Yidun Wan

Twisted quantum double model of topological phases in two dimensions

We propose a new discrete model—the twisted quantum double model—of 2D topological phases based on a finite group G and a 3-cocycleover G. The detailed properties of the ground states are studied, and we find that the ground-state subspace can be characterized in terms of the twisted quantum double D � (G) of G. Whenis the trivial 3-cocycle, the model becomes Kitaevs quantum double model based on the finite group G, in which the elementary excitations are known to be classified by the quantum double D(G) of G. Our model can be viewed as a Hamiltonian extension of the Dijkgraaf-Witten topological gauge theories to the discrete graph case with gauge group being a finite group. We also demonstrate a duality between a large class of Levin-Wen string-net models and certain twisted quantum double models, by mapping the string-net 6j symbols to the corresponding 3-cocycles. The paper is presented in a way such that it is accessible to a wide range of physicists.

Revisiting entanglement entropy of lattice gauge theories

A bstractIt is realized recently that the entanglement entropy in gauge theories is ambiguous because the Hilbert space cannot be expressed as a simple direct product of Hilbert spaces defined on the two regions; different ways of dividing the Hilbert spaces near the boundary leads to significantly different result, to the extreme that it could annihilate the otherwise finite topological entanglement entropy between two regions altogether. In this article, we first show that the topological entanglement entropy in the Kitaev model [1] which is not a true gauge theory, is free of ambiguity. Then, we give a physical interpretation, from the perspectives of what can be measured in an experiment, to the purported ambiguity of true gauge theories, where the topological entanglement arises as redundancy in counting the degrees of freedom along the boundary separating two regions. We generalize these discussions to non-Abelian gauge theories.

Propagation and interaction of chiral states in quantum gravity

Abstract We study the stability, propagation and interactions of braid states in models of quantum gravity in which the states are four-valent spin networks embedded in a topological three manifold and the evolution moves are given by the dual Pachner moves. There are results for both the framed and unframed cases. We study simple braids made up of two nodes which share three edges, which are possibly braided and twisted. We find three classes of such braids, those which both interact and propagate, those that only propagate, and the majority that do neither.

Twisted gauge theory model of topological phases in three dimensions

We propose an exactly solvable lattice Hamiltonian model of topological phases in

Conserved quantities and the algebra of braid excitations in quantum gravity

3+1

C, P, and T of braid excitations in quantum gravity

dimensions, based on a generic finite group

Generalized ADE classification of topological boundaries and anyon condensation

G

Non-adiabatic Fast Control of Mixed States Based on Lewis–Riesenfeld Invariant

and a

Effective theory of braid excitations of quantum geometry in terms of Feynman diagrams

4

From effective Hamiltonian to anomaly inflow in topological orders with boundaries

-cocycle