Electron interactions in graphene in a strong magnetic field

Graphene in the quantum Hall regime exhibits a multi-component structure due to the electronic spin and chirality degrees of freedom. While the applied field breaks the spin symmetry explicitly, we show that the fate of the chirality SU(2) symmetry is more involved: the leading symmetry-breaking terms differ in origin when the Hamiltonian is projected onto the central (n=0) rather than any of the other Landau levels. Our description at the lattice level leads to a Harper equation; in its continuum limit, the ratio of lattice constant a and magnetic length l_B assumes the role of a small control parameter in different guises. The leading symmetry-breaking terms are direct (n=0) and exchange (n different from 0) terms, which are algebraically small in a/l_B. We comment on the Haldane pseudopotentials for graphene, and evaluate the easy-plane anisotropy of the graphene ferromagnet.Comment: 4 pages, 1 figure; revised version contains a more detailed comparison with experimental results; accepted for publication in PR

Analysis of the long-range random field quantum antiferromagnetic Ising model

We introduce a solvable quantum antiferromagnetic model. The model, with Ising spins in a transverse field, has infinite range antiferromagnetic interactions with random fields on each site, following an arbitrary distribution. As is well-known, frustration in the random field Ising model gives rise to a many-valley structure in the spin-configuration space. In addition, the antiferromagnetism also induces a regular frustration even for the ground state. In this paper, we investigate analytically the critical phenomena in the model, having both randomness and frustration and we report some analytical results for it.Comment: 18 pages, 5 figures, Euro. Phys. J B (to be published

Doping a topological quantum spin liquid: slow holes in the Kitaev honeycomb model

We present a controlled microscopic study of mobile holes in the spatially anisotropic (Abelian) gapped phase of the Kitaev honeycomb model. We address the properties of (i) a single hole [its internal degrees of freedom as well as its hopping properties]; (ii) a pair of holes [their (relative) particle statistics and interactions]; (iii) the collective state for a finite density of holes. We find that each hole in the doped model has an eight-dimensional internal space, characterized by three internal quantum numbers: the first two "fractional" quantum numbers describe the binding to the hole of the fractional excitations (fluxes and fermions) of the undoped model, while the third "spin" quantum number determines the local magnetization around the hole. The fractional quantum numbers also encode fundamentally distinct particle properties, topologically robust against small local perturbations: some holes are free to hop in two dimensions, while others are confined to hop in one dimension only; distinct hole types have different particle statistics, and in particular, some of them exhibit non-trivial (anyonic) relative statistics. These particle properties in turn determine the physical properties of the multi-hole ground state at finite doping, and we identify two distinct ground states with different hole types that are stable for different model parameters. The respective hopping dimensionalities manifest themselves in an electrical conductivity approximately isotropic in one ground state and extremely anisotropic in the other one. We also compare our microscopic study with related mean-field treatments, and discuss the main discrepancies between the two approaches, which in particular involve the possibility of binding fractional excitations as well as the particle statistics of the holes.Comment: 29 pages, 14 figures, published version with infinitesimal change

Quantum spin liquids: a large-S route

This paper explores the large-S route to quantum disorder in the Heisenberg antiferromagnet on the pyrochlore lattice and its homologues in lower dimensions. It is shown that zero-point fluctuations of spins shape up a valence-bond solid at low temperatures for one two-dimensional lattice and a liquid with very short-range valence-bond correlations for another. A one-dimensional model demonstrates potential significance of quantum interference effects (as in Haldane's gap): the quantum melting of a valence-bond order yields different valence-bond liquids for integer and half-integer values of S.Comment: Proceedings of Highly Frustrated Magnetism 2003 (Grenoble), 6 LaTeX page

Adiabaticity enhancement in the classical transverse field Ising chain, and its effective non-Hermitian description

We analyse the near-adiabatic dynamics in a ramp through the critical point (CP) of the classical transverse field Ising chain. This is motivated, conceptually, by the fact that this CP -- unlike its quantum counterpart -- experiences no thermal or quantum fluctuations, and technically by the tractability of its effective model. For a `half-ramp' from ferromagnet to CP, the longitudinal and transverse magnetization scale as $\tau^{-1/3}$ and $\tau^{-2/3}$, respectively, with $1/\tau$ the ramp rate, in accord with Kibble-Zurek theory. For ferro- to paramagnetic ramps across the CP, however, they stay closer, $\tau^{-1/2}$ and $\tau^{-1}$, to adiabaticity. This adiabaticity enhancement compared to the half ramp is understood by casting the dynamics in the paramagnet in the form of a non-hermitian Dirac Hamiltonian, with the CP playing the role of an exceptional point, opening an additional decay channel.Comment: 6 pages, 3 figure

Multicolored quantum dimer models, resonating valence-bond states, color visons, and the triangular-lattice t_2g spin-orbital system

The spin-orbital model for triply degenerate t_2g electrons on a triangular lattice has been shown to be dominated by dimers: the phase diagram contains both strongly resonating, compound spin-orbital dimer states and quasi-static, spin-singlet valence-bond (VB) states. To elucidate the nature of the true ground state in these different regimes, the model is mapped to a number of quantum dimer models (QDMs), each of which has three dimer colors. The generic multicolored QDM, illustrated for the two- and three-color cases, possesses a topological color structure, "color vison" excitations, and broad regions of resonating VB phases. The specific models are analyzed to gain further insight into the likely ground states in the superexchange and direct-exchange limits of the electronic Hamiltonian, and suggest a strong tendency towards VB order in all cases.Comment: 16 pages, 12 figure

Quantum spin liquid at finite temperature: proximate dynamics and persistent typicality

Quantum spin liquids are long-range entangled states of matter with emergent gauge fields and fractionalized excitations. While candidate materials, such as the Kitaev honeycomb ruthenate $\alpha$-RuCl$_3$, show magnetic order at low temperatures $T$, here we demonstrate numerically a dynamical crossover from magnon-like behavior at low $T$ and frequencies $\omega$ to long-lived fractionalized fermionic quasiparticles at higher $T$ and $\omega$. This crossover is akin to the presence of spinon continua in quasi-1D spin chains. It is further shown to go hand in hand with persistent typicality down to very low $T$. This aspect, which has also been observed in the spin-1/2 kagome Heisenberg antiferromagnet, is a signature of proximate spin liquidity and emergent gauge degrees of freedom more generally, and can be the basis for the numerical study of many finite-$T$ properties of putative spin liquids.Comment: 13 pages, 11 figures, accepted versio

Classical generalized constant coupling model for geometrically frustrated antiferromagnets

A generalized constant coupling approximation for classical geometrically frustrated antiferromagnets is presented. Starting from a frustrated unit we introduce the interactions with the surrounding units in terms of an internal effective field which is fixed by a self consistency condition. Results for the magnetic susceptibility and specific heat are compared with Monte Carlo data for the classical Heisenberg model for the pyrochlore and kagome lattices. The predictions for the susceptibility are found to be essentially exact, and the corresponding predictions for the specific heat are found to be in very good agreement with the Monte Carlo results.Comment: 4 pages, 3 figures, 2 columns. Discussion about the zero T value of the pyrochlore specific heat correcte