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String-net condensation: A physical mechanism for topological phases

- Michael Levin, X. Wen
- Physics
- 26 April 2004

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,''… Expand

Detecting topological order in a ground state wave function.

- Michael Levin, X. Wen
- Computer SciencePhysical review letters
- 23 October 2005

TLDR

Anomalous edge states and the bulk-edge correspondence for periodically-driven two dimensional systems

- M. Rudner, N. Lindner, E. Berg, Michael Levin
- Physics
- 13 December 2012

Recently, several authors have investigated topological phenomena in periodically-driven systems of non-interacting particles. These phenomena are identified through analogies between the Floquet… Expand

Tensor renormalization group approach to two-dimensional classical lattice models.

- Michael Levin, Cody P. Nave
- Physics, Computer SciencePhysical review letters
- 27 November 2006

TLDR

Braiding statistics approach to symmetry-protected topological phases

- Michael Levin, Z. Gu
- Physics
- 14 February 2012

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."… Expand

Particle-hole symmetry and the Pfaffian state.

- Michael Levin, B. Halperin, B. Rosenow
- PhysicsPhysical review letters
- 3 July 2007

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… Expand

Protected edge modes without symmetry

- Michael Levin
- Physics, Mathematics
- 30 January 2013

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… Expand

Tensor-product representations for string-net condensed states

- Z. Gu, Michael Levin, B. Swingle, X. Wen
- Physics
- 16 September 2008

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… Expand

Braiding statistics of loop excitations in three dimensions.

- Chenjie Wang, Michael Levin
- PhysicsPhysical review letters
- 28 March 2014

TLDR

Fractional topological insulators.

- Michael Levin, A. Stern
- PhysicsPhysical review letters
- 15 June 2009

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