Deconfined quantum criticality

4 problems

• Do complex fixed points explain the pseudocritical drift at deconfined transitions?

  Contested

  One explanation of the slow drift is that the true critical point has moved slightly into complex values of the couplings, so the system behaves almost critically over a very large range of lengths. This idea predicts specific scaling dimensions that can be computed and checked.

• Is the easy-plane deconfined transition continuous?

  Contested

  If the spins are restricted to rotate in a plane, the same transition may behave differently and is linked by predicted dualities to other field theories. Simulations disagree on whether it is continuous.

• Find a material with a continuous Neel to valence-bond-solid transition

  Open

  Deconfined criticality has been seen mostly in computer models. The goal is a real magnet where the change from magnetic order to a pattern of spin singlets happens continuously or nearly so.

• Is the Neel to valence-bond-solid transition in the J-Q model continuous?

  Contested

  In the J-Q model a magnetic (Neel) state turns into a state of locked spin pairs (a valence-bond solid) as a four-spin coupling grows. Simulations show slowly drifting critical exponents, so it is unclear whether the transition is continuous or a very weak jump.