Landau ordering phase transitions beyond the Landau paradigm

TL;DR

This work demonstrates that continuous Landau ordering transitions in $3+1$-D bosonic systems can realize universality classes beyond the Landau-Ginzburg-Wilson framework, described by deconfined gauge theories with massless Dirac fermions at a fixed point (Landau transitions beyond Landau description, or LBL). By coupling Dirac fermions to an $SU(2)$ gauge field and tuning a fermion mass $m$, the authors obtain a massless critical point that mediates a transition between a trivial phase and a time-reversal–broken confined phase, with the global symmetry $G= PSp(N_f)$ protecting the fixed point and ensuring projective realization of $G$ on critical modes. They derive two diverging length scales near criticality, yielding exponents $ u=1$ and $ u_{conf}=y$ (with $y=rac{N_f}{11}$ for $SU(2)$ with fundamental fermions), and find an unusually large anomalous dimension $\\eta=4$ with $\ riangle_{\phi}=3$, giving $eta=3y$. The analysis extends to large-$N_c$ generalizations ($Sp(N_c)$ and $SU(N_c)$) and to alternate confinement scenarios (U(1) and $\mathbb{Z}_2$ spin liquids), revealing continuous Landau-forbidden deconfined transitions in $3+1$-D and highlighting the role of higher gauge structure and symmetry protection in driving novel critical behavior.

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.

Figures (6)

• Figure 1: A schematic plot of the phase diagram. In addition to the standard Ising universality class the transition can also occur through a distinct 'deconfined critical' universality class.
• Figure 2: A schematic plot of the RG flow showing both the Ising and the alternate deconfined critical fixed points for the same phase transition.
• Figure 3: RG flow and phase diagram of the parton theory as a function of the fermion mass. For $m<0$, we are free to choose a regularization such that the gauge theory has trivial $\theta$ term and thus flows to a trivial confined phase. On the contrary, for $m>0$, at low energy the gauge theory has $\theta=\pi$, which leads to a flow to a confined phase that spontaneously breaks the $\mathcal{T}$ symmetry.
• Figure 4: A finite temperature phase diagram of the beyond Landau transition.
• Figure 5: 1d $SU(3)$ spin chain with fundamental spin at each site. The nearest neighbor spins interact with each other through a Heisenberg Hamiltonian with interaction strength labeled in the figure. For $\delta\neq 0$, one unit cell contains three spins. For $\delta=0$ the system has enlarged translational symmetry. The Hamiltonian has a site-centered parity symmetry.