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- Topological insulator of bosons in 3d via dyon condensation and the statistical Witten effect.

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PIRSA Number:

13040117

In

this talk, I will construct a symmetry protected topological phase of bosons in

3d with particle number conservation and time reversal symmetries, which is the

direct bosonic analogue of the familiar electron topological insulator. The

construction employs a parton decomposition of bosons, followed by condensation

of parton-monopole composites. The surface of the resulting state supports a

gapped symmetry respecting phase with intrinsic toric code topological order

where both e and m anyons carry charge 1=2.

It

is well-known that one signature of the 3d electron topological insulator is

the Witten

eect:

if the system is coupled to a compact electromagnetic gauge eld, a monopole in

the

bulk acquires a half-odd-integer polarization charge. I will discuss the

corresponding

phenomenon

for the constructed topological insulator of bosons: a monopole can remain

electrically

neutral, but its statistics are transmuted from bosonic to fermionic. This

\sta-

tistical

Witten eect" guarantees that the surface is either gapless, symmetry

broken or

carries

an intrinsic topological order.

©2012 Perimeter Institute for Theoretical Physics