Deconfined Criticality: Generic First-Order Transition in the SU(2) Symmetry Case

Monte Carlo simulations of the SU(2)-symmetric deconfined critical point action reveal strong violations of scale invariance for the deconfinement transition. We find compelling evidence that the generic runaway renormalization flow of the gauge coupling is to a weak first-order transition, similar to the case of $\mathrm{U}(1)\times \mathrm{U}(1)$ symmetry. Our results imply that recent numeric studies of the Nèel antiferromagnet to valence bond solid quantum phase transition in SU(2)-symmetric models were not accurate enough in determining the nature of the transition.

Figure 1

Phase diagram of the SU(2)-symmetric DCP action (1). First-order transitions VBS-2SF are shown as a solid red line up to the bicritical point $g_{bc}\approx 2.0$.

Figure 2

Flowgrams for the short-range model. The lower horizontal line features the O(4) universality scaling behavior, so that for $g<g_c\approx 0.95$ all flows are attracted to this line. The upper horizontal line is the tricritical separatrix (marked as TP). Above it, flows diverge due to the first-order transition detected by the bimodal distribution of energy.

Figure 3

A typical flowgram of the gauge-invariant superfluid stiffness in the ${\mathrm{NCCP}}^1$ model. The inset shows a fan of diverging flows for $0.125<g<1.4$.

Figure 4

Data collapse for the ${\mathrm{NCCP}}^1$ flows. The yellow line is a fit representing the master curve. The horizontal axis is the scale-reduced variable $C(g)L$, with $C(g)=[\exp (bg)-1]/[\exp (b{g}_1)-1]$, $b=2.28\pm 0.02$, and $g_1=1.3$. Error bars are shown for all data points.

Figure 5

Evolution towards the bimodal energy distribution with increasing system size indicative of the first-order deconfinement transition ($g=1.65$).