Order by disorder and gauge-like degeneracy in quantum pyrochlore antiferromagnet

The (three-dimensional) pyrochlore lattice antiferromagnet with Heisenberg spins of large spin length $S$ is a highly frustrated model with an macroscopic degeneracy of classical ground states. The zero-point energy of (harmonic order) spin wave fluctuations distinguishes a subset of these states. I derive an approximate but illuminating {\it effective Hamiltonian}, acting within the subspace of Ising spin configurations representing the {\it collinear} ground states. It consists of products of Ising spins around loops, i.e has the form of a $Z_2$ lattice gauge theory. The remaining ground state entropy is still infinite but not extensive, being $O(L)$ for system size $O(L^3)$. All these ground states have unit cells bigger than those considered previously.Comment: 4pp, one figur

Phase diagram of an anisotropic frustrated ferromagnetic spin-1/2 chain in a magnetic field: a density matrix renormalization group study

We study the phase diagram of a frustrated spin-1/2 ferromagnetic chain with anisotropic exchange interactions in an external magnetic field, using the density matrix renormalization group method. We show that an easy-axis anisotropy enhances the tendency towards multimagnon bound states, while an easy-plane anisotropy favors chirally ordered phases. In particular, a moderate easy-plane anisotropy gives rise to a quantum phase transition at intermediate magnetization. We argue that this transition is related to the finite-field phase transition experimentally observed in the spin-1/2 compound LiCuVO_4.Comment: The final published versio

Simplex solid states of SU(N) quantum antiferromagnets

I define a set of wavefunctions for SU(N) lattice antiferromagnets, analogous to the valence bond solid states of Affleck, Kennedy, Lieb, and Tasaki (AKLT), in which the singlets are extended over N-site simplices. As with the valence bond solids, the new simplex solid (SS) states are extinguished by certain local projection operators, allowing us to construct Hamiltonians with local interactions which render the SS states exact ground states. Using a coherent state representation, we show that the quantum correlations in each SS state are calculable as the finite temperature correlations of an associated classical model, with N-spin interactions, on the same lattice. In three and higher dimensions, the SS states can spontaneously break SU(N) and exhibit N-sublattice long-ranged order, as a function of a discrete parameter which fixes the local representation of SU(N). I analyze this transition using a classical mean field approach. For N>2 the ordered state is selected via an "order by disorder" mechanism. As in the AKLT case, the bulk representations fractionalize at an edge, and the ground state entropy is proportional to the volume of the boundary.Comment: 14 pages, 8 figures, minor typos correcte

Quantum and Classical Spins on the Spatially Distorted Kagome Lattice: Applications to Volborthite

In Volborthite, spin-1/2 moments form a distorted Kagom\'e lattice, of corner sharing isosceles triangles with exchange constants $J$ on two bonds and $J'$ on the third bond. We study the properties of such spin systems, and show that despite the distortion, the lattice retains a great deal of frustration. Although sub-extensive, the classical ground state degeneracy remains very large, growing exponentially with the system perimeter. We consider degeneracy lifting by thermal and quantum fluctuations. To linear (spin wave) order, the degeneracy is found to stay intact. Two complementary approaches are therefore introduced, appropriate to low and high temperatures, which point to the same ordered pattern. In the low temperature limit, an effective chirality Hamiltonian is derived from non-linear spin waves which predicts a transition on increasing $J'/J$, from $\sqrt 3\times \sqrt 3$ type order to a new ferrimagnetic {\em striped chirality} order with a doubled unit cell. This is confirmed by a large-N approximation on the O($n$) model on this lattice. While the saddle point solution produces a line degeneracy, $O(1/n)$ corrections select the non-trivial wavevector of the striped chirality state. The quantum limit of spin 1/2 on this lattice is studied via exact small system diagonalization and compare well with experimental results at intermediate temperatures. We suggest that the very low temperature spin frozen state seen in NMR experiments may be related to the disconnected nature of classical ground states on this lattice, which leads to a prediction for NMR line shapes.Comment: revised, section V about exact diagonalization is extensively rewritten, 17 pages, 11 figures, RevTex 4, accepted by Phys. Rev.

