Speaker
Olexei Motrunich
(California Institute of Technology)
Description
We study a $U(1)\times U(1)$ system with short-range
interactions and mutual $\theta$ statistics in (2+1)
dimensions, using $\theta=\pi$ and $\theta=2\pi/3$ as
two examples. We are able to reformulate the model to
eliminate the sign problem, and perform a Monte Carlo
study. We find a phase diagram containing a phase with
only small loops and two phases with one species of
proliferated loop. In the intermediate coupling regime in
the $\theta=2\pi/3$ case, we also find a phase where both
species of loop condense, but without any gapless modes
and with a quantized cross-transverse response. On the
other hand, in the $\theta=\pi$ case this intermediate
coupling region exhibits a first order (coexistence) segment
along the self-dual line. Lastly, for $\theta=2\pi/n$ and
when the energy cost of loops becomes small, we find a
phase which is a condensate of bound states, each made up
of $n$ particles of one species and a vortex of the other.
We define several exact reformulations of the model, which
allow us to precisely describe each phase in terms of gapped
excitations. We propose field-theoretic descriptions of the
phases and phase transitions, which are particularly
interesting on the "self-dual" line where both species have
identical interactions.
This talk is based on two papers:
1) Scott D. Geraedts and Olexei I. Motrunich,
"Monte Carlo Study of a U(1)xU(1) system with $\pi$-
statistical Interaction",
Phys. Rev. B. 85, 045114 (2012) (arXiv:1110.6561).
2) Scott D. Geraedts and Olexei I. Motrunich,
"Phases and phase transitions in a U(1)xU(1) system with
$\theta=2\pi/3$ mutual statistics",
arXiv:1205.1790.
