Susceptibility of entanglement entropy: a universal indicator of quantum criticality

TL;DR

This paper introduces a universal measure based on entanglement entropy susceptibility that signals quantum criticality, demonstrating its effectiveness through analytical proofs and numerical analysis of exactly solvable spin models.

Contribution

It provides the first analytical proof of power laws in entanglement entropy susceptibility near quantum critical points in spin models, linking information geometry to quantum phase transitions.

Findings

Finite size scaling of susceptibility indicates criticality.

Power laws verified in transverse field Ising and XY models.

Potential applications in quantum dynamics and non-integrable systems.

Abstract

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.