QLunch: Entanglement of excited states

Speaker: Lucas Hackl 

Title: Entanglement of exited states

In this talk, I will discuss what one can learn about a quantum system from the entanglement properties of its eigenstates. Many remarkable results have been obtained for the entanglement entropy of ground states, while for excited states there is a wide gap between what is expected and what has been shown. For quadratic fermionic systems, I will review the following properties:

Typicality: The average entanglement entropy of subsystems of random pure states approaches the maximal possible value for large Hilbert spaces. Hence, typical pure states are (nearly) maximally entangled. For translationally invariant systems, we prove that this is not the case for typical eigenstates, where the maximal value is only reached for vanishing subsystem fractions.

Universality: For the XY spin model, we discover universal properties in the average entanglement entropy of eigenstates, namely the average entanglement entropy approaches a universal function of the subsystem ratio, when taking the thermodynamic limit. We present a combination of numerical and analytical evidence that this universality extends to all translationally invariant quadratic fermionic systems.

Criticality: For the paradigmatic quantum Ising model (XY with γ=1), we find that the subleading finite size correction to the average entanglement entropy signals quantum criticality, being order one at the critical field and vanishing otherwise.