Diagnosing order by disorder in quantum spin systems

In this paper we study the frustrated J1-J2 quantum Heisenberg model on the square lattice for J2 > 2J1, in a magnetic field. In this regime the classical system is known to have a degenerate manifold of lowest energy configurations, where standard thermal order by disorder occurs. In order to study its quantum version we use a path integral formulation in terms of coherent states. We show that the classical degeneracy in the plane transverse to the magnetic field is lifted by quantum fluctuations. Collinear states are then selected, in a similar pattern to that set by thermal order by disorder, leaving a Z2 degeneracy. A careful analysis reveals a purely quantum mechanical effect given by the tunneling between the two minima selected by fluctuations. The effective description contains two planar (XY -like) fields conjugate to the total magnetization and the difference of the two sublattice magnetizations. Disorder in either or both of these fields produces the locking of their conjugate observables. Furthermore, within this scenario we argue that the quantum state is close to a product state.Comment: 8 pages, 3 figure

Adsorption on carbon nanotubes: quantum spin tubes, magnetization plateaus, and conformal symmetry

We formulate the problem of adsorption onto the surface of a carbon nanotube as a lattice gas on a triangular lattice wrapped around a cylinder. This model is equivalent to an XXZ Heisenberg quantum spin tube. The geometric frustration due to wrapping leads generically to four magnetization plateaus, in contrast to the two on a flat graphite sheet. We obtain analytical and numerical results for the magnetizations and transition fields for armchair, zig-zag and chiral nanotubes. The zig-zags are exceptional in that one of the plateaus has extensive zero temperature entropy in the classical limit. Quantum effects lift up the degeneracy, leaving gapless excitations which are described by a $c=1$ conformal field theory with compactification radius quantized by the tube circumference.Comment: 5 pages, 6 figure

Random bond XXZ chains with modulated couplings

The magnetization behavior of q-periodic antiferromagnetic spin 1/2 Heisenberg chains under uniform magnetic fields is investigated in a background of disorder exchange distributions. By means of both real space decimation procedures and numerical diagonalizations in XX chains, it is found that for binary disorder the magnetization exhibits wide plateaux at values of 1+2(p-1)/q, where p is the disorder strength. In contrast, no spin gaps are observed in the presence of continuous exchange distributions. We also study the magnetic susceptibility at low magnetic fields. For odd q-modulations the susceptibility exhibits a universal singularity, whereas for q even it displays a non-universal power law behavior depending on the parameters of the distribution.Comment: 4 pages, 3 figures. Final version to appear in PR

Competing interactions in the XYZ model

We study the interplay between a XY anisotropy $\gamma$, exchange modulations and an external magnetic field along the z direction in the XYZ chain using bosonization and Lanczos diagonalization techniques. We find an Ising critical line in the space of couplings which occur due to competing relevant perturbations which are present. More general situations are also discussed.Comment: 6 pages, 6 figure

Hilbert Space of Isomorphic Representations of Bosonized Chiral QCD2QCD_2

We analyse the Hilbert space structure of the isomorphic gauge non-invariant and gauge invariant bosonized formulations of chiral $QCD_2$ for the particular case of the Jackiw-Rajaraman parameter $a = 2$. The BRST subsidiary conditions are found not to provide a sufficient criterium for defining physical states in the Hilbert space and additional superselection rules must to be taken into account. We examine the effect of the use of a redundant field algebra in deriving basic properties of the model. We also discuss the constraint structure of the gauge invariant formulation and show that the only primary constraints are of first class.Comment: LaTeX, 19 page

Massive and Massless Behavior in Dimerized Spin Ladders

We investigate the conditions under which a gap vanishes in the spectrum of dimerized coupled spin-1/2 chains by means of Abelian bosonization and Lanczos diagonalization techniques. Although both interchain ($J'$) and dimerization ($\delta$) couplings favor a gapful phase, it is shown that a suitable choice of these interactions yields massless spin excitations. We also discuss the influence of different arrays of relative dimerization on the appearance of non-trivial magnetization plateaus.Comment: 5 pages, RevTex, 5 Postscript figure

Non-perturbative effective field theory for two-leg antiferromagnetic spin ladders

We study the long wavelength limit of a spin 1/2 Heisenberg antiferromagnetic two-leg ladder, treating the interchain coupling in a non-perturbative way. We perform a mean field analysis and then include exactly the fluctuations. This allows for a discussion of the phase diagram of the system and provides an effective field theory for the low energy excitations. The coset fermionic Lagrangian obtained corresponds to a perturbed SU(4)_1/U(1) Conformal Field Theory (CFT). This effective theory is naturally embedded in a SU(2)_2 x Z_2 CFT, where perturbations are easily identified in terms of conformal operators in the two sectors. Crossed and zig-zag ladders are also discussed using the same approach.Comment: 14 pages LaTeX, 5 PostScript figures included using epsfig.sty; minor corrections and a few references adde

Exactly solvable Ising--Heisenberg chain with triangular XXZ-Heisenberg plaquettes

A mixed Ising-Heisenberg spin system consisting of triangular XXZ-Heisenberg spin clusters assembled into a chain by alternating with Ising spins interacting to all three spins in the triangle is considered. The exact solution of the model is given in terms of the generalized decoration--iteration map and within the transfer-matrix technique. Exact expressions for thermodynamic functions are derived. Ground state phase diagrams, thermodynamic and magnetic properties of the system are examined.Comment: 16 pages, 12 figure

Spinons and parafermions in fermion cosets

We introduce a set of gauge invariant fermion fields in fermionic coset models and show that they play a very central role in the description of several Conformal Field Theories (CFT's). In particular we discuss the explicit realization of primaries and their OPE in unitary minimal models, parafermion fields in $Z_k$ CFT's and that of spinon fields in $SU(N)_k, k=1$ Wess-Zumino-Witten models (WZW) theories. The higher level case ($k>1$) will be briefly discussed. Possible applications to QHE systems and spin-ladder systems are addressed.Comment: 6 pages, Latex file. Invited talk at International Seminar dedicated to the memory of D.V.Volkov, Kharkov, January 5-7, 199

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.Comment: 5 pages, 6 figures, final version to appear in Phys.Rev.