Quantum Phases in Two-Dimensional Frustrated Spin-1/2 Antiferromagnets

Sindzingre, Philippe; Lhuillier, C.; Fouet, J.-B.

doi:10.1142/s0217979203020168

Cited by 10 publications

(19 citation statements)

References 45 publications

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“…One striking feature is the large value of the dimer density on the two bonds facing the impurity (distance d = 2). This can be interpreted as a (singlet) dimer crystallization as found in prior studies of the Heisenberg quantum antiferromagnet [16][17][18] . Our study reveals that this phenomena is very robust and depends weakly on the supposed phase, liquid (λ < λ C ) or crystalline (λ > λ C ), of the model.…”

Section: A Local Dimer Modulationsupporting

confidence: 56%

“…Let us now discuss our results in the light of the recently obtained 17 O NMR experimental spectra on the Kagome QHAF Herberthsmithite material which contains an intrinsic small Zinc substitution in the Copper Kagome planes 12 . Although the experimental NMR spectra are strongly broaden by quadrupolar effects typical of powders, two separate structures can clearly be followed from high to low temperatures.…”

Section: B Herberthsmithite Described As a Valence Bond Glassmentioning

confidence: 90%

“…In other words, the bond exchange interaction S i · S j (in units of the exchange coupling J) acts on all bonds of the kagome lattice except on the four bonds connected to the impurity. Using Lanczos exact diagonalizations (LED) of small clusters of the kagome QHAF 15 , it has been shown that a single impurity tends to 'localize' two singlet bonds next to it [16][17][18] . Although this local phenomenon is well captured even on very small clusters 13 , LED of the QHAF do not allow to investigate reliably the perturbation of the media at larger distances from the impurity, which can be probed e.g.…”

Section: A Impurities Described As Vacanciesmentioning

confidence: 99%

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Impurity-doped kagome antiferromagnet: A quantum dimer model approach

Poilblanc

Ralko

2010

Phys. Rev. B

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The doping of quantum Heisenberg antiferromagnets on the kagome lattice by non-magnetic impurities is investigated within the framework of a generalized quantum dimer model (QDM) describing a) the valence bond crystal (VBC), b) the dimer liquid and c) the critical region on equal footing. Following the approach by Ralko et al. [Phys. Rev. Lett. 101, 117204 (2008)] for the square and triangular lattices, we introduce the (minimal) extension of the QDM on the Kagome lattice to account for spontaneous creation of mobile S=1/2 spinons at finite magnetic field. Modulations of the dimer density (at zero or finite magnetic field) and of the local field-induced magnetization in the vicinity of impurities are computed using Lanczos Exact Diagonalization techniques on small clusters (48 and 75 sites). The VBC is clearly revealed from its pinning by impurities, while, in the dimer liquid, crystallization around impurities involves only two neighboring dimers. We also find that a next-nearest-neighbor ferromagnetic coupling favors VBC order. Unexpectedly, a small size spinon-impurity bound state appears in some region of the the dimer liquid phase. In contrast, in the VBC phase the spinon delocalizes within a large region around the impurity, revealing the weakness of the VBC confining potential. Lastly, we observe that an impurity concentration as small as 4% enhances dimerization substantially. These results are confronted to the Valence Bond Glass scenario [R.R.P. Singh, Phys. Rev. Lett. 104, 177203 (2010)] and implications to the interpretation of the Nuclear Magnetic Resonance spectra of the Herbertsmithite compound are outlined.

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Section: A Local Dimer Modulationsupporting

confidence: 56%

Section: B Herberthsmithite Described As a Valence Bond Glassmentioning

confidence: 90%

Section: A Impurities Described As Vacanciesmentioning

confidence: 99%

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Impurity-doped kagome antiferromagnet: A quantum dimer model approach

Poilblanc

Ralko

2010

Phys. Rev. B

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“…Due to the truncated Hilbert space we cannot expect to recover the entire spectrum. Surprisingly however the CORE tower of states successfully reproduces the general features observed in ED calculations of the same model: 28 (a) a set of QDJS with the correct degeneracy and quantum numbers (in the folded Brillouin zone); (b) a reduced number of magnon states at intermediate energies, both set of states rather well separated from the high energy part of the spectrum. While the QDJS seem not to be affected by the CORE decimation procedure, clearly some of the magnon modes get eliminated by the basis truncation.…”

Section: A Plaquette Latticesupporting

confidence: 54%

Numerical contractor renormalization method for quantum spin models

2004

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We demonstrate the utility of the numerical contractor renormalization (CORE) method for quantum spin systems by studying one-and two-dimensional model cases. Our approach consists of two steps: (i) building an effective Hamiltonian with longer ranged interactions up to a certain cutoff using the CORE algorithm and (ii) solving this new model numerically on finite clusters by exact diagonalization and performing finite-size extrapolations to obtain results in the thermodynamic limit. This approach, giving complementary information to analytical treatments of the CORE Hamiltonian, can be used as a semiquantitative numerical method. For ladder-type geometries, we explicitely check the accuracy of the effective models by increasing the range of the effective interactions until reaching convergence. Our results in the perturbative regime and also away from it are in good agreement with previously established results. In two dimensions we consider the plaquette lattice and the kagomé lattice as nontrivial test cases for the numerical CORE method. As it becomes more difficult to extend the range of the effective interactions in two dimensions, we propose diagnostic tools (such as the density matrix of the local building block) to ascertain the validity of the basis truncation. On the plaquette lattice we have an excellent description of the system in both the disordered and the ordered phases, thereby showing that the CORE method is able to resolve quantum phase transitions. On the kagomé lattice we find that the previously proposed twofold degenerate S =1/2 basis can account for a large number of phenomena of the spin 1 / 2 kagomé system. For spin 3 / 2, however, this basis does not seem to be sufficient. In general we are able to simulate system sizes which correspond to an 8 ϫ 8 lattice for the plaquette lattice or a 48-site kagomé lattice, which are beyond the possibilities of a standard exact diagonalization approach.

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“…Such a system (having so far no experimental realization among solid state systems) is a paradigmatic, although not yet fully understood (cf. [10]) example of a quantum spin liquid of type II [11].…”

mentioning

confidence: 99%

Atomic Fermi Gas in the Trimerized Kagomé Lattice at2/3Filling

et al. 2005

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We study low temperature properties of a spinless interacting Fermi gas in the trimerized kagomé lattice. The case of two fermions per trimer is described by a quantum spin 1/2 model on the triangular lattice with couplings depending on the bond directions. Using exact diagonalizations we show that the system exhibits nonstandard properties of a quantum spin-liquid crystal, combining a planar antiferromagnetic order with an exceptionally large number of low-energy excitations.

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Quantum Phases in Two-Dimensional Frustrated Spin-1/2 Antiferromagnets

Cited by 10 publications

References 45 publications

Impurity-doped kagome antiferromagnet: A quantum dimer model approach

Impurity-doped kagome antiferromagnet: A quantum dimer model approach

Numerical contractor renormalization method for quantum spin models

Atomic Fermi Gas in the Trimerized Kagomé Lattice at2/3Filling

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