Continuous transition between fractional quantum Hall and superfluid states

We develop a theory of a direct, continuous quantum phase transition between a bosonic Laughlin fractional quantum Hall state and a superfluid, generalizing the Mott insulator to superfluid phase diagram of bosons to allow for the breaking of time-reversal symmetry. The direct transition can be protected by a spatial symmetry, and the critical theory is a pair of Dirac fermion fields coupled to an emergent Chern-Simons gauge field. The transition may be achieved in optical traps of ultracold atoms by starting with a $\nu =1/2$ bosonic Laughlin state and tuning an appropriate periodic potential to change the topology of the composite fermion band structure.

Figure 1

Proposed phase diagram and renormalization-group flows including the Mott insulator, superfluid, and $\nu =1/2$ Laughlin FQH state, for fixed average particle number. We have defined $m_{\pm }\equiv m_1\pm m_2$ [see Eq. (7)]; $m_{-}$ is a symmetry-breaking field, so the direct transition between the FQH state and the SF can occur if the symmetry is preserved. The red points on the horizontal and vertical axes indicate the three stable phases, while the blue points at the origin and the diagonals indicate the unstable critical fixed points.

Figure 2

Evolution (schematic) of composite fermion bands as a periodic potential is turned on and tuned in an appropriate way. Red labels filled states and blue labels empty states. The flat bands on the far left indicate the Landau levels indexed by $n$.