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# Faculty

## XIAO-GANG WEN

Cecil and Ida Green Professor of Physics

**EMAIL: **wen@dao.mit.edu

**PHONE: **(617) 253-5016

**OFFICE: **6C-317

**ASSISTANT: **Lesley Keaney (617) 253-4878

**RELATED LINKS: **

### Area of Physics:

### Research Interests

- Theory of Strongly Correlated Electronic Systems
- Theory of Topological Order and Quantum Order
- Theory of High Temperature Superconductors
- Origin and Unification of Elementary Particles (such as light and electrons)
- Theory of Quantum Hall Effect and Non-Abelian Statistics

Prof. Wen’s main research area is condensed matter theory. He introduced the notion of topological order and quantum order to describe a new class of matter states. This opens up a new research direction in condensed matter physics. He found that states with topological order contain non-trivial boundary excitations and developed chiral Luttinger theory for the boundary states. The boundary states can become ideal conduction channel which may leads to device application of topological phases. He also proposed a special class of topological order: non-Abelian quantum Hall states. They contain emergent particles with non-Abelian statistics which generalizes the well known Bose and Fermi statistics. Non-Abelian particles may allow us to perform fault tolerant quantum computations. He found that string-net condensations can give rise to a large class of topological orders. In particular, string-net condensation provides a unified origin of photons, electrons, and other elementary particles. It unifies two fundamental phenomena: gauge interactions and Fermi statistics. He also proposed the SU(2) gauge theory of high temperasture superconductors.

### Biographical Sketch

Xiao-Gang Wen received a BS in physics from University of Science and Technology of China in 1982 and a Ph.D. in physics from Princeton University in 1987.

He studied superstring theory under theoretical physicist Edward Witten at Princeton University. Wen later switched his research field to condensed matter physics while working with theoretical physicists Robert Schrieffer, Frank Wilczek, Anthony Zee in Institute for Theoretical Physics, UC Santa Barbara (1987-1989).

He became a five-year member of IAS at Princeton in 1989 and joint MIT in 1991. Wen is a Cecil and Ida Green professor of Physics at MIT, a Distinguished Moore Scholar at Caltech, and a Distinguished Research Chair at Perimeter Institute.

### Selected Publications

**Classification of Gapped Symmetric Phases in 1D Spin Systems**

Xie Chen, Zheng-Cheng Gu, Xiao-Gang Wen

arXiv:1008.3745

*(Classified gapped symmetric phases for 1D qubit systems through local unitary transformations and the projective representations of the symmetry group.)***Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order**

Xie Chen, Zheng-Cheng Gu, Xiao-Gang Wen

arXiv:1004.3835

*(Introduced the notion of long-range quantum entanglement through local unitary transformation. Long-range quantum entanglement is the essence of topological order and quantum order.)***A lattice bosonic model as a quantum theory of gravity**

Zheng-Cheng Gu and Xiao-Gang Wen

gr-qc/0606100

*(Constructed a quantum qubit model on a lattice which gives rise to emergent gravitons.)***A unification of light and electrons through string-net condensation in spin models**

Michael A. Levin and Xiao-Gang Wen

Rev. Mod. Phys. 77, 871 (2005); cond-mat/0407140

*(String-net condensation provides a way to unify light and electrons, or more precisely, to unify gauge interaction and Fermi statistics.)***String-net condensation: A physical mechanism for topological phases**

Michael Levin and Xiao-Gang Wen

Phys. Rev. B71, 045110 (2005). cond-mat/0404617

*(Pointed out that all the gauge theories and doubled Chern-Simons theories can be realized in lattice spin models through different string-net condensations. Found a mechanism to make the ends of condensed string to have Fermi, fractionali, or non-Abelian statistics. Found the mathematical foundation of topological order and string-net condensation -- Tensor Category Theory. Used tensor category theory to classify T and P symmetric topological orders.)***Quantum Orders and Symmetric Spin Liquids**

Xiao-Gang Wen

Phys. Rev. B65, 165113 (2002). cond-mat/0107071

*(Introduced a concept -- quantum order -- through Projective Symmetry Group.)***Doping a Mott Insulator: Physics of High Temperature Superconductivity**

Patrick A. Lee, Naoto Nagaosa, Xiao-Gang Wen

Rev. Mod. Phys. 78, 17–85 (2006); cond-mat/0410445

*(A review of the SU(2) slave-boson theory of high Temperature superconductors.)***Non-Abelian Statistics in FQH states**

Xiao-Gang Wen

Phys. Rev. Lett. 66, 802 (1991)

*(One of the first papers to propose and construct non-Abelian FQH states.)***Chiral Luttinger Liquid and the Edge Excitations in the FQH States**

Xiao-Gang Wen

Phys. Rev. B41 12838 (1990).

*(Predicted power-law tunneling I-V curve between FQH edges, which was observed by F. P. Milliken, C. P. Umbach and R. A. Webb; Solid State Comm. 97, 309, 1995; A. M. Chang, L. N. Pfeiffer, and K. W. West; Phys. Rev. Lett. 77, 2538, 1996 )***Topological Orders in Rigid States**

Xiao-Gang Wen

Int. J. Mod. Phys. B4, 239 (1990)

*(The first detailed discussion of topological order. Proposed a conjecture: the non-Abelian Berry's phase of degenerate ground states and the induced modular transformation completely characterizes topological orders.)*

*Last updated on March 5, 2015 2:57 PM*