Excited-state entanglement and thermal mutual information in random spin chains

TL;DR

This paper investigates the entanglement and thermal mutual information in excited states of random spin chains using a real-space renormalization group method, revealing universal behaviors and differences from ground states.

Contribution

It introduces the application of RSRG-X to analyze excited states in random spin chains, uncovering universal entanglement properties and their differences from ground states.

Findings

Entanglement entropy of excited states remains logarithmically divergent.

Thermal mutual information does not diverge logarithmically in excited states.

The coefficient of divergence in the XX model extends over a universal interval.

Abstract

Entanglement properties of excited eigenstates (or of thermal mixed states) are difficult to study with conventional analytical methods. We approach this problem for random spin chains using a recently developed real-space renormalization group technique for excited states ("RSRG-X"). For the random $XX$ and quantum Ising chains, which have logarithmic divergences in the entanglement entropy of their (infinite-randomness) critical ground states, we show that the entanglement entropy of excited eigenstates retains a logarithmic divergence while the mutual information of thermal mixed states does not. However, in the $XX$ case the coefficient of the logarithmic divergence extends from the universal ground-state value to a universal interval due to the degeneracy of excited eigenstates. These models are noninteracting in the sense of having free-fermion representations, allowing strong numerical checks of our analytical predictions.