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Universal properties of highly frustrated quantum magnets in strong magnetic fields
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10.1063/1.2780166
/content/aip/journal/ltp/33/9/10.1063/1.2780166
http://aip.metastore.ingenta.com/content/aip/journal/ltp/33/9/10.1063/1.2780166

Figures

Image of FIG. 1.
FIG. 1.

Three examples of one-dimensional spin lattices admitting localized magnons: the diamond chain (hard-monomer universality class) (a), the frustrated two-leg ladder (one-dimensional hard-dimer universality class) (b), the kagomé-like chain, originally introduced in Ref. 29 (one-dimensional hard-dimer universality class) (c).

Image of FIG. 2.
FIG. 2.

Three examples of two-dimensional spin lattices admitting localized magnons: the kagomé lattice (hard-hexagon universality class) (a), the checkerboard lattice (large-hard-square universality class) (b), the frustrated bilayer lattice (hard-square universality class) (c). We also show auxiliary lattice-gas models (hard hexagons on a triangular lattice, large hard squares on a square lattice, and hard squares on a square lattice) which describe low-energy degrees of freedom of the spin models in strong magnetic fields.

Image of FIG. 3.
FIG. 3.

The checkerboard lattice. A localized magnon which occupies a larger area than the smallest possible one (a). A three-magnon state which is not a large-hard-square state because of the nested “defect” state at the lower left side of the lattice; one magnon is localized on each of the three loops (b).

Image of FIG. 4.
FIG. 4.

, , and versus at low temperatures; , and versus around the saturation field. From left to right: diamond chain with , , frustrated two-leg ladder with , , kagomé-like chain with . We set the field range and the temperature range . The exact diagonalization (ED) data (symbols) refer to finite systems of sizes (diamond chain and frustrated ladder) and (kagomé-like chain). The analytical predictions for hard monomers (HM) and one-dimensional hard dimers (HD) are shown by lines.

Image of FIG. 5.
FIG. 5.

versus around the saturation field for the frustrated bilayer lattice with , . The exact diagonalization data (filled symbols) refer to a finite spin system of sites. The analytical results (unfilled symbols) refer to a finite hard-square system of sites. The Monte Carlo simulation data (lines) are obtained for the hard-square system on finite lattices with up to .

Tables

Generic image for table
Table I.

The degeneracies and the energy gaps for various finite frustrated bilayer lattices: exact diagonalization data for finite systems with versus hard-square predictions. is the number of sites in the spin lattice, DGS is the degeneracy of the ground state as follows from exact diagonalization for a given , #HSS is the number of configurations with hard squares, and is the energy gap between the ground state and the first excited state in units of . The dots for indicate omitted sectors with .

Generic image for table
Table II.

The degeneracies and the energy gaps for the kagomé lattice: exact diagonalization data for finite systems versus hard-hexagon predictions. is the number of sites in the spin lattice, DGS is the degeneracy of the ground state as follows from exact diagonalization for a given , #HHS is the number of configurations with hard hexagons, and is the energy gap between the ground state and the first excited state in units of . Dots indicate some sectors with which have been omitted for larger values of . For the two-magnon sector one has and .

Generic image for table
Table III.

The degeneracies and the energy gaps for various finite checkerboard lattices: exact diagonalization data for finite systems versus large-hard-square predictions. is the number of sites in the spin lattice, DGS is the degeneracy of the ground state as follows from exact diagonalization for a given , #LHSS is the number of configurations with large hard squares, is the energy gap between the ground state and the first excited state in units of . Dots indicate some sectors with which have been omitted for larger values of . For the two-magnon sector one has and .

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/content/aip/journal/ltp/33/9/10.1063/1.2780166
2007-09-01
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Universal properties of highly frustrated quantum magnets in strong magnetic fields
http://aip.metastore.ingenta.com/content/aip/journal/ltp/33/9/10.1063/1.2780166
10.1063/1.2780166
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