Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest timereversal symmetric topological orders in 3+1 dimensions
Abstract
We propose a generic construction of exactly soluble local bosonic models that realize various topological orders with gappable boundaries. In particular, we construct an exactly soluble bosonic model that realizes a (3+1)dimensional [(3+1)D] Z_{2}gauge theory with emergent fermionic Kramers doublet. We show that the emergence of such a fermion will cause the nucleation of certain topological excitations in spacetime without pin^{+} structure. The exactly soluble model also leads to a statistical transmutation in (3+1)D. In addition, we construct exactly soluble bosonic models that realize 2 types of timereversal symmetryenriched Z_{2} topological orders in 2+1 dimensions, and 20 types of simplest timereversal symmetryenriched topological (SET) orders which have only one nontrivial pointlike and stringlike topological excitation. Many physical properties of those topological states are calculated using the exactly soluble models. We find that some timereversal SET orders have pointlike excitations that carry Kramers doublet, a fractionalized timereversal symmetry. We also find that some Z_{2} SET orders have stringlike excitations that carry anomalous (nononsite) Z_{2} symmetry, which can be viewed as a fractionalization of Z_{2} symmetry on strings. Our construction is based on cochains and cocycles in algebraic topology, which is very versatile. In principle, it can also realize emergent topological field theory beyond the twisted gauge theory.
 Publication:

Physical Review B
 Pub Date:
 May 2017
 DOI:
 10.1103/PhysRevB.95.205142
 arXiv:
 arXiv:1612.01418
 Bibcode:
 2017PhRvB..95t5142W
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 50 pages, 12 figures, 3 tables. This is a much extended version