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Symmetry-protected quantum spin Hall phases in two dimensions
1Institute for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China.
Physical Review Letters
|February 26, 2013
Summary
Symmetry-protected topological states in 2D exhibit unique edge excitations. These phases, characterized by SU(2) or SO(3) symmetry, show quantized spin Hall conductance, offering new insights into topological matter.
Area of Science:
- Condensed Matter Physics
- Quantum Field Theory
- Topological Phases of Matter
Background:
- Symmetry-protected topological (SPT) states are a class of quantum matter characterized by short-range entanglement and preserved symmetries.
- Nontrivial SPT states possess symmetry-protected gapless edge excitations, distinguishing them from trivial phases.
- In two dimensions (2D), SPT phases with SU(2) or SO(3) symmetry are abundant and can be theoretically described.
Purpose of the Study:
- To investigate the nature of 2D SPT states with SU(2) or SO(3) symmetry.
- To understand the relationship between these SPT phases and their boundary excitations.
- To characterize the quantized transport properties, specifically spin Hall conductance, of these topological phases.
Main Methods:
- Description of SPT phases using SU(2) or SO(3) nonlinear-sigma models with a quantized topological theta term.
- Analysis of boundary phenomena by mapping the theta term to the Wess-Zumino-Witten term at open boundaries.
- Calculation of spin Hall conductance for SU(2) and SO(3) symmetric SPT phases.
Main Results:
- Identified an infinite number of nontrivial 2D SPT phases characterized by SU(2) or SO(3) symmetry.
- Demonstrated that boundary excitations decouple into left and right movers, with only left movers carrying quantum numbers when theta > 0.
- Quantized spin Hall conductance: half-integer for SU(2) SPT phases and even-integer for SO(3) SPT phases.
- Established that both SU(2) and SO(3) SPT phases are U(1) SPT phases with even-integer quantized Hall conductance.
Conclusions:
- SU(2) and SO(3) SPT phases in 2D exhibit distinct quantized spin Hall conductances.
- The Wess-Zumino-Witten term governs the gapless edge excitations, leading to quantized transport properties.
- These findings provide a unified framework for understanding various topological phases of matter through their symmetry properties and boundary behaviors.
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