Susceptibility of entanglement entropy: a universal indicator of quantum criticality

A measure of how sensitive the entanglement entropy is in a quantum system, has been proposed and its information geometric origin is discussed. It has been demonstrated for two exactly solvable spin systems, that thermodynamic criticality is directly \textit{indicated} by finite size scaling of the global maxima and turning points of the susceptibility of entanglement entropy through numerical analysis - obtaining power laws. Analytically we have proved those power laws for $| \ \lambda_c(N)-\lambda_c^{\infty}|$ as $N\to \infty$ in the cases of finite 1D transverse field ising model (TFIM) ($\lambda=h$) and XY chain ($\lambda=\gamma$). The integer power law appearing for XY model has been verified using perturbation theory in $\mathcal{O}(\frac{1}{N})$ and the fractional power law appearing in the case of TFIM, is verified by an exact approach involving Chebyshev polynomials, hypergeometric functions and complete elliptic integrals. Furthermore a set of potential applications of this quantity under quantum dynamics and also for non-integrable systems, are briefly discussed. The simplicity of this setup for understanding quantum criticality is emphasized as it takes in only the reduced density matrix of appropriate rank.