# Symmetry Protected Topological Phases

Symmetry protected topological phases have the exotic property of hosting gapless / nontrivial edge states around an otherwise â€˜normal' looking bulk. The non-trivialness of the phases is protected by certain global symmetry of the system, like time reversal, charge conservation, spin rotation, etc. Such phases lie outside the conventional symmetry breaking paradigm of Landau and generalize the special properties of topological insulators and superconductors from free fermion systems to general interacting boson, fermion and spin systems. We did a series of work on constructing models with nontrivial SPT orders, exploring their physical properties (exotic edge states), and classifying all possible SPT phases. Related publications can be found here.

#### Selected Publications

- "Symmetry Protected Topological Orders in Interacting Bosonic Systems", Xie Chen, Zheng-Cheng Gu, Zheng-Xin Liu, Xiao-Gang Wen,
*Science*338, 1604 (2012)

(A systematic construction of bosonic SPT phases with any internal symmetry and in any dimension.) - "Symmetry protected topological orders and the group cohomology of their symmetry group", Xie Chen, Zheng-Cheng Gu, Zheng-Xin Liu, Xiao-Gang Wen,
*Phys. Rev. B*87, 155114 (2011)

(A systematic construction of bosonic SPT phases with any internal symmetry and in any dimension.) - "Two-dimensional symmetry protected topological orders and their protected gapless edge excitations", Xie Chen, Zheng-Xin Liu, Xiao-Gang Wen,
*Phys. Rev. B*84, 235141 (2011)

(Construction of nontrivial 2D SPT model with Z_2 symmetry. The non trivialness of the boundary is proven using the matrix product operator formalism.) - "Classification of Gapped Symmetric Phases in One-dimensional Spin Systems", Xie Chen, Zheng-Cheng Gu, and Xiao-Gang Wen,
*Phys. Rev. B*83, 035107 (2011)

(Classification of 1D SPT phases using the matrix product state formalism.)"Symmetry protected topological phases from decorated domain walls", Xie Chen, Yuan-Ming Lu, Ashvin Vishwanath,*Nature Communications*5, Article number 3507, (2014)

(A physically intuitive picture for constructing a large class of symmetry protected topological phases.) - "Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator", Xie Chen, Lukasz Fidkowski, Ashvin Vishwanath,
*Phys. Rev. B*89, 165132 (2014)

(A proposal that the 2D surface of 3D topological insulators can be gapped without breaking symmetry due to strong interaction and results in exotic topological properties on the surface.)