The sawtooth chain: From Heisenberg spins to Hubbard electrons
arXiv:0806.0922 · doi:10.1142/S0217979208050176
Abstract
We report on recent studies of the spin-half Heisenberg and the Hubbard model on the sawtooth chain. For both models we construct a class of exact eigenstates which are localized due to the frustrating geometry of the lattice for a certain relation of the exchange (hopping) integrals. Although these eigenstates differ in details for the two models because of the different statistics, they share some characteristic features. The localized eigenstates are highly degenerate and become ground states in high magnetic fields (Heisenberg model) or at certain electron fillings (Hubbard model), respectively. They may dominate the low-temperature thermodynamics and lead to an extra low-temperature maximum in the specific heat. The ground-state degeneracy can be calculated exactly by a mapping of the manifold of localized ground states onto a classical hard-dimer problem, and explicit expressions for thermodynamic quantities can be derived which are valid at low temperatures near the saturation field for the Heisenberg model or around a certain value of the chemical potential for the Hubbard model, respectively.
arXiv comment16 pages, 6 figure, the paper is based on an invited talk on the XXXI International Workshop on Condensed Matter Theories, Bangkok, Dec 2007; notation of x-axis in Fig.6 corrected, references updated
References in corpus (27)
- Quantum magnetism in the paratacamite family: towards an ideal kagome lattice
- Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices
- Enhanced magnetocaloric effect in frustrated magnets
- Ladders in a magnetic field: a strong coupling approach
- Magnetization plateaus in frustrated antiferromagnetic quantum spin models
- Exact low-temperature behavior of kagome antiferromagnet at high fields
- Magnetization plateaux and jumps in a class of frustrated ladders: A simple route to a complex behaviour
- Exact eigenstates and macroscopic magnetization jumps in strongly frustrated spin lattices
- Quantum magnetism in two dimensions: From semi-classical Néel order to magnetic disorder
- Universal low-temperature behavior of frustrated quantum antiferromagnets in the vicinity of the saturation field
- Independent magnon states on magnetic polytopes
- Enhanced magnetocaloric effect in frustrated magnetic molecules with icosahedral symmetry
- Finite low-temperature entropy of some strongly frustrated quantum spin lattices in the vicinity of the saturation field
- High field properties of geometrically frustrated magnets
- Absence of magnetic order for the spin-half Heisenberg antiferromagnet on the star lattice
- Magnetic-field induced spin-Peierls instability in strongly frustrated quantum spin lattices
- Exact many-electron ground states on the diamond Hubbard chain
- Lattice gas description of pyrochlore and checkerboard antiferromagnets in a strong magnetic field
- Frustration effects in magnetic molecules
- Linear independence of localized magnon states
- Low-temperature thermodynamics for a flat-band ferromagnet: Rigorous versus numerical results
- Linear energy bounds for Heisenberg spin systems
- Exact eigenstates of highly frustrated spin lattices probed in high fields
- Entropy of fermionic models on highly frustrated lattices
- Structural instability of two- and three-dimensional pyrochlore spin lattices in high magnetic fields
- Variational Mote Carlo Study of Flat Band Ferromagnetism -- Application to CeRh_3 B_2
- Enhanced low-temperature entropy and flat-band ferromagnetism in the t-J model on the sawtooth lattice
Cited by in corpus (23)
- Low-temperature properties of the Hubbard model on highly frustrated one-dimensional lattices
- Dynamic and thermodynamic properties of the generalised diamond chain model for azurite
- Delta chain with ferromagnetic and antiferromagnetic interactions at the critical point
- Magneto-thermal properties of the Heisenberg-Ising orthogonal-dimer chain with triangular XXZ-clusters
- Magnetization process of atacamite: a case of weakly coupled sawtooth chains
- Lattice distortions in a sawtooth chain with Heisenberg and Ising bonds
- Delta chain with anisotropic ferromagnetic and antiferromagnetic interactions
- Enhancement of magnetization plateaus in low dimensional spin systems
- From kagome strip to kagome lattice: Realizations of frustrated S=1/2 antiferromagnets in Ti(III) fluorides
- Flat-band physics in the spin-1/2 sawtooth chain
- Variety of order-by-disorder phases in the asymmetric zigzag ladder: From the delta chain to the chain
- Localized dynamics following a quantum quench in a non-integrable system: An example on the sawtooth ladder
- Analytical and numerical studies of the one-dimensional sawtooth chain
- Electric field driven flat bands: Enhanced magnetoelectric and electrocaloric effects in frustrated quantum magnets
- Particle Statistics, Frustration, and Ground-State Energy
- Frustration induced noncollinear magnetic order phase in one-dimensional Heisenberg chain with alternating antiferromagnetic and ferromagnetic next nearest neighbor interactions
- Quantum Heisenberg model on a sawtooth-chain lattice: Rotation-invariant Green's function method
- Ground-state degeneracy and low-temperature thermodynamics of correlated electrons on highly frustrated lattices
- Antikink dispersions of the - sawtooth spin-1/2 anisotropic Heisenberg antiferromagnetic chain
- Spin triangle chain with ferromagnetic and antiferromagnetic interactions on the transition line
- Ferromagnetic Order of Reduced Magnetic Moments in a Frustrated Sawtooth Chain of the Magnetic Semiconductor ZnYbS
- Magnetization of electronic ground states in frustrated superstable graphs
- On flat bands in the -- XXZ sawtooth chain