In our final (?) preprint of 2024, J. De Nardis' group and I, in collaboration with S. Gopalakrishnan from Princeton, explore spectra, correlations, and entanglement in ensembles of {random} Matrix Product States (MPS)! 😀
Check out the details here: arxiv.org/abs/2412.14261

Finally, we compute SREs in the ground state of a 2D free fermionic model with topological features, demonstrating that our method effectively handles the challenges of higher-dimensional systems.

We also support these numerical results with analytical findings for a set of related quantities, specifically the Participation Entropies in the computational (Fock) basis, for which we derive an explicit formula that shows the same behavior (Haar - log corrections).

Building on this, we looked into how much 'magic' you get from *typical* (random) Fermionic Gaussian States. It turns out, they show about the same amount of magic as generic many-body (Haar) states, with corrections which are logarithmic in the system size.

This was likely due to the lack of suitable analytical or computational tools to probe this feature. For example, Tensor Networks may struggle with free fermionic states, as these can exhibit volume-law entanglement.

First day at the fantastic Many-Body Quantum Magic (MBQM) workshop in Abu Dhabi! :) Happy to be here as invited speaker! Thanks to all the organizers!