Exact low-temperature properties of a class of highly frustrated Hubbard models

We study the repulsive Hubbard model both analytically and numerically on a family of highly frustrated lattices which have one-electron states localized on isolated trapping cells. We construct and count exact many-electron ground states for a wide range of electron densities and obtain closed-form expressions for the low-temperature thermodynamic quantities. Furthermore, we find that saturated ferromagnetism is obtained only for sufficiently high electron densities and large Hubbard repulsion $U$ while there is no finite average moment in the ground states at lower densities.Comment: 8 pages, 7 figures, accepted for publication in Phys. Rev.

Planar pyrochlore: a strong-coupling analysis

Recent investigations of the two-dimensional spin-1/2 checkerboard lattice favor a valence bond crystal with long range quadrumer order [J.-B. Fouet et al., preprint cond-mat/0108070]. Starting from the limit of isolated quadrumers, we perform a complementary analysis of the evolution of the spectrum as a function of the inter quadrumer coupling j using both, exact diagonalization (ED) and series expansion (SE) by continuous unitary transformation. We compute (i) the ground state energy, (ii) the elementary triplet excitations, (iii) singlet excitations on finite systems and find very good agreement between SE and ED. In the thermodynamic limit we find a ground state energy substantially lower than documented in the literature. The elementary triplet excitation is shown to be gapped and almost dispersionless, whereas the singlet sector contains strongly dispersive modes. Evidence is presented for the low energy singlet excitations in the spin gap in the vicinity of j=1 to result from a large downward renormalization of local high-energy states.Comment: 4 pages REVTeX4 including 3 figures: published version (minor changes

Low-temperature thermodynamics for a flat-band ferromagnet: Rigorous versus numerical results

The repulsive Hubbard model on a sawtooth chain exhibits a lowest single-electron band which is completely dispersionless (flat) for a specific choice of the hopping parameters. We construct exact many-electron ground states for electron fillings up to 1/4. We map the low-energy degrees of freedom of the electron model to a model of classical hard dimers on a chain and, as a result, obtain the ground-state degeneracy as well as closed-form expressions for the low-temperature thermodynamic quantities around a particular value of the chemical potential. We compare our analytical findings with complementary numerical data. Although we consider a specific model, we believe that some of our results like a low-temperature peak in the specific heat are generic for flat-band ferromagnets.Comment: 5 pages, 1 figure; accepted for publication as a Rapid Communication in Physical Review

Multi-triplet bound states and finite-temperature dynamics in highly frustrated quantum spin ladders

Low-dimensional quantum magnets at finite temperatures present a complex interplay of quantum and thermal fluctuation effects in a restricted phase space. While some information about dynamical response functions is available from theoretical studies of the one-triplet dispersion in unfrustrated chains and ladders, little is known about the finite-temperature dynamics of frustrated systems. Experimentally, inelastic neutron scattering studies of the highly frustrated two-dimensional material SrCu$_2$(BO$_3$)$_2$ show an almost complete destruction of the one-triplet excitation band at a temperature only 1/3 of its gap energy, accompanied by strong scattering intensities for apparent multi-triplet excitations. We investigate these questions in the frustrated spin ladder and present numerical results from exact diagonalization for the dynamical structure factor as a function of temperature. We find anomalously rapid transfer of spectral weight out of the one-triplet band and into both broad and sharp spectral features at a wide range of energies, including below the zero-temperature gap of this excitation. These features are multi-triplet bound states, which develop particularly strongly near the quantum phase transition, fall to particularly low energies there, and persist to all the way to infinite temperature. Our results offer valuable insight into the physics of finite-temperature spectral functions in SrCu$_2$(BO$_3$)$_2$ and many other highly frustrated spin systems.Comment: 22 pages, 19 figures; published version: many small modification

Numerical study of magnetization plateaux in the spin-1/2 kagome Heisenberg antiferromagnet

We clarify the existence of several magnetization plateaux for the kagome $S=1/2$ antiferromagnetic Heisenberg model in a magnetic field. Using approximate or exact localized magnon eigenstates, we are able to describe in a similar manner the plateau states that occur for magnetization per site $m=1/3$, $5/9$, and $7/9$ of the saturation value. These results are confirmed using large-scale Exact Diagonalization on lattices up to 63 sites.Comment: 8 pages; minor changes; published versio

Efficient Quantum Monte Carlo simulations of highly frustrated magnets: the frustrated spin-1/2 ladder

Quantum Monte Carlo simulations provide one of the more powerful and versatile numerical approaches to condensed matter systems. However, their application to frustrated quantum spin models, in all relevant temperature regimes, is hamstrung by the infamous "sign problem." Here we exploit the fact that the sign problem is basis-dependent. Recent studies have shown that passing to a dimer (two-site) basis eliminates the sign problem completely for a fully frustrated spin model on the two-leg ladder. We generalize this result to all partially frustrated two-leg spin-1/2 ladders, meaning those where the diagonal and leg couplings take any antiferromagnetic values. We find that, although the sign problem does reappear, it remains remarkably mild throughout the entire phase diagram. We explain this result and apply it to perform efficient quantum Monte Carlo simulations of frustrated ladders, obtaining accurate results for thermodynamic quantities such as the magnetic specific heat and susceptibility of ladders up to L=200 rungs (400 spins 1/2) and down to very low temperatures.Comment: 26 pages including 12 figures; this version: minor modifications in sections 3.3 and 4.

Effect of Dzyaloshinski-Moriya interaction on spin-polarized neutron scattering

For magnetic materials containing many lattice imperfections (e.g., nanocrystalline magnets), the relativistic Dzyaloshinski-Moriya (DM) interaction may result in nonuniform spin textures due to the lack of inversion symmetry at interfaces. Within the framework of the continuum theory of micromagnetics, we explore the impact of the DM interaction on the elastic magnetic small-angle neutron scattering (SANS) cross section of bulk ferromagnets. It is shown that the DM interaction gives rise to a polarization-dependent asymmetric term in the spin-flip SANS cross section. Analysis of this feature may provide a means to determine the DM constant.Comment: 10 pages, 7 figure