Lattice gas description of pyrochlore and checkerboard antiferromagnets in a strong magnetic field

Quantum Heisenberg antiferromagnets on pyrochlore and checkerboard lattices in a strong external magnetic field are mapped onto hard-core lattice gases with an extended exclusion region. The effective models are studied by the exchange Monte Carlo simulations and by the transfer matrix method. The transition point and the critical exponents are obtained numerically for a square-lattice gas of particles with the second-neighbor exclusion, which describes a checkerboard antiferromagnet. The exact structure of the magnon crystal state is determined for a pyrochlore antiferromagnet.Comment: 11 pages, accepted versio

Conserved Growth on Vicinal Surfaces

A crystal surface which is miscut with respect to a high symmetry plane exhibits steps with a characteristic distance. It is argued that the continuum description of growth on such a surface, when desorption can be neglected, is given by the anisotropic version of the conserved KPZ equation (T. Sun, H. Guo, and M. Grant, Phys. Rev. A 40, 6763 (1989)) with non-conserved noise. A one--loop dynamical renormalization group calculation yields the values of the dynamical exponent and the roughness exponent which are shown to be the same as in the isotropic case. The results presented here should apply in particular to growth under conditions which are typical for molecular beam epitaxy.Comment: 10 pages, uses revte

Influence of lattice distortions in classical spin systems

We investigate a simple model of a frustrated classical spin chain coupled to adiabatic phonons under an external magnetic field. A thorough study of the magnetization properties is carried out both numerically and analytically. We show that already a moderate coupling with the lattice can stabilize a plateau at 1/3 of the saturation and discuss the deformation of the underlying lattice in this phase. We also study the transition to saturation where either a first or second order transition can occur, depending on the couplings strength.Comment: Submitted to Phys. Rev.

Spin-orbit effects in Na4_4Ir3_3O8_8, a hyper-kagom\'{e} lattice antiferromagnet

We consider spin-orbit coupling effects in Na$_4$Ir$_3$O$_8$, a material in which Ir$^{4+}$ spins form an hyper-kagom\'{e} lattice, a three-dimensional network of corner-sharing triangles. We argue that both low temperature thermodynamic measurements and the impurity susceptibility induced by dilute substitution of Ti for Ir are suggestive of significant spin-orbit effects. Because of uncertainties in the crystal-field parameters, we consider two limits in which the spin-orbit coupling is either weak or strong compared to the non-cubic atomic splittings. A semi-microscopic calculation of the exchange Hamiltonian confirms that indeed large antisymmetric Dzyaloshinskii-Moriya (DM) and/or symmetric exchange anisotropy may be present. In the strong spin-orbit limit, the Ir-O-Ir superexchange contribution consists of unfrustrated strong symmetric exchange anisotropy, and we suggest that spin-liquid behavior is unlikely. In the weak spin-orbit limit, and for strong spin-orbit and direct Ir-Ir exchange, the Hamiltonian consists of Heisenberg and DM interactions. The DM coupling is parametrized by a three component DM vector (which must be determined empirically). For a range of orientation of this vector, frustration is relieved and an ordered state occurs. For other orientations, even the classical ground states are very complex. We perform spin-wave and exact diagonalization calculations which suggest the persistence of a quantum spin liquid in the latter regime. Applications to Na$_4$Ir$_3$O$_8$ and broader implications are discussed.Comment: 22 pages, 15 figures. submit to prb. New references are adde

Bohr-Sommerfeld quantization of spin Hamiltonians

The Bohr-Sommerfeld rule for a spin system is obtained, including the first quantum corrections. The rule applies to both integer and half-integer spin, and respects Kramers degeneracy for time-reversal invariant systems. It is tested for various models, in particular the Lipkin-Meshkov-Glick model, and found to agree very well with exact results.Comment: Revtex 4, no figures, 1 tabl