Stabilizer Entropy and entanglement complexity in the Sachdev-Ye-Kitaev model

by Barbara Jasser

Wednesday 19 Feb 2025, 16:00 → 17:00 Europe/Rome

2G26

The Sachdev-Ye-Kitaev (SYK) model is of paramount importance for the understanding of both strange metals and a theory of two-dimensional gravity. In this talk, we consider the interpolation between the four-body (SYK4) model, which is chaotic, with an exponential density of states at low energy, and the intergable two-body (SYK2), which has a polynomially vanishing gap. Remarkably, both models exhibit a volume law for entanglement. One might wonders what makes these two regimes so different. Entanglement has been deeply investigated to better understand both the chaotic nature of the SYK4 and its connection to holographic theory but the transition to SYK2 shows that entanglement alone is not enough. The second layer of quantum complexity is given by non-stabilizerness, a crucial resource in the context of universal quantum computation, error correction and quantum simulation. 

We study the interplay between non-stabilizerness and entanglement entropy in both the ground state and highly excited states of the SYK4+SYK2 model. The interplay between these quantities is assessed also through universal statistics of the entanglement spectrum and its anti-flatness. We find that SYK4 is indeed characterized by a complex pattern of both entanglement and non-stabilizer resources while SYK2 is non-universal and not complex. In conclusion, we discuss the fragility and robustness of these features depending on the interpolation parameter.