Landau ordering phase transitions beyond the Landau paradigm

TL;DR

This paper introduces new universality classes of continuous phase transitions in 3+1D bosonic systems that go beyond traditional Landau theory, involving deconfined gauge theories and massless Dirac fermions.

Contribution

It demonstrates the existence of Landau transitions beyond Landau description (LBL) with stable fixed points requiring a global symmetry, and constructs novel quantum critical phenomena including a Landau-forbidden deconfined critical point.

Findings

Identified LBL phase transitions with deconfined gauge theories.

Showed stability of LBL fixed points depends on a non-anomalous global symmetry.

Constructed a 3+1D deconfined critical point between two Landau-allowed phases.

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.