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Symmetry protected topological orders and the group cohomology of their symmetry group

- Xie Chen, Z. Gu, Zhengxin Liu, X. Wen
- Physics
- 23 June 2011

Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G. They can all be smoothly connected to the same trivial product state if we break the… Expand

Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order

We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering… Expand

Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order

Two gapped quantum ground states in the same phase are connected by an adiabatic evolution which gives rise to a local unitary transformation that maps between the states. On the other hand, gapped… Expand

Classification of gapped symmetric phases in one-dimensional spin systems

Quantum many-body systems divide into a variety of phases with very different physical properties. The questions of what kinds of phases exist and how to identify them seem hard, especially for… Expand

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

Symmetry-protected topological orders for interacting fermions: Fermionic topological nonlinear σ models and a special group supercohomology theory

Symmetry-protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry $G$, which can all be smoothly connected to the trivial product states if we break the… Expand

Symmetry-Protected Topological Orders in Interacting Bosonic Systems

- Xie Chen, Z. Gu, Zhengxin Liu, X. Wen
- PhysicsScience
- 21 December 2012

TLDR

Loop Optimization for Tensor Network Renormalization.

We introduce a tensor renormalization group scheme for coarse graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality.… 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

Complete classification of one-dimensional gapped quantum phases in interacting spin systems

Quantum phases with different orders exist with or without breaking the symmetry of the system. Recently, a classification of gapped quantum phases which do not break time reversal, parity or on-site… Expand

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