Related papers: Chiral Edge States Emerging on Anyon-Net
A key hallmark of quantum Hall physics is the existence of topological chiral states at the system boundary. Signatures of these edge states have been experimentally observed in cold atoms by using different approaches, including notably…
We construct exactly solvable models for a wide class of symmetry enriched topological (SET) phases. Our construction applies to 2D bosonic SET phases with finite unitary onsite symmetry group $G$ and we conjecture that our models realize…
The spin 1 bilinear-biquadratic model on square lattice in the region $0<\phi<\pi/4$ is studied in a fermion representation with a p-wave pairing BCS type mean-field theory. Our results show there may exist a non-trivial gapped spin liquid…
Tensor networks are an efficient platform to represent interesting quantum states of matter as well as to compute physical observables and information-theoretic quantities. We present a general protocol to construct fixed-point tensor…
We construct (2+1)-dimensional lattice systems, which we call fusion surface models. These models have finite non-invertible symmetries described by general fusion 2-categories. Our method can be applied to build microscopic models with,…
We study the emergence of topological matter in two-dimensional systems of neutral Rydberg atoms in Ruby lattices. While Abelian anyons have been predicted in such systems, non-Abelian anyons, which would form a substrate for fault-tolerant…
We present a family of electron-based coupled-wire models of bosonic orbifold topological phases, referred to as twist liquids, in two spatial dimensions. All local fermion degrees of freedom are gapped and removed from the topological…
We propose a unified scheme to identify phase transitions out of the $\mathbb{Z}_2$ Abelian topological order, including the transition to a non-Abelian chiral spin liquid. Using loop gas and and string gas states [H.-Y. Lee, R. Kaneko, T.…
Constructing systems that exhibit time-scales much longer than those of the underlying components, as well as emergent dynamical and collective behavior, is a key goal in fields such as synthetic biology and materials self-assembly.…
Chiral edge states are highly sought-after as paradigmatic topological states relevant to both quantum information processing and dissipationless electron transport. Using superconducting transmon-based quantum computers, we demonstrate…
We study the topological order that arises from chiral states with ${\rm SU}(N)$ or ${\rm SO}(N)$ edge-state symmetry. This extends our previous study of topological orders that descend from the bosonic $E_8$ quantum Hall state. We use…
Fractional statistics give rise to quantum behaviors that differ fundamentally from those of bosons and fermions. While two-dimensional anyons play a major role in strongly correlated systems and topological quantum computing, the nature of…
Topological photonic systems offer light transport that is robust against defects and disorder, promising a new generation of chip-scale photonic devices and facilitating energy-efficient on-chip information routing and processing. However,…
Bipartite quantum systems from the chiral universality classes admit topologically protected zero modes at point defects. However, in two-dimensional systems these states can be difficult to separate from compacton-like localized states…
We construct two-dimensional non-Abelian topologically ordered states by strongly coupling arrays of one-dimensional quantum wires via interactions. In our scheme, all charge degrees of freedom are gapped, so the construction can use either…
The same bulk two-dimensional topological phase can have multiple distinct, fully-chiral edge phases. We show that this can occur in the integer quantum Hall states at $\nu=8$ and 12, with experimentally-testable consequences. We show that…
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…
Anyons exist as point like particles in two dimensions and carry braid statistics which enable interactions that are independent of the distance between the particles. Except for a relatively few number of models which are analytically…
Matrix product states (MPS) have proven to be a very successful tool to study lattice systems with local degrees of freedom such as spins or bosons. Topologically ordered systems can support anyonic particles which are labeled by conserved…
We explicitly show that the differences, with respect to the appearance of topological phases, between the traditional Haldane model, which utilises a honeycomb lattice structure, to that of the Haldane model imbued onto a brick-wall…