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
Check out the paper for more details! arxiv.org/pdf/2412.05367 Thanks to my co-authors, Mario Collura, Vincenzo Alba and Jacopo De Nardis!
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.
The algorithm relies only on the two-point correlation function (covariance matrix) of the state, is both simple and efficient, and can evaluate SREs for systems with up to ~100 or even ~1000 fermionic modes... 🤯
In a new work, arxiv.org/abs/2412.05367 me and collaborators investigate the nonstabilizerness of free fermions😀In particular, we propose an algorithm to sample Fermionic Gaussian States in the space of Pauli operators, enabling the efficient estimation of SREs.
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.
'Magic'🧙♂️ is a key resource of the quantum world. After the introduction of Stabilizer Rényi Entropies (SREs), a practical measure of magic, many applications to many-body physics also emerged. However, evaluating magic in simple non-interacting fermionic systems remained elusive...
{Happy also for writing my first post on this platform}
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!
