M. D. Grynberg

From classical to quantum Kagomé antiferromagnet in a magnetic field

We study the magnetic properties of the Kagome antiferromagnet going from the classical limit to the deep quantum regime of spin ½ systems. In all the cases there are special values for the magnetization, 1/3 in particular, in which a singular behavior is observed to occur in both the classical and quantum cases. We show clear evidence for a magnetization plateau for all S, in a wide range of XXZ anisotropies and for the occurrence of quantum order by disorder effects.

GROUND-STATE MAGNETIZATION OF POLYMERIZED SPIN CHAINS

We investigate the ground-state magnetization plateaus appearing in spin-1/2 polymerized Heisenberg chains under external magnetic fields. The associated fractional quantization scenario and the exponents which characterize the opening of gapful excitations are analyzed by means of Abelian bosonization methods. Our conclusions are fully supported by the extrapolated results obtained from Lanczos diagonalizations of finite systems.

Directed diffusion of reconstituting dimers

We discuss the dynamical aspects of an asymmetric version of assisted diffusion of hard core particles on a ring studied by Menon et al (1997 J. Stat. Phys. 86 1237). The asymmetry brings in phenomena like kinematic waves and effects of the Kardar-Parisi-Zhang non-linearity, which combine with the feature of strongly broken ergodicity, a characteristic of the model. A central role is played by a single non-local invariant, the irreducible string, whose interplay with the driven motion of reconstituting dimers, arising from the assisted hopping, determines the asymptotic dynamics and scaling regimes. These are investigated both analytically and numerically through sector-dependent mappings to the asymmetric simple exclusion process.

Quasi-periodic spin chains in a magnetic field

We study the interplay between a (quasi) periodic coupling array and an external magnetic field in a spin-1/2 XXZ chain. A new class of magnetization plateaux are obtained by means of Abelian bosonization methods which give rise to a sufficient quantization condition. The investigation of magnetic phase diagrams via exact diagonalization of finite clusters finds a complete agreement with the continuum treatment in a variety of situations.

Diffusion in disordered lattices and related heisenberg ferromagnets

We study the diffusion of classical hard-core particles in disordered lattices within the formalism of a quantum spin representation. This analogy enables an exact treatment of noninstantaneous correlation functions at finite particle densities in terms of single spin excitations in disordered ferromagnetic backgrounds. Applications to diluted chains and percolation clusters are discussed. It is found that density fluctuations in the former exhibit a stretched exponential decay while an anomalous power law asymptotic decay is conjectured for the latter.

Quantum phase transitions in trimerized zigzag spin ladders

We analyze the effects of a trimerized modulation in a quantum spin

Quantum approach to nucleation times of kinetic Ising ferromagnets.

S=\frac12

Ground state and low-lying excitations of the spin-1/2 XXZ model on the Kagomé lattice at magnetization 1/3

zig-zag ladder at the magnetization plateau

Nonuniversal nonequilibrium critical dynamics with disorder.

M=1/3

Nonuniversal dynamics of dimer growing interfaces.

. Such periodicity is argued to be stemmed from lattice deformations by phonons. The interplay between frustration and exchange modulation is well described by an effective triple sine-Gordon field theory close to the homogeneous ladder and by block-spin perturbation theory in the weakly coupled trimers regime. The characteristic triple degeneracy of the ground state for homogeneous ladders gives place to modulation driven quantum phase transitions, leading to a rich phase diagram including up-up-down, quantum plateau and gapless plateau states.