Long-Range Nematic Order in Two-Dimensional Active Matter

Abstract: Working in two space dimensions, we show that the orientational order emerging from self-propelled polar particles aligning nematically is quasi-long-ranged beyond $\ell_{\rm r}$, the scale associated to induced velocity reversals, which is typically extremely large and often cannot even be measured. Below $\ell_{\rm r}$, nematic order is long-range. We construct and study a hydrodynamic theory for this de facto phase and show that its structure and symmetries differ from conventional descriptions of active nematics. We check numerically our theoretical predictions, in particular the presence of $\pi$-symmetric propagative sound modes, and provide estimates of all scaling exponents governing long-range space-time correlations.