Fractionalized gapless quantum vortex liquids

The standard theoretical approach to gapless spin liquid phases of two-dimensional frustrated quantum antiferromagnets invokes the concept of fermionic slave particles into which the spin fractionalizes. As an alternate we explore different kinds of gapless spin liquid phases in frustrated quantum magnets with XY anisotropy where the vortex of the spin fractionalizes into gapless itinerant fermions. The resulting gapless fractionalized vortex liquid phases are studied within a slave particle framework that is dual to the usual one. We demonstrate the stability of some such phases and describe their properties. We give an explicit construction in an XY-spin-1 system on triangular lattice, and interpret it as a critical phase in the vicinity of spin-nematic states.National Science Foundation (U.S.) (DMR-1305741

Composite fermion duality for half-filled multicomponent Landau levels

We study the interplay of particle-hole symmetry and fermion-vortex duality in multicomponent half-filled Landau levels, such as quantum Hall gallium arsenide bilayers and graphene. For the ν=1/2+1/2 bilayer, we show that particle-hole-symmetric interlayer Cooper pairing of composite fermions leads to precisely the same phase as the electron exciton condensate realized in experiments. This equivalence is easily understood by applying the recent Dirac fermion formulation of ν=1/2 to two components. It can also be described by Halperin-Lee-Read composite fermions undergoing interlayer p[subscript x]+ip[subscript y] pairing. A renormalization group analysis showing strong instability to interlayer pairing at large separation d→∞ demonstrates that two initially decoupled composite Fermi liquids can be smoothly tuned into the conventional bilayer exciton condensate without encountering a phase transition. We also discuss multicomponent systems relevant to graphene, derive related phases including a Z[subscript 2] gauge theory with spin-half visons, and argue for symmetry-enforced gaplessness under full SU(N[subscript f]) flavor symmetry when the number of components N[subscript f] is even.MIT Department of Physics Pappalardo ProgramUnited States. Dept. of Energy (Grant DE-SC0008739)Simons Foundation (Simons Investigator Award

Nearly flat Chern bands in moiré superlattices

Topology and electron interactions are two central themes in modern condensed matter physics. Here, we propose graphene-based systems where both the band topology and interaction effects can be simply controlled with electric fields. We study a number of systems of twisted double layers with small twist angle where a moiré superlattice is formed. Each layer is chosen to be either AB-stacked bilayer graphene, ABC-stacked trilayer graphene, or hexagonal boron nitride. In these systems, a vertical applied electric field enables control of the bandwidth, and interestingly also the Chern number. We find that the Chern numbers of the bands associated with each of the two microscopic valleys can be ±0,±1,±2,±3 depending on the specific system and vertical electrical field. We show that these graphene moiré superlattices are promising platforms to realize a number of fascinating many-body phenomena, including (fractional) quantum anomalous Hall effects. We also discuss conceptual similarities and implications for modeling twisted bilayer graphene systems.National Science Foundation (U.S.) (Grant DMR-1608505)Simons Foundation (Simons Investigator Award)Gordon and Betty Moore Foundation (Grant GBMF4541)STC Center for Integrated Quantum Materials (Grant DMR-1231319

Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids

Non UBCUnreviewedAuthor affiliation: Massachusetts Institute of TechnologyFacult

Statistical Mechanics

8.333 is the first course in a two-semester sequence on statistical mechanics. Basic principles are examined in 8.333: the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Postulates of classical statistical mechanics, micro canonical, canonical, and grand canonical distributions; applications to lattice vibrations, ideal gas, photon gas. Quantum statistical mechanics; Fermi and Bose systems. Interacting systems: cluster expansions, van der Waal's gas, and mean-field theory

Quantum phase transition from an antiferromagnet to a spin liquid in a metal

We study quantum phase transitions from easy-plane antiferromagnetic metals to paramagnetic metals in Kondo-Heisenberg lattice systems. If the paramagnetic metal is a fractionalized Fermi liquid then the universal critical properties of the phase transition are unaffected for a weak Kondo coupling even when the Fermi surface intersects the magnetic zone boundary. This is in striking contrast to the conventional theory of phase transitions between paramagnetic and antiferromagnetic metals where any Kondo coupling is strongly relevant, and leads to a Landau-damped “Hertz-Millis” theory. The electron quasiparticle remains well defined in the quantum critical regime and the critical spin fluctuations only contribute subleading corrections to the various properties of conduction electrons.National Science Foundation (Grant No. DMR-0705255

Integer Quantum Hall Effect for Bosons

A simple physical realization of an integer quantum Hall state of interacting two dimensional bosons is provided. This is an example of a symmetry-protected topological (SPT) phase which is a generalization of the concept of topological insulators to systems of interacting bosons or fermions. Universal physical properties of the boson integer quantum Hall state are described and shown to correspond with those expected from general classifications of SPT phases.National Science Foundation (U.S.) (Grant DMR-1005434