Quantum Info: “Spreading globally, remembering locally: Two views of the PXP Model” by Francesco Perciavalle (Università della Calabria & INFN)

Title: “Spreading globally, remembering locally: Two views of the PXP Model”

Venue & Time: Gray Room 3 / 11:30

Speaker: Francesco Perciavalle (Università della Calabria & INFN)

Abstract: The PXP model describes chains of Rydberg atoms in the blockade regime, where no two neighbouring atoms can be excited at the same time. Most of its spectrum obeys the eigenstate thermalization hypothesis. A small set of non-thermal eigenstates, the quantum many-body scars, breaks it: they cause the Néel state to return repeatedly to its initial configuration. Scarred and ergodic dynamics are usually told apart by global memory, meaning whether the full wave function comes back. This talk looks at the PXP model from two other angles, drawn from two works that are, at the moment, separate.

The first view is global. How far does the wave function spread across the blockaded Fock space? Dynamics from the Néel state reaches exponentially many configurations despite its revivals, yet in the thermodynamic limit it covers a vanishing fraction of the space. The ergodic polarized state covers a finite fraction close to random-state anticoncentration, but chiral symmetry caps that fraction at one third. A weak quasiperiodic field lifts this cap and raises the occupied fraction to one half. The Néel state needs a field strong enough to destroy the scars before it gets there. Stronger fields then reduce the spreading for both states, without necessarily leading to localization.

The second view is local. Can a system keep memory of its initial state on small subsystems while its global dynamics stays complex and non-periodic? We call this local reminiscence and study it through local fidelities and local observables. Two families of states, θ-symmetric states and blockaded (Fibonacci) states, show robust local reminiscence: their local fidelities stay near unity, and the fluctuations shrink as the system grows.

These two views look at the same model from opposite ends: one asks how widely the dynamics spreads, the other what it keeps locally. They give complementary pictures of weak ergodicity breaking in constrained Rydberg dynamics. The talk will also discuss several perspectives that emerge from these recent results, among them the prospect of bringing the two approaches together.

The talk is based on the works:

F. Perciavalle, Fock-space delocalization and its control in scarred-vs-ergodic dynamics.
https://doi.org/10.48550/arXiv.2610.40805

F. Perciavalle, G.M. Rizzo, F. Plastina, N. Lo Gullo. Local reminiscence in the PXP model.
https://doi.org/10.48550/arXiv.2509.19944