## Symmetry protection of critical phases and global anomaly in 1+1 dimensions

**Speaker:**Prof. Masaki Oshikawa, University of Tokyo

**When:**March 18, 2015 (Wed), 11:00AM to 12:00PM (add to my calendar)

**Location:**SCI 328

**Hosted by:**Claudio Chamon

*This event is part of the Condensed Matter Theory Seminar Series. *

Abstract:
Classification of gapless quantum phases remains very much open.
Symmetries are naturally expected to play an important role here,
as in the case of gapped quantum phases.
In this talk, we argue that there is a protection of bulk gapless
critical phases by discrete symmetry. This symmetry protection is
analogous to that of the well-known (gapped) Symmetry-Protected
Topological (SPT) phases; here we show that the concept can be
generalized to bulk gapless critical phases. We demonstrate this
for the SU(2)-symmetric quantum antiferromagnetic chains and
their effective field theory, SU(2) Wess-Zumino-Witten (WZW)
theory as an example. The SU(2) WZW theory is characterized
by a natural number k, which is called level.
In the presence of the SU(2) and a certain discrete Z$*2$
symmetry of the WZW theory, which corresponds to the
translation symmetry of the spin chain, we find that
a renormalization-group (RG) flow is possible between SU(2)
WZW theories only if the difference in the levels is even.
That is, gapless critical phases in 1+1 dimension with the SU(2), the
Z$*2$, and the Lorentz symmetries are classified into the two
"symmetry-protected'' categories: one corresponds to even levels and
the other to odd levels.

(in collaboration with S. C. Furuya)