**Research**

I am a condensed matter theorist working on strongly correlated quantum systems, with a focus on the interplay of strong interactions and quantum entanglement, leading to new emergent phenomena both in thermal equilibrium and in non-equilibrium quantum systems. Some of my recent research interests include: thermalization, quantum hydrodynamics, non-equilibrium steady states, quantum entanglement, tensor networks, many-body localization, disordered systems, driven quantum systems, quasiperiodic systems, topological phases of matter and topological phase transitions.

See below a few selected research topics I have been working on recently. For more details, click on the titles.

The laws of thermodynamics can break down in disordered quantum systems that are isolated from external heat sources, due to the localization of excitations that would ordinarily transport energy among distant regions to establish thermal equilibrium. Such many-body localized (MBL) systems have the remarkable property that almost all high-energy excited states behave like zero-temperature quantum ground states. This raises the intriguing possibility that quantum coherent phenomena such as quantum and topological order or quantum criticality, typically associated with zero-temperature systems, can occur in arbitrarily “hot” matter. Cold atomic, molecular, and trapped ion systems offer a promising experimental platform to explore these theoretical ideas. Much of my recent work has been devoted to understanding the universal nature of the dynamics in the MBL phase and near the many-body delocalization transition to an ergodic state. Learn More.

The study of closed quantum systems out-of-equilibrium, with or without disorder, opens the door to new and exciting conceptual questions about dynamics, thermalization, universality and dynamical phase transitions beyond traditional condensed matter paradigms. In addition to being theoretically appealing, these questions are strongly motivated by the rapid progress in ultra-cold atomic, molecular, and trapped ion systems that offer promising experimental platforms to investigate the dynamics of closed quantum systems. More generally, recent experimental advances in ultrafast optics and pump-probe spectroscopy, solid-state qubits, ultracold gases or quantum nanostructures have opened up exciting avenues for non-equilibrium quantum physics, with many open questions such as quantum transport beyond linear-response or the existence of novel dynamical phases of matter with no equilibrium counterparts. A central theme in my research is studying the non-equilibrium dynamics of low-dimensional strongly-correlated quantum systems, with some emphasis on entanglement spreading, quantum quenches, hydrodynamics and far-from-equilibrium transport. Learn More.

Entanglement is one of the most counterintuitive and “spooky” features of quantum mechanics. The information theoretic perspective of quantum entanglement entropy has proven an increasingly useful tool to understand and classify quantum phases of matter, and it has already revolutionized our understanding of the equilibrium properties of strongly-interacting quantum systems. Quantum information promises to do the same for non-equilibrium quantum dynamics. I am broadly interested in entanglement properties of many-body quantum systems, both at zero temperature and in non-equilibrium settings. This includes the study of topological phases of matter that have a long-range pattern of entanglement, and quantum phase transitions between distinct topological phases. Recently, I have also been interested in the “geometry” of quantum entanglement, tensor networks, and “entanglement phase transitions” where entanglement changes abruptly at a critical point. Learn More.

Many systems of current interest — such as quasicrystals, twisted bilayer graphene, and cold atoms in bichromatic laser potentials — are inhomogeneous, but with quasiperiodic rather than random modulation of the couplings. Quasiperiodic patterns are deterministic and have long-range spatial correlations: thus the central limiting arguments that describe random critical points fail in the quasiperiodic case. The study of such quasiperiodic systems is in its infancy: how is quantum criticality modified in the presence of quasiperiodic modulations? What is the nature of the many-body localization transition in quasiperiodic potentials? Can quasiperiodic systems host new topological phenomena and lead to novel dynamical phases of matter? I have been working recently on these questions, as well as on the non-equilibrium dynamics of quasi-periodically driven quantum systems. Learn More.