Entanglement Entropy Fluctuations in Quantum Ising Chains

TL;DR

This paper derives exact analytical expressions for entanglement entropy fluctuations in infinite quantum Ising chains, revealing divergence near critical points and a vanishing relative fluctuation at criticality.

Contribution

It provides the first analytical calculation of the second central moment of entanglement entropy in quantum Ising chains, highlighting fluctuation behavior near phase transitions.

Findings

Entanglement entropy fluctuations diverge logarithmically near the critical point.

Relative entanglement fluctuation vanishes at the critical point.

Exact analytical expressions for entropy dispersion are obtained for infinite chains.

Abstract

The Ising chains in a transverse magnetic field of constant strength (h=1) and with the spin interaction value \lambda are considered. In the case of infinitely long chain, exact analytical expressions are found for the second central moment (dispersion) of the entropy operator S^\hat=-ln\rho with reduced density matrix \rho which corresponds to a semi-infinite part of the model in the ground state. It is shown that in the vicinity of a critical point \lambda_c=1, the entanglement entropy fluctuation \Delta S (square root of dispersion) diverges as \Delts S\sim[ln(1/|1-\lambda|)]^{1/2}. Taking into account the known behavior of the entanglement entropy S, this leads to that the value of relative entanglement fluctuation \delta S=(\Delta S)/S vanishes at the critical point, i.e. in fact a state with nonfluctuating entanglement is realized.