• Computational Physics
• Condensed Matter Physics
• Entanglement
• Sachdev-Ye-Kitaev

The SYK model is a strongly coupled many-body quantum system: it features spinless fermions on a zero-dimensional lattice with L sites, that are coupled all-to-all through q-fermion interaction (we study the case with q=4). We expect from it an highly entangling nature, and we probe this feature by means of the computation of the von Neumann entropy for the density matrix of a subsystem A (usually with L_A/L=1/2), when the total system is in a pure state. We consider three kinds of pure states: ground state, state reached after unitary evolution and state reached after the evolution dictated by the interplay of unitary and projective dynamics (implemented with the protocols of projective measurement and of quantum jumps). In the first two cases we find a quadratic growth with the size of the system for the entanglement (this is a finite size artifact, as the growth can be at most linear asymptotically); turning on measurements, quadratic growth survives for weak measurements, than becomes purely linear: this suggests that for the SYK model we have a robust volume law, and no measurement induced transition to an area law behavior (as seen for other less entangling systems, as the Ising model) occurs.