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String-net condensation: A physical mechanism for topological phases
We show that quantum systems of extended objects naturally give rise to a large class of exotic phases---namely topological phases. These phases occur when extended objects, called ``string-nets,''
Detecting topological order in a ground state wave function.
A way to detect a kind of topological order using only the ground state wave function which directly measures the total quantum dimension D= Sum(id2i).
Anomalous edge states and the bulk-edge correspondence for periodically-driven two dimensional systems
Recently, several authors have investigated topological phenomena in periodically-driven systems of non-interacting particles. These phenomena are identified through analogies between the Floquet
Tensor renormalization group approach to two-dimensional classical lattice models.
A simple real space renormalization group technique for two-dimensional classical lattice models that is fundamentally based on the theory of quantum entanglement is described and demonstrated by computing the magnetization of the triangular lattice Ising model.
Braiding statistics approach to symmetry-protected topological phases
We construct a 2D quantum spin model that realizes an Ising paramagnet with gapless edge modes protected by Ising symmetry. This model provides an example of a "symmetry-protected topological phase."
Particle-hole symmetry and the Pfaffian state.
We show that the particle-hole conjugate of the Pfaffian state-or "anti-Pfaffian" state-is in a different universality class from the Pfaffian state, with different topological order. The two states
Protected edge modes without symmetry
We discuss the question of when a gapped 2D electron system without any symmetry has a protected gapless edge mode. While it is well known that systems with a nonzero thermal Hall conductance, $K_H
Tensor-product representations for string-net condensed states
We show that general string-net condensed states have a natural representation in terms of tensor product states (TPSs). These TPSs are built from local tensors. They can describe both states with
Braiding statistics of loop excitations in three dimensions.
It is found that different short-range entangled bosonic states with the same (Z(N))(K) symmetry (i.e., different symmetry-protected topological phases) can be distinguished by their three-loop braiding statistics.
Fractional topological insulators.
Generalizations of two-dimensional topological insulators which can be realized in interacting, time reversal invariant electron systems, which contain excitations with fractional charge and statistics in addition to protected edge modes are analyzed.