Andrea Pizzi
(Christ's College, Cambridge)

At the level of local observables and due to the eigenstate thermalization hypothesis (ETH), isolated systems of many interacting particles tend to quickly thermalize and forget about their past. This paradigm needs not apply to wavefunction amplitudes, objects of increasing relevance for modern quantum computers and simulators. Here, we unveil the structure of the many-body wavefunction in chaotic spin models. Despite the eigenstates fulfilling ETH and being strongly entangled, exponentially many of them are genuinely scarred, that is, have an enlarged weight along underlying classical unstable periodic orbits. Scarring underpins an anomalous (non-Porter-Thomas) statistics of the wavefunction amplitudes, and makes the system more likely to be found on an orbit it was initialized on, retaining a memory of its past and weakly breaking ergodicity. We demonstrate the ubiquity of scarring in many-body systems by considering a large family of spin models, including some of the most popular ones from condensed matter physics. Some features of scarring even extend beyond periodic orbits, giving rise to “quantum trails” along generic (non-periodic) trajectories. Our findings prove structure in spite of chaos in many-body quantum systems.
 

Zoom registration link:
https://zoom.us/meeting/register/EfoaG7Q1Q6O2VLxf-q1RyA