This paper reviews progress on the fractional quantum Hall effect (FQHE) based what we term Hamiltonian theories, i.e., theories that proceed from microscopic electronic to final solution via a sequence of transformations and approximations, in either or path-integral approach, as compared with exact diagonalization trial wave functions. The authors focus Chern-Simons which electrons are converted fermions bosons carry along flux tubes, their own extended theory, paired pseudovortices form...

We synthesize and study single crystals of a new double-perovskite ${\mathrm{Sr}}_{2}{\mathrm{YIrO}}_{6}$. Despite two strongly unfavorable conditions for magnetic order, namely, pentavalent ${\mathrm{Ir}}^{5+}(5{d}^{4})$ ions which are anticipated to have ${J}_{\text{eff}}=0$ singlet ground states in the strong spin-orbit coupling (SOC) limit geometric frustration face-centered cubic structure formed by ${\mathrm{Ir}}^{5+}$ ions, we observe this iridate undergo novel transition at...

We study a d=2 Ising model where the veritcal bonds are fixed and ferromagnetic horizontal can vary randomly in sign magnitude (within some limits) but same within each now. The therefore generalizes that of McCoy Wu since it allows for interesting case frustration. use transfer matrix to map our problem collection random field d=1 problems about which lot is known. find generally three transitions: Griffiths transition, its dual version, one with infinite correlation length index...

We present a Chern-Simons theory of the fractional quantum Hall effect in which flux attachment is followed by transformation that effectively attaches correlation holes. extract correlated wavefunctions, compute drift and cyclotron currents (due to inhomogeneous density), exhibit Read operator, operators create quasi-particles show how bare kinetic energy can get quenched replaced one due interactions. find for $\nu =1/2$ low has neutral quasiparticles give effective hamiltonian constraints.

We study the ground state of hard-core bosons with nearest-neighbor hopping and interactions on triangular Kagom\'e lattices by mapping to a system spins ($S={1\over2}$), which we analyze using spin-wave theory. find that both display superfluid supersolid (a coexistence solid) order as parameters filling are varied. Quantum fluctuations seem large enough in raise interesting possibility disordered state.

We revisit the effect of local interactions on quadratic band touching (QBT) Bernal honeycomb bilayer model using renormalization group (RG) arguments and quantum Monte Carlo (QMC) simulations. present a RG argument which predicts, contrary to previous studies, that weak do not flow strong coupling even if free dispersion has QBT. Instead, they generate linear term in dispersion, causes back coupling. Consistent with this scenario, unbiased QMC simulations Hubbard we find compelling evidence...

We report the successful synthesis of single crystals layered iridate (Na${}_{1\ensuremath{-}x}$Li${}_{x}$)${}_{2}$IrO${}_{3}$, $0\ensuremath{\le}x\ensuremath{\le}0.9$, and a thorough study its structural, magnetic, thermal, transport properties. This compound allows controlled interpolation between Na${}_{2}$IrO${}_{3}$ Li${}_{2}$IrO${}_{3}$, while maintaining quantum magnetism honeycomb Ir${}^{4+}$ planes. The measured phase diagram demonstrates suppression N\'eel temperature ${T}_{N}$ at...

Motivated by experimental studies of graphene in the quantum Hall regime, we revisit phase diagram a single sheet at charge neutrality. Because spin and valley degeneracies, interactions play crucial role determining nature ground state. We show that, generically within Hartree-Fock approximation, regime interest there is region coexistence between magnetic bond orders diagram. demonstrate this result both continuum lattice models, argue that naturally provides possible explanation for...

Monolayer graphene at charge neutrality in a quantizing magnetic field is quantum Hall ferromagnet. Due to the spin and valley (near) degeneracies, there plethora of possible ground states. Previous theoretical work, based on stringent ultra short-range assumption symmetry-allowed interactions, predicts phase diagram with distinct regions spin-polarized, canted antiferromagnetic, inter-valley coherent, density wave order. While early experiments suggested that system was antiferromagnetic...

