Fracton Self-Statistics.

Fracton order describes novel quantum phases of matter that host quasiparticles with restricted mobility and, thus, lies beyond the existing paradigm of topological order. In particular, excitations that cannot move without creating multiple excitations are called fractons. Here, we address a fundamental open question-can the notion of self-exchange statistics be naturally defined for fractons, given their complete immobility as isolated excitations? Surprisingly, we demonstrate how fractons can be exchanged and show that their self-statistics is a key part of the characterization of fracton orders.

Fractons from Vector Gauge Theory.

Motivated by the prediction of fractonic topological defects in a quantum crystal, we utilize a reformulated elasticity duality to derive a description of a fracton phase in terms of coupled vector U(1) gauge theories. The fracton order and restricted mobility emerge as a result of an unusual Gauss law where electric field lines of one gauge field act as sources of charge for others. At low energies this vector gauge theory reduces to the previously studied fractonic symmetric tensor gauge theory.

Topological states from topological crystals.

We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry-protected topological states can be adiabatically deformed into a special class of states we call topological crystals. A topological crystal in, for example, three dimensions is a real-space assembly of finite-sized pieces of topological states in one and two dimensions protected by the local symmetry group alone, arranged in a configuration invariant under the spatial group and glued together such that there is no open edge or end.

Hallmarks of the Mott-metal crossover in the hole-doped pseudospin-1/2 Mott insulator Sr2IrO4.

The physics of doped Mott insulators remains controversial after decades of active research, hindered by the interplay among competing orders and fluctuations. It is thus highly desired to distinguish the intrinsic characters of the Mott-metal crossover from those of other origins. Here we investigate the evolution of electronic structure and dynamics of the hole-doped pseudospin-1/2 Mott insulator Sr2IrO4.

Quantum spin ices and topological phases from dipolar-octupolar doublets on the pyrochlore lattice.

We consider a class of d- and f-electron systems in which dipolar-octupolar Kramers doublets arise on the sites of the pyrochlore lattice. For such doublets, two components of the pseudospin transform like a magnetic dipole, while the other transforms like a component of the magnetic octupole tensor. Based on a symmetry analysis, we construct and study models of dipolar-octupolar doublets in itinerant and localized limits.

Mott insulators of ultracold fermionic alkaline Earth atoms: underconstrained magnetism and chiral spin liquid.

We study Mott insulators of fermionic alkaline earth atoms, described by Heisenberg spin models with enhanced SU(N) symmetry. In dramatic contrast to SU(2) magnetism, more than two spins are required to form a singlet. On the square lattice, the classical ground state is highly degenerate and magnetic order is thus unlikely.

Projected-wave-function study of the spin-1/2 Heisenberg model on the Kagomé lattice.

We perform a Gutzwiller projected-wave-function study for the spin-1/2 Heisenberg model on the Kagomé lattice to compare energies of several spin-liquid states. The result indicates that a U(1)-Dirac spin-liquid state has the lowest energy. Furthermore, even without variational parameters, the energy turns out to be very close to that found by exact diagonalization.