Abstract
We explore and construct a class of bosonic short-range entangled (BSRE) states in all spatial dimensions, which are higher dimensional generalizations of the well-known Kitaev's state in [Ann. Phys. (N.Y.) 321, 2 (2006); http://online.kitp.ucsb.edu/online/topomat11/kitaev]. These BSRE states share the following properties: (1) their bulk is fully gapped and nondegenerate; (2) their boundary is described by a “self-dual” rank- antisymmetric tensor gauge field, and it is guaranteed to be gapless without assuming any symmetry; (3) their boundary has intrinsic gravitational anomaly once coupled to the gravitational field; (4) their bulk is described by an effective Chern-Simons field theory with rank- antisymmetric tensor fields, whose matrix is identical to that of the state in ; (5) the existence of these BSRE states leads to various bosonic symmetry protected topological (BSPT) states as their descendants in other dimensions; (6) these BSRE states can be constructed by confining fermionic degrees of freedom from eight copies of SRE states with fermionic ; (7) after compactifying the BSRE state on a closed dimensional manifold, depending on the topology of the compact manifold, the system could reduce to nontrivial BSRE states.
- Received 4 November 2014
- Revised 21 January 2015
DOI:https://doi.org/10.1103/PhysRevB.91.054406
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