At and near charge neutrality, monolayer graphene in a perpendicular magnetic field is quantum Hall ferromagnet. In addition to the highly symmetric Coulomb interaction, residual lattice-scale interactions, Zeeman, sublattice couplings determine fate of ground state. Going beyond simplest model with ultra-short-range more generic couplings, one finds integer phases that show coexistence lattice order parameters. Here, we fractional states vicinity neutrality have even richer phase diagrams,...

There is convincing numerical evidence that fractional quantum Hall (FQH)-like ground states arise in fractionally filled Chern bands (FCB). Here we show the Hamiltonian theory of Composite Fermions (CF) can be as useful describing FCB it was FQHE continuum. We are able to introduce CFs into problem even though there no external magnetic field by following a two-stage process. First construct an algebraically exact mapping which expresses electron density projected band, ${\rho}_{{\tiny...

We demonstrate that in the presence of Coulomb interactions, electrons graphene behave like a critical system, supporting power law correlations with interaction-dependent exponents. An asymptotic analysis shows origin this behavior lies particle-hole scattering, for which interaction induces anomalously close approaches. With increasing strength relevant changes from real to complex, leading an unusual instability characterized by complex-valued susceptibility thermodynamic limit....

Inspired by the recently proposed Dirac composite fermion picture for half-filled Landau level authors extend previously developed Hamiltonian formalism to incorporate considerations of particle-hole symmetry. They show that magnetic translation algebra can be represented in enlarged space fermions, with symmetry manifestly defined. A Hartree-Fock approximation then leads a Fermi liquid fermions.

A three-dimensional lattice of Heisenberg spins with nearest-neighbor interactions is studied by numerical simulation under the constraint that no free topological singularities (hedgehogs) are allowed. Only pairs oppositely charged hedgehogs permitted in sum over configurations. disordering transition exponents different from usual found and tentatively identified as a pure spin wave transition.

Three-dimensional Weyl semimetals have pairs of topologically protected nodes whose projections onto the surface Brillouin zone are end points zero-energy states called Fermi arcs. At endpoints arcs, extend into and hybridized with bulk. Here, we consider a two-dimensional junction two identical surfaces twisted respect to each other tunnel coupled. Confining ourselves commensurate angles (such that larger unit cell preserves reduced translation symmetry at interface) enables us analyze...

Recent experiments on quantum Hall bilayers near total filling factor 1 have demonstrated that they support an imperfect two-dimensional superfluidity, in which there is nearly dissipationless transport at nonvanishing temperature observed both counterflow resistance and interlayer tunneling. We argue this behavior may be understood terms of a coherence network induced the bilayer by disorder, incompressible, coherent state exists narrow regions separating puddles dense vortex-antivortex...

We consider $C{P}^{N\ensuremath{-}1}$ models in $d+1$ dimensions around Lifshitz fixed points with dynamical critical exponent $z$, the large-$N$ expansion. It is shown that these are asymptotically free and dynamically generate a mass for fields all $d=z$. demonstrate that, $z=d=2$, initially nondynamical gauge field acquires kinetic terms way similar to usual $1+1$ dimensions. Lorentz invariance emerges generically low-energy electrodynamics, nontrivial dielectric constant given by inverse...

This article demonstrates the profound reconstruction of Fermi arcs at an interface between surfaces two Weyl semimetals, which exhibits a strong dependence on relative twist angle them. Most prominently, as this passes through special ``arcless angles'', loops states with no connection to bulk appear in moir\'e Brillouin zone. Such have interesting resonance signatures optical conductivity system magnetic field perpendicular interface.

Bilayer graphene exhibits a rich phase diagram in the quantum Hall regime, arising from multitude of internal degrees freedom, including spin, valley, and orbital indices. The variety fractional states between filling factors $1 < \nu \leq 2$ suggests, among other things, transition valley-unpolarized polarized at perpendicular electric field $D^{*}$. We find behavior $D^{*}$ with $\nu$ changes markedly as $B$ is reduced. At $\nu = 2$, may even vanish when sufficiently small. present...