We develop a bosonization scheme for the two-dimensional electron gas in the presence of an uniform magnetic field perpendicular to the two-dimensional system when the filling factor \nu = 1. We show that the elementary neutral excitations of this system, known as magnetic excitons, can be treated approximately as bosons and we apply the method to the interacting system. We show that the Hamiltonian of the fermionic system is mapped into an interacting bosonic Hamiltonian, where the dispersion relation of the bosons agrees with previous RPA calculations. The interaction term accounts for the formation of two-boson bound states. We discuss a possible relation between these excitations and the skyrmion-antiskyrmion pair, in analogy with the ferromagnetic Heisenberg model. Finally, we analyze the semiclassical limit of the interacting bosonic Hamiltonian and show that the results are in agreement with those derived from the model of Sondhi {\it et al.} for the quantum Hall skyrmion.Comment: Revised version, new figure

In certain Mott-insulating dimerized antiferromagnets, triplet excitations of the paramagnetic phase display both three-particle and four-particle interactions. When such a magnet undergoes a quantum phase transition into a magnetically ordered state, the three-particle interaction becomes part of the critical theory provided that the lattice ordering wave vector is zero. One microscopic example is the staggered-dimer antiferromagnet on the square lattice, for which deviations from O(3) universality have been reported in numerical studies. Using both symmetry arguments and microscopic calculations, we show that a nontrivial cubic term arises in the relevant order-parameter quantum field theory, and we assess its consequences using a combination of analytical and numerical methods. We also present finite-temperature quantum Monte Carlo data for the staggered-dimer antiferromagnet which complement recently published results. The data can be consistently interpreted in terms of critical exponents identical to that of the standard O(3) universality class, but with anomalously large corrections to scaling. We argue that the cubic interaction of critical triplons, although irrelevant in two spatial dimensions, is responsible for the leading corrections to scaling due to its small scaling dimension.

We study the flat-band ferromagnetic phase of a topological Hubbard model within a bosonization formalism and, in particular, determine the spin-wave excitation spectrum. We consider a square lattice Hubbard model at 1/4-filling whose free-electron term is the π-flux model with topologically nontrivial and nearly flat energy bands. The electron spin is introduced such that the model either explicitly breaks time-reversal symmetry (correlated flat-band Chern insulator) or is invariant under time-reversal symmetry (correlated flat-band Z2 topological insulator). We generalize for flat-band Chern and topological insulators the bosonization formalism [Phys. Rev. B 71, 045339 (2005)] previously developed for the two-dimensional electron gas in a uniform and perpendicular magnetic field at filling factor ν = 1. We show that, within the bosonization scheme, the topological Hubbard model is mapped into an effective interacting boson model. We consider the boson model at the harmonic approximation and show that, for the correlated Chern insulator, the spin-wave excitation spectrum is gapless while, for the correlated topological insulator, gapped. We briefly comment on the possible effects of the boson-boson (spin-wave-spin-wave) coupling.

We study the plaquette valence-bond solid phase of the spin-1/2 J1-J2 antiferromagnet Heisenberg model on the square lattice within the bond-operator theory. We start by considering four S = 1/2 spins on a single plaquette and determine the bond operator representation for the spin operators in terms of singlet, triplet, and quintet boson operators. The formalism is then applied to the J1-J2 model and an effective interacting boson model in terms of singlets and triplets is derived. The effective model is analyzed within the harmonic approximation and the previous results of Zhitomirsky and Ueda [Phys. Rev. B 54, 9007 (1996)] are recovered. By perturbatively including cubic (triplet-triplet-triplet and singlet-triplet-triplet) and quartic interactions, we find that the plaquette valence-bond solid phase is stable within the parameter region 0.34 < J2/J1 < 0.59, which is narrower than the harmonic one. Differently from the harmonic approximation, the excitation gap vanishes at both critical couplings J2 = 0.34 J1 and J2 = 0.59 J1. Interestingly, for J2 < 0.48 J1, the excitation gap corresponds to a singlet-triplet excitation at the Γ point while, for J2 > 0.48 J1, it is related to a singlet-singlet excitation at the X = (π/2, 0) point of the tetramerized Brillouin zone.

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We develop a non-perturbative bosonization approach for bilayer quantum Hall systems at νT = 1, which allows us to systematically study the existence of an exciton condensate in these systems. An effective boson model is derived and the excitation spectrum is calculated both in the Bogoliubov and in the Popov approximations. In the latter case, we show that the ground state of the system is an exciton condensate only when the distance between the layers is very small compared to the magnetic length, indicating that the system possibly undergoes another phase transition before the incompressible-compressible one. The effect of a finite electron interlayer tunnelling is included and a quantitative phase diagram is proposed.

Motivated by experiments on nonmagnetic triangular-lattice Mott insulators, we study one candidate paramagnetic phase, namely the columnar dimer (or valence-bond) phase. We apply variants of the bond-operator theory to a dimerized and spatially anisotropic spin-1/2 Heisenberg model and determine its zero-temperature phase diagram and the spectrum of elementary triplet excitations (triplons). Depending on model parameters, we find that the minimum of the triplon energy is located at either a commensurate or an incommensurate wave vector. Condensation of triplons at this commensurate-incommensurate transition defines a quantum Lifshitz point, with effective dimensional reduction that possibly leads to nontrivial paramagnetic (e.g., spin-liquid) states near the closing of the triplet gap. We also discuss the two-particle decay of high-energy triplons, and we comment on the relevance of our results for the organic Mott insulator EtMe 3 P[Pd(dmit) 2 ] 2 .

We study the quantum Hall effect in graphene at filling factors = 0 and = ± 1, concentrating on the quantum Hall ferromagnetic regime, within a nonperturbative bosonization formalism. We start by developing a bosonization scheme for electrons with two discrete degrees of freedom ͑spin-1 / 2 and pseudospin-1 / 2͒ restricted to the lowest Landau level. Three distinct phases are considered, namely, the so-called spinpseudospin, spin, and pseudospin phases. The first corresponds to a quarter-filled ͑ =−1͒ lowest Landau level, while the others to a half-filled ͑ =0͒ lowest Landau level. In each case, we show that the elementary neutral excitations can be treated approximately as a set of n-independent kinds of boson excitations. The boson representations of the projected electron density, the spin, pseudospin, and mixed spin-pseudospin density operators are derived. We then apply the developed formalism to the effective continuous model, which includes SU͑4͒ symmetry breaking terms, recently proposed by Alicea and Fisher ͓Phys. Rev. B 74, 075422 ͑2006͔͒. For each quantum Hall state, an effective interacting boson model is derived and the dispersion relations of the elementary excitations are analytically calculated. We propose that the charged excitations ͑quantum Hall skyrmions͒ can be described as a coherent state of bosons. We calculate the semiclassical limit of the boson model derived from the SU͑4͒ invariant part of the original fermionic Hamiltonian and show that it agrees with the results of Arovas et al. ͓Phy. Rev. B 59, 13147 ͑1999͔͒ for SU͑N͒ quantum Hall skyrmions. We briefly discuss the influence of the SU͑4͒ symmetry breaking terms in the skyrmion energy.