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.

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.

We derive the general continuum model for a bilayer system of staggered-flux square lattices, with arbitrary elastic deformation in each layer. Applying this general continuum model to the case where the two layers are rigidly rotated relative to each other by a small angle, we obtain the band structure of the twisted bilayer staggered-flux square lattice. We show that this band structure exhibits a magic continuum in the sense that an exponential reduction of the Dirac velocity and bandwidths occurs in a large parameter regime.

We consider quantum many body systems with generalized symmetries, such as the higher form symmetries introduced recently, and the 'tensor symmetry'. We consider a general form of lattice Hamiltonians which allow a certain level of nonlocality. Based on the assumption of dual generalized symmetries, we explicitly construct low energy excited states. We also derive the 't Hooft anomaly for the general Hamiltonians after 'gauging' the dual generalized symmetries.