Carroll at Phase Separation

Abstract: Asymptotic behavior of generic Tomonaga-Luttinger liquid in the vicinity of phase-separated regions is known to produce an instability where well-known relativistic Conformal Field Theory (CFT) techniques fail. In this letter, we introduce an analytic paradigm which solves this important issue. We show that there is an emergent Carrollian symmetry when phase separation is reached and techniques of Carroll CFT, as opposed to its relativistic relative, is central to the understanding of the physics. We work with the analogous spinless fermionic system in this region and capture the transition across this phase separation. Our numerical results corroborate the density-density correlations intrinsically computed using Carroll CFT.