Tuesday, June 18, 2013

1306.3695 (Peng Ye et al.)

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
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.
View original: http://arxiv.org/abs/1306.3695

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