This is a nice practical technique for open quantum systems with relatively low entanglement. The introduction lays out exactly what regime they're aiming at:
1. Affordable (laptop scale)
2. Captures "sufficient" quantum effects (low entanglement regime; you accurately can't simulate a quantum computer with this)
3. Straightforward to implement.
From a cursory glance, it does all three. I'm slightly surprised that TWA hasn't been applied to open systems extensively before, but it was always a relatively obscure technique. I'm guessing this should be quite useful in practice for e.g. AMO and cavity systems with relatively large dissipation terms that prevent entanglement build up. However, I'd guess this wouldn't do very well near phase transitions. All-in-all, a nice new technique for a regime that didn't have too many options.
Physicist here. The superconductivity in layered graphene is indeed surprisingly strange, but this popular article may not do it justice. Here are some older articles on the same topic that may be more informative:
Let me briefly say why some reasons this topic is so interesting. Electrons in a crystal always have both potential energy (electrical repulsion) and kinetic energy (set by the atomic positions and orbitals). The standard BCS theory of superconductivity only works well when the potential energy is negligible, but the most interesting superconductors --- probably including all high temperature ones like the cuprates --- are in the regime where potential energy is much stronger than kinetic energy. These are often in the class of "unconventional" superconductors where vanilla BCS theory does not apply. The superconductors in layered (and usually twisted) graphene lie in that same regime of large potential/kinetic energy. However, their 2d nature makes many types of measurements (and some types of theories) much easier. These materials might be the best candidate available to study to get a handle on how unconventional superconductivity "really works". (Besides superconductors, these same materials have oodles of other interesting phases of matter, many of which are quite exotic.)
Also physicist here. I've worked on conventional superconductors, but never on unconventional ones. Last I heard, it was believed to be mediated by magnons (rather than phonons). Who claims it is due to Coulomb interaction?
Alright, this one is pretty interesting but, as usual, it needs some amount of background to appreciate it properly. Let me try to make an elementary summary.
Electrons in a crystal are partially governed by a "quantum metric" on the "Brillouin zone manifold" [1]. Metric tensors on manifolds famously appear in general relativity, and are a central object in differential geometry (hence the accurate moniker "quantum geometry"). "Quantum geometry" is a hot topic in condensed matter physics in the last few years, and governs or is connected to many important quantities. For instance, the integral of the quantum metric is proportional to the conductivity (in the disorder-free regime) [2]. This paper makes a more-or-less direct measurement of the quantum metric in the material CoSn.
