Our modern understanding of phase transitions is built on Landau's theory,
which, among other things, dictates when it may be possible to have a
continuous transition between two phases. For example, a continuous
transition between two phases with unrelated orders is forbidden in this
theory without special fine tuning.
In this talk I will argue that in the case of quantum phase transition,
precisely such `Landau forbidden' phase transition may occur. In
particular, a theory for a direct continuous transition between the Neel
and VBS phases of a two dimensional quantum magnet will be presented. This
critical theory is naturally described in terms of fractionalized
excitations (spinons) and a conserved flux that only emerges at the
transition. The critical theory will be developed by starting from the
Neel ordered phase and understanding precisely the role played by
hedgehog defects in the Neel field.
The possible relevance of this physics to phenomena in strongly correlated
materials will be briefly discussed.
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