The universality of chaotic many-body dynamics has long been identified by random matrix theory, leading to the Eigenstate Thermalization Hypothesis (ETH).
In this lecture, I will present the full version of ETH, which encompasses correlations among matrix elements needed to describe dynamical correlations of different times. Then, I will show how this ansatz can be highly simplified by the...
Quantum many-body systems are genuinely characterized by ergodic behavior
according to the principles of statistical mechanics. In this set of lectures,
I will discuss how such ergodic behavior can be broken by different kinds of
mechanisms including integrability, many-body localization, gauge symmetries
and local constraints.
Quantum many-body systems are genuinely characterized by ergodic behavior
according to the principles of statistical mechanics. In this set of lectures,
I will discuss how such ergodic behavior can be broken by different kinds of
mechanisms including integrability, many-body localization, gauge symmetries
and local constraints.
Recently, there has been remarkable progress in realizing constrained models and lattice gauge theories in a number of experimental platforms, ranging from trapped ions to cold-atoms in optical lattices, Rydberg atoms arrays and superconducting qubits. In this lecture I will introduce the basic ingredients needed to engineer local constraints and gauge symmetries and will review experimental...
Highly-excited states of quantum many-body systems are typically described well by the eigenstate thermalization hypothesis and show volume law entanglement entropy. In models with quantum many-body scars, however, a few states at high energies behave differently. These scar states typically have area law entanglement entropy and form a tower of states with equidistant energies. The scar...
Experiments involving the behavior of quantum magnetic systems in the non-ergodic regime have been difficult to access due to a lack of clearly defined theoretical targets. The situation is changing with the realization that experiments can access the signatures of non-ergodic behavior both in the dynamical correlations in the weakly out-of-equilibrium scattering regime as well as under...
Ultracold atoms and molecules offer intriguing opportunities for probing the quantum dynamics of quantum many-body systems. Initial states, lattice geometries and interactions can be fully tuned to explore novel regimes of quantum transport. Atoms can be counted one-by-one using quantum gas microscopy, giving access to the full counting statistics and non-local correlations. In this lecture, I...
