# Classification of gapped symmetric phases in one-dimensional spin systems

@article{Chen2011ClassificationOG, title={Classification of gapped symmetric phases in one-dimensional spin systems}, author={Xie Chen and Zheng-Cheng Gu and Xiao-Gang Wen}, journal={Physical Review B}, year={2011}, volume={83}, pages={035107} }

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 strongly interacting systems. Here we make an attempt to answer these questions for gapped interacting quantum spin systems whose ground states are short-range correlated. Based on the local unitary equivalence relation between short-range-correlated states in the same phase, we classify possible quantum…

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## References

SHOWING 1-10 OF 51 REFERENCES

Understanding Quantum Phase Transitions

- Physics
- 2010

NEW DIRECTIONS AND NEW CONCEPTS IN QUANTUM PHASE TRANSITIONS Finite Temperature Dissipation and Transport Near Quantum Critical Points, Subir Sachdev Dissipation, Quantum Phase Transitions, and…

Quantum computation and quantum information

- PhysicsMathematical Structures in Computer Science
- 2007

This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers deal…

Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons

- Physics
- 2005

and

Cirac, talk given on 'International Workshop on Density Matrix Renormalization Group and Other Advances on Numerical Renormalization Group Methods

- 2010

New J. Phys

- New J. Phys
- 2010

Phys. Rev. B

- Phys. Rev. B
- 2010

Phys. Rev. B

- Phys. Rev. B
- 2010

Phys. Rev. B

- Phys. Rev. B
- 2010

Phys. Rev. Lett

- Phys. Rev. Lett
- 2010

Phys. Rev. B

- Phys. Rev. B
- 2009