Abstract
Continuous phase transitions associated with the onset of a spontaneously broken symmetry are thought to be successfully described by the Landau-Ginzburg-Wilson-Fisher theory of fluctuating order parameters. In this work we show that such transitions can admit new universality classes which cannot be understood in terms of a theory of order parameter fluctuations. We explicitly demonstrate continuous time reversal symmetry breaking quantum phase transitions of $3+1$-D bosonic systems described by critical theories expressed in terms of a deconfined gauge theory with massless Dirac fermions instead of the fluctuating Ising order parameter. We dub such phase transitions "Landau transitions beyond Landau description" (LBL). A key feature of our examples is that the stability of the LBL fixed points requires a crucial global symmetry, which is non-anomalous, unbroken, and renders no symmetry protected topological phase throughout the phase diagram. Despite this, there are elementary critical fluctuations of the phase transition that transform projectively under this symmetry group. We also construct examples of other novel quantum critical phenomena, notably a continuous Landau-forbidden deconfined critical point between two Landau-allowed phases in $3+1$-D.
Highlights
The standard example of continuous equilibrium phase transitions is that associated with the onset of a broken symmetry
The symmetry breaking is captured by a Landau order parameter
One or both phases may have order not captured by a Landau order parameter
Summary
The standard example of continuous equilibrium phase transitions is that associated with the onset of a broken symmetry. The LGWF paradigm is known to fail in a few different situations One or both phases may have order not captured by a Landau order parameter (e.g., quantum Hall or other topological phases). More surprisingly, it is known that there are Landau-forbidden second order quantum phase transitions between two phases that themselves are Landau allowed [2,3,4,5,6,7] Such phase transitions are more naturally described in terms of fractionalized degrees of freedom which rear their heads only at the critical point but are absent (confined) in either of the two phases. We will find an alternate route through a “deconfined critical” universality class with emergent fermions and gauge fields At this deconfined critical fixed point, the symmetry G acts nontrivially on the critical degrees of freedom. These examples generalize similar phenomena known in 2 + 1-D, and settle the matterof-principle question on whether such continuous quantum phase transitions can occur in 3 + 1-D
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