# From String Nets to Nonabelions

@article{Fidkowski2006FromSN, title={From String Nets to Nonabelions}, author={Lukasz M. Fidkowski and Michael H. Freedman and C. Nayak and Kevin Walker and Zhenghan Wang}, journal={Communications in Mathematical Physics}, year={2006}, volume={287}, pages={805-827} }

We discuss Hilbert spaces spanned by the set of string nets, i.e. trivalent graphs, on a lattice. We suggest some routes by which such a Hilbert space could be the low-energy subspace of a model of quantum spins on a lattice with short-ranged interactions. We then explain conditions which a Hamiltonian acting on this string net Hilbert space must satisfy in order for the system to be in the DFib (Doubled Fibonacci) topological phase, that is, be described at low energy by an SO(3)3 × SO(3)3…

## 29 Citations

Topological phases: An expedition off lattice

- Physics, Mathematics
- 2011

Abstract Motivated by the goal to give the simplest possible microscopic foundation for a broad class of topological phases, we study quantum mechanical lattice models where the topology of the…

Topological order from quantum loops and nets

- Physics
- 2008

Abstract I define models of quantum loops and nets that have ground states with topological order. These make possible excited states comprised of deconfined anyons with non-abelian braiding. With…

Characterization of topological phase transitions from a non-Abelian topological state and its Galois conjugate through condensation and confinement order parameters

- PhysicsPhysical Review B
- 2021

Topological phases exhibit unconventional order that cannot be detected by any local order parameter. In the framework of Projected Entangled Pair States (PEPS), topological order is characterized by…

A pr 2 00 8 Topological order from quantum loops and nets

I define models of quantum loops and nets which have ground states with topological order. These make possible excited states comprised of deconfined anyons with non-abelian braiding. With the…

Galois Conjugates of Topological Phases

- Physics, Mathematics
- 2012

Galois conjugation relates unitary conformal field theories and topological quantum field theories (TQFTs) to their nonunitary counterparts. Here we investigate Galois conjugates of quantum double…

A Nonperturbative Proposal for Nonabelian Tensor Gauge Theory and Dynamical Quantum Yang-Baxter Maps

- Physics
- 2010

We propose a nonperturbative approach to nonabelian two-form gauge theory. We formulate the theory on a lattice in terms of plaquette as fundamental dynamical variable, and assign U(N) Chan-Paton…

Hamiltonian models for topological phases of matter in three spatial dimensions

- Physics, Mathematics
- 2016

We present commuting projector Hamiltonian realizations of a large class of (3+1)D topological models based on mathematical objects called unitary G-crossed braided fusion categories. This…

Tensor Network Approach to Phase Transitions of a Non-Abelian Topological Phase.

- Physics, MedicinePhysical review letters
- 2020

A generic quantum-net wave function with two tuning parameters dual with each other is proposed, and the norm of the wave function can be exactly mapped into a partition function of the two-coupled ϕ^{2}-state Potts models, where ϕ=(sqrt[5]+1)/2 is the golden ratio.

Tutte chromatic identities from the Temperley-Lieb algebra

- Mathematics, Physics
- 2009

This paper introduces a conceptual framework, in the context of quantum topology and the algebras underlying it, for analyzing relations obeyed by the chromatic polynomial . Q/ of planar graphs.…

Non-Abelian Anyons and Topological Quantum Computation

- Physics
- 2008

Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of…

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