Dynamical quantum phase transitions

6 problems

• Do dynamical transitions occur only for quenches across critical points

  Open

  Kinks in the return probability were first found for sudden changes that cross an ordinary phase transition. Some models show kinks without such a crossing, and others show a crossing without kinks, and the rule that decides which happens is missing.

• Can a local measurement detect a dynamical transition in large systems

  Open

  The return probability shrinks exponentially with system size, so it cannot be measured in big systems. The question is whether some quantity measured on a few sites shows the same sharp kinks.

• Do dynamical quantum phase transitions survive at finite temperature

  Open

  The theory is built for pure starting states at zero temperature. For warm starting states several competing definitions exist, and they disagree on whether the sharp kinks remain.

• When dynamical transitions coincide with equilibrium criticality or order

  Partially resolved

  The kinks in the return probability were first linked to crossing an ordinary phase transition, but counterexamples exist in both directions. A general rule for when they match is missing.

• Do dynamical transition times coincide with zeros of the order parameter

  Open

  In some models the kinks happen exactly when the measured order of the system passes through zero, in others they do not. When the two coincide is unknown.

• Universal scaling near dynamical transitions in interacting systems

  Open

  Ordinary phase transitions have universal exponents shared by very different materials. Whether the kinks in the return probability have universal exponents in interacting two- and three-dimensional systems is not known.