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

Understand

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.