Universal finite-size amplitude and anomalous entangment entropy of $z=2$ quantum Lifshitz criticalities in topological chains

We consider Lifshitz criticalities with dynamical exponent z=2 z=2 that emerge in a class of topological chains. There, such criticality plays fundamental role describing transitions between symmetry-enriched conformal field theories (CFTs). report that, at critical points one spatial dimension, the finite-size correction to energy scales system size, L display="inline">L , as \sim L^{-2} display="inline">∼L−2 universal and anomalously large coefficient. The behavior originates from specific dispersion around Fermi surface, \epsilon \propto \pm k^2 display="inline">ϵ∝±k2 . also show entanglement entropy exhibits non-logarithmic dependence on l/L display="inline">l/L where l display="inline">l is length sub-system. In limit l\ll display="inline">l≪L maximally-entangled ground state has entropy, S(l/L)=S_0+(l/L)\log(l/L) display="inline">S(l/L)=S0+)log) Here S_0 display="inline">S0 some non-universal originating short-range correlations. novel long-range correlation mediated by zero mode low sector. work paves way study effects offers an insight into criticalities.