Vacancies in Generic Kitaev Spin Liquids.

The Kitaev honeycomb model supports gapless and gapped quantum spin liquid phases. Its exact solvability relies on extensively many locally conserved quantities. Any real-world manifestation of these phases would include imperfections in the form of disorder and interactions that break integrability.

Identifying the ν=5/2 Topological Order through Charge Transport Measurements.

We propose an experiment to identify the topological order of the ν=5/2 state through a measurement of the electric conductance of a mesoscopic device. Our setup is based on interfacing ν=2,5/2, and 3 in the same device. Its conductance can unambiguously establish or rule out the particle-hole symmetric Pfaffian topological order, which is supported by recent thermal measurements.

Temperature Enhancement of Thermal Hall Conductance Quantization.

The quest for non-Abelian quasiparticles has inspired decades of experimental and theoretical efforts, where the scarcity of direct probes poses a key challenge. Among their clearest signatures is a thermal Hall conductance with quantized half-integer value in units of κ_{0}=π^{2}k_{B}^{2}T/3h (T is temperature, h the Planck constant, k_{B} the Boltzmann constant). Such values were recently observed in a quantum-Hall system and a magnetic insulator.

Time-Crystalline Topological Superconductors.

Time crystals form when arbitrary physical states of a periodically driven system spontaneously break discrete time-translation symmetry. We introduce one-dimensional time-crystalline topological superconductors, for which time-translation symmetry breaking and topological physics intertwine-yielding anomalous Floquet Majorana modes that are not possible in free-fermion systems. Such a phase exhibits a bulk magnetization that returns to its original form after two drive periods, together with Majorana end modes that recover their initial form only after four drive periods.

Theory of Disorder-Induced Half-Integer Thermal Hall Conductance.

The thermal Hall conductance in the half-filled first Landau level was recently measured to take the quantized noninteger value κ_{xy}=5/2 (in units of temperature times π^{2}k_{B}^{2}/3h), which indicates a non-Abelian phase of matter. Such exotic states have long been predicted to arise at this filling factor, but the measured value disagrees with numerical studies, which predict κ_{xy}=3/2 or 7/2. We resolve this contradiction by invoking the disorder-induced formation of mesoscopic puddles with locally κ_{xy}=3/2 or 7/2.

Bosonic Analogue of Dirac Composite Fermi Liquid.

We introduce a particle-hole-symmetric metallic state of bosons in a magnetic field at odd-integer filling. This state hosts composite fermions whose energy dispersion features a quadratic band touching and corresponding 2π Berry flux protected by particle-hole and discrete rotation symmetries. We also construct an alternative particle-hole symmetric state-distinct in the presence of inversion symmetry-without Berry flux.

Explicit Derivation of Duality between a Free Dirac Cone and Quantum Electrodynamics in (2+1) Dimensions.

We explicitly derive the duality between a free electronic Dirac cone and quantum electrodynamics in (2+1) dimensions (QED_{3}) with N=1 fermion flavors. The duality proceeds via an exact, nonlocal mapping from electrons to dual fermions with long-range interactions encoded by an emergent gauge field. This mapping allows us to construct parent Hamiltonians for exotic topological-insulator surface phases, derive the particle-hole-symmetric field theory of a half-filled Landau level, and nontrivially constrain QED_{3} scaling dimensions.

Anomalous Quasiparticle Symmetries and Non-Abelian Defects on Symmetrically Gapped Surfaces of Weak Topological Insulators.

We show that boundaries of 3D weak topological insulators can become gapped by strong interactions while preserving all symmetries, leading to Abelian surface topological order. The anomalous nature of weak topological insulator surfaces manifests itself in a nontrivial action of symmetries on the quasiparticles; most strikingly, translations change the anyon types in a manner impossible in strictly 2D systems with the same symmetry. As a further consequence, screw dislocations form non-Abelian defects that trap Z_{4} parafermion zero modes.

Theory of a continuous stripe melting transition in a two-dimensional metal: a possible application to cuprate superconductors.

We construct a theory of continuous stripe melting quantum phase transitions in two-dimensional metals and the associated Fermi surface reconstruction. Such phase transitions are strongly coupled but yet theoretically tractable in situations where the stripe ordering is destroyed by proliferating doubled dislocations of the charge stripe order. The resulting non-Landau quantum critical point has strong stripe fluctuations which we show decouple dynamically from the Fermi surface even though static stripe ordering reconstructs the Fermi surface.