Temperature driven quenches in the Ising model: appearance of negative R\'enyi mutual information

TL;DR

This paper investigates the dynamics of the transverse field Ising chain after a local quench, revealing that Rnyi mutual information can be negative for indices greater than 2, which is a novel and surprising finding in many-body physics.

Contribution

It provides the first realistic many-body example where Rnyi mutual information becomes negative for b1>2, supported by both numerical and analytical analysis.

Findings

Rnyi mutual information scales logarithmically with subsystem size.

For b1>2, the mutual information can be negative, contrary to typical expectations.

The same prefactor governs the time dependence of mutual information before relaxation.

Abstract

We study the dynamics of the transverse field Ising chain after a local quench in which two independently thermalised chains are joined together and are left to evolve unitarily. In the emerging non-equilibrium steady state the R\'enyi mutual information with different indices are calculated between two adjacent segments of the chain, and are found to scale logarithmically in the subsystem size. Surprisingly, for R\'enyi indices $\alpha>2$ we find cases where the prefactor of the logarithmic dependence is negative. The fact that the naively defined R\'enyi mutual information might be negative has been pointed out before, however, we provide the first example for this scenario in a realistic many-body setup. Our numerical and analytical results indicate that in this setup it can be negative for any index $\alpha>2$ while it is always positive for $\alpha <2.$ Interestingly, even for $\alpha>2$ the calculated prefactors show some universal features: for example, the same prefactor is also shown to govern the logarithmic time dependence of the R\'enyi mutual information before the system relaxes locally to the steady state. In particular, it can decrease in the non-equilibrium evolution after the quench.