The Hubbard model, formulated by physicist John Hubbard in the 1960s1, is a simple theoretical model of interacting quantum particles in a lattice. The model is thought to capture the essential physics of high-temperature superconductors, magnetic insulators and other complex quantum many-body ground states2,3. Although the Hubbard model provides a greatly simplified representation of most real materials, it is nevertheless difficult to solve accurately except in the one-dimensional case2,3.

We experimentally investigate the origin of two-magnon scattering (TMS) in heavy-metal (HM)/ferromagnet (FM)/oxide heterostructures (FM = Co, Ni81Fe19, or Fe60Co20B20) by varying the materials located above and below the FM layer. We show that strong TMS in HM/FM/oxide systems arises primarily at the HM/FM interface and increases with the strength of the interfacial spin-orbit coupling and magnetic roughness at this interface. TMS at the FM/oxide interface is relatively weak, even in systems where spin-orbit coupling at this interface generates strong interfacial magnetic anisotropy.

Motivated by recent experiments, we explore the kinetics of Bose-Einstein condensation in the upper band of a double-well optical lattice. These experiments engineer a nonequilibrium situation in which the highest energy state in the band is macroscopically occupied. The system subsequently relaxes and the condensate moves to the lowest energy state.

We construct a family of translationally invariant lattice models with a large number (N) of orbitals at every site coupled together via single-electron tunneling. By tuning the relative strength of the electronic bandwidth and on-site interactions, which have a modified Sachdev-Ye-Kitaev form, we demonstrate a number of unusual features at strong coupling and in the large-N limit.

Recent experimental observations of apparently hydrodynamic electronic transport have generated much excitement. However, the understanding of the observed nonlocal transport (whirlpool) effects and parabolic (Poiseuille-like) current profiles has largely been motivated by a phenomenological analogy to classical fluids. This is due to difficulty in incorporating strong correlations in quantum mechanical calculation of transport, which has been the primary angle for interpreting the apparently hydrodynamic transport.

Magnetic monopoles have been proposed as emergent quasiparticles in pyrochlore spin ice compounds. However, unlike semiconductors and two-dimensional electron gases where the charge degree of freedom can be actively controlled by chemical doping, interface modulation, and electrostatic gating, there is as of yet no analogue of these effects for emergent magnetic monopoles. To date, all experimental investigations have been limited to large ensembles comprised of equal numbers of monopoles and antimonopoles in bulk crystals.

Recent developments in twisted and lattice-mismatched bilayers have revealed a rich phase space of van der Waals systems and generated excitement. Among these systems are heterobilayers, which can offer new opportunities to control van der Waals systems with strong in plane correlations such as spin-orbit-assisted Mott insulator α-RuCl3. Nevertheless, a theoretical ab initio framework for mismatched heterobilayers without even approximate periodicity is sorely lacking.

We review the physics of pair-density wave (PDW) superconductors. We begin with a macroscopic description that emphasizes order induced by PDW states, such as charge-density wave, and discuss related vestigial states that emerge as a consequence of partial melting of the PDW order. We review and critically discuss the mounting experimental evidence for such PDW order in the cuprate superconductors, the status of the theoretical microscopic description of such order, and the current debate on whether the PDW is a mother order or another competing order in the cuprates.

The unusual correlated state that emerges in URu2Si2 below THO = 17.5 K is known as “hidden order†because even basic characteristics of the order parameter, such as its dimensionality (whether it has one component or two), are “hidden.†We use resonant ultrasound spectroscopy to measure the symmetry-resolved elastic anomalies across THO. We observe no anomalies in the shear elastic moduli, providing strong thermodynamic evidence for a one-component order parameter.

We investigate the critical behavior of the entanglement transition induced by projective measurements in (Haar) random unitary quantum circuits. Using a replica approach, we map the calculation of the entanglement entropies in such circuits onto a two-dimensional statistical-mechanics model. In this language, the area-to volume-law entanglement transition can be interpreted as an ordering transition in the statistical-mechanics model. We derive the general scaling properties of the entanglement entropies and mutual information near the transition using conformal invariance.