D topologically ordered spin systems. In this paper, we study tensor…
Raman-assisted hopping may be used to realize the anyon Hubbard model in one-dimensional optical lattices. We propose a feasible scenario that significantly improves the proposal of [T. Keilmann et al., Nature Commun. 2, 361 (2011)],…
We construct three quasi-supersymmetric $G^3$ GUT models with $S_3$ symmetry and gauge coupling unification from intersecting D6-branes on Type IIA orientifolds. The Standard Model fermions and Higgs doublets can be embedded into the…
Our work explores fusions, the multidimensional counterparts of mean-preserving contractions and their extreme and exposed points. We reveal an elegant geometric/combinatorial structure for these objects. Of particular note is the…
We present a non-compact (4 + 1) dimensional model with a local strong four-fermion interaction supplementing it with gravity. In the strong coupling regime it reveals the spontaneous translational symmetry breaking which eventually leads…
A mechanism is presented through which very light scalar degrees of freedom obeying the nonlinear sigma model equation can emerge in spontaneously broken gauge theories. The mechanism operates in extra dimensional theories in which a) there…
We introduce a pentagon equation solver, available as part of SageMath, and use it to construct braid group representations associated to certain anyon systems. We recall the category-theoretic framework for topological quantum computation…
In this paper we introduce a one-dimensional model of $su(2)_k$ anyons in which the number of anyons can fluctuate by means of a pairing term. The model can be tuned to a point at which one can determine the exact zero-energy ground states,…
Building on the infinite-component Chern--Simons theory of three-dimensional fracton phases by Ma et al. [Phys. Rev. B 105, 195124 (2022)] and the Toeplitz braiding of anyons by Li et al.~[Phys. Rev B 110, 205108 (2024)], we show that…
We derive a necessary and sufficient criterion for when a two dimensional gapped many-body system with Abelian anyons and a unitary $\mathbb{Z}_2$ symmetry has a protected gapless edge mode. Our criterion is phrased in terms of edge…
The fusion basis of Fibonacci anyons supports unitary braid representations that can be utilized for universal quantum computation. We show a mapping between the fusion basis of three Fibonacci anyons, $\{|1\rangle, |\tau\rangle\}$, and the…
It was well known that there are $e$-particles and $m$-strings in the 3-dimensional (spatial dimension) toric code model, which realizes the 3-dimensional $\mathbb{Z}_2$ topological order. Recent mathematical result, however, shows that…
We introduce group-theoretical fusion 2-categories, a strong categorification of the notion of a group-theoretical fusion 1-category. Physically speaking, such fusion 2-categories arise by gauging subgroups of a global symmetry. We show…
We analyze theories in which a supersymmetric sector is coupled to a supersymmetry-breaking sector described by a non-linear realization. We show how to consistently couple N=1 supersymmetric matter to non-supersymmetric matter in such a…
We introduce both an exactly solvable model and a coupled-layer construction for an exotic, three-dimensional phase of matter with immobile topological excitations that carry a protected internal degeneracy. Unitary transformations on this…
The description of a system of vortices in terms of dual fields provides a window to new phases of the system. It was found recently that dualizing a 3+1-d boson-fermion system leads to a system of fermions and vortices interacting via a…
We study abelian planon-only fracton orders: a class of three-dimensional (3d) gapped quantum phases in which all fractional excitations are abelian particles restricted to move in planes with a common normal direction. In such systems, the…
Supersymmetric unification in warped space provides new possibilities for model building. I argue that the picture of warped supersymmetric unification arises naturally through the AdS/CFT correspondence from the assumption that…
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…
A topological quantum computer should allow intrinsically fault-tolerant quantum computation, but there remains uncertainty about how such a computer can be implemented. It is known that topological quantum computation can be implemented…