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Article overview
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Bosonic symmetry-protected topological phases with charge and spin symmetries: response theory and dynamical gauge theory in 2D, 3D, and the surface of 3D | Peng Ye
; Juven Wang
; | Date: |
16 Jun 2013 | Abstract: | A large class of symmetry-protected topological phases (SPT) in boson / spin
systems have been recently predicted by the group cohomology theory. In this
work, we consider SPT states at least with charge symmetry (U(1) or Z_N) or
spin S^z rotation symmetry (U(1) or Z_N) in 2D, 3D, and the surface of 3D,
which is physically much closer to possible realization in realistic physical
systems. If both are U(1), we apply external electromagnetic field / spin gauge
field to study the charge/spin response. For the SPT examples we consider, many
variants of Witten effects and different versions of anomalous quantum Hall
effect are found and systematically discussed in the 3D SPT bulk and its
surface, respectively. With the same symmetry, the surface of 3D SPT bulk
admits anomalous response theory compared to 2D SPT state, which is justified
by the K_G-matrix Chern-Simons term for external gauge fields based on the
hydrodynamical approach to topological liquids. If charge or spin symmetry
reduces to Z_N by considering charge-N or spin-N condensate, instead of
utilizing the linear response approach, we gauge the charge/spin symmetry,
leading to a dynamical gauge theory with some remaining global symmetry. The 3D
dynamical gauge theory describes a symmetry-enriched topological phase (SET),
i.e. a topologically ordered state with global symmetry which admits nontrivial
ground state degeneracy depending on spatial manifold topology. For the SPT
examples we consider, the corresponding SET states are described by dynamical
topological gauge theory with topological BF term + axionic Theta-term in
three-dimensional bulk and the chiral boson theory with quantum anomaly on the
surface. This generic promotion from SPT to SET by gauging a normal subgroup of
the total global symmetry of SPT can be further studied in numerical
simulation, in order to diagnose the nature of SPT order before gauging. | Source: | arXiv, 1306.3695 | Services: | Forum | Review | PDF | Favorites |
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