Electrons in two-dimensional semiconductor moiré materials are more delocalized around the lattice sites than those in conventional solids1,2. The non-local contributions to the magnetic interactions can therefore be as important as the Anderson superexchange3, which makes the materials a unique platform to study the effects of competing magnetic interactions3,4. Here we report evidence of strongly frustrated magnetic interactions in a Wigner–Mott insulator at a two-thirds (2/3) filling of the moiré lattice in angle-aligned WSe2/WS2 bilayers.

Models for nonunitary quantum dynamics, such as quantum circuits that include projective measurements, have recently been shown to exhibit rich quantum critical behavior. There are many complementary perspectives on this behavior. For example, there is a known correspondence between d-dimensional local nonunitary quantum circuits and tensor networks on a [D=(d+1)]-dimensional lattice.

The semiclassical description of two-dimensional (2d) metals based on the quasiparticle picture suggests that there is a universal threshold of the resistivity: the resistivity of a 2d metal is bounded by the so called Mott-Ioffe-Regal (MIR) limit, which is at the order of h/e2. If a system remains metallic while its resistivity is beyond the MIR limit, it is referred to as a "bad metal", which challenges our theoretical understanding as the very notion of quasiparticles is invalidated.

Supersymmetry has been studied at a linear level between normal modes of metamaterials described by rigidity matrices and non-interacting quantum Hamiltonians. The connection between classical and quantum was made through the matrices involved in each problem. Recently, insight into the behavior of nonlinear mechanical systems was found by defining topological indices via the Poincaré-Hopf index. It turns out, because of the mathematical similarity, this topological index shows a way to approach supersymmetric quantum theory from classical mechanics.

It has been proposed that an extended version of the Hubbard model which potentially hosts rich correlated physics may be well simulated by the transition metal dichalcogenide (TMD) moiré heterostructures. Motivated by recent reports of continuous metal-insulator transition (MIT) at half filling, as well as correlated insulators at various fractional fillings in TMD moiré heterostructures, we propose a theory for the potentially continuous MIT with fractionalized electric charges.

We study the gauging of a global U(1) symmetry in a gapped system in (2+1)d. The gauging procedure has been well-understood for a finite global symmetry group, which leads to a new gapped phase with emergent gauge structure and can be described algebraically using the mathematical framework of modular tensor category (MTC). We develop a categorical description of U(1) gauging in a MTC, taking into account the dynamics of U(1) gauge field absent in the finite group case.

We investigate a family of invertible phases of matter with higher-dimensional exotic excitations in even spacetime dimensions, which includes and generalizes the Kitaev’s chain in 1+1d. The excitation has Z2 higher-form symmetry that mixes with the spacetime Lorentz symmetry to form a higher group spacetime symmetry. We focus on the invertible exotic loop topological phase in 3+1d.

We investigate the behavior of higher-form symmetries at various quantum phase transitions. We consider discrete 1-form symmetries, which can be either part of the generalized concept “categorical symmetry" (labelled as Z-N(1)) introduced recently, or an explicit Z(1) 1-form symmetry.

Many advancements have been made in the field of topological mechanics. The majority of the work, however, concerns the topological invariant in a linear theory. In this Letter, we present a generic prescription to define topological indices that accommodates nonlinear effects in mechanical systems without taking any approximation. Invoking the tools of differential geometry, a Z-valued quantity in terms of a topological index in differential geometry known as the Poincaré-Hopf index, which features the topological invariant of nonlinear zero modes (ZMs), is predicted.