Ground states and excitations of a one-dimensional<i>kagomé</i>-like antiferromagnet

Waldtmann, Ch.; Kreutzmann, H.; Schollwöck, Ulrich; Maisinger, K.; Everts, H. U.

doi:10.1103/physrevb.62.9472

Cited by 38 publications

(25 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The same behavior of the magnetization of a ferrimagnetic phase has previously been observed in an exact-diagonalization study of a one-dimensional kagomé-like antiferromagnet. 23 At the FM-IC phase boundary, the magnetization becomes spatially modulated with an incommensurate wave vector q ord =2k min .…”

Section: Numerical Results Of the Sp"n… Formalismmentioning

confidence: 99%

Heisenberg antiferromagnet with anisotropic exchange on the kagomé lattice: Description of the magnetic properties of volborthite

Yavors’kii¹,

Apel²,

Everts³

2007

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

We study the properties of the Heisenberg antiferromagnet with spatially anisotropic nearest-neighbor exchange couplings on the kagomé net, i.e., with coupling J in one lattice direction and couplings JЈ along the other two directions. For J / JЈ տ 1, this model is believed to describe the magnetic properties of the mineral volborthite. In the classical limit, it exhibits two kinds of ground state: a ferrimagnetic state for J / JЈ Ͻ 1/2 and a large manifold of canted spin states for J / JЈ Ͼ 1 / 2. To include quantum effects self-consistently, we investigate the Sp͑N͒ symmetric generalization of the original SU͑2͒ symmetric model in the large-N limit. In addition to the dependence on the anisotropy, the Sp͑N͒ symmetric model depends on a parameter that measures the importance of quantum effects. Our numerical calculations reveal that, in the -J / JЈ plane, the system shows a rich phase diagram containing a ferrimagnetic phase, an incommensurate phase, and a decoupled chain phase, the latter two with short-and long-range order. We corroborate these results by showing that the boundaries between the various phases and several other features of the Sp͑N͒ phase diagram can be determined by analytical calculations. Finally, the application of a block-spin perturbation expansion to the trimerized version of the original spin-1 / 2 model leads us to suggest that in the limit of strong anisotropy, J / JЈ ӷ 1, the ground state of the original model is a collinearly ordered antiferromagnet, which is separated from the incommensurate state by a quantum phase transition.

show abstract

Section: Numerical Results Of the Sp"n… Formalismmentioning

confidence: 99%

Heisenberg antiferromagnet with anisotropic exchange on the kagomé lattice: Description of the magnetic properties of volborthite

Yavors’kii¹,

Apel²,

Everts³

2007

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

show abstract

“…On the theoretical side however, the nature of the ground state of the NN spin-1/2 quantum Heisenberg antiferromagnet (QHAF) on the kagomé lattice is still elusive and intensively debated. Exact diagonalization studies have revealed a magnetically disordered ground state and a huge number of singlet excitations below the triplet gap [18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Using approximate numerical techniques various claims as to the nature of the ground state have been made.…”

Section: Introductionmentioning

confidence: 99%

Valence-bond crystals in the kagomé spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study

2012

View full text Add to dashboard Cite

In this paper, we do a complete classification of valence-bond crystals (VBCs) on the kagomé lattice based on general arguments of symmetry only and thus identify many new VBCs for different unit cell sizes. For the spin-1/2 Heisenberg antiferromagnet, we study the relative energetics of competing gapless spin liquids (SLs) and VBC phases within the class of Gutzwillerprojected fermionic wave functions using variational Monte Carlo techniques, hence implementing exactly the constraint of one fermion per site. By using a state-of-the-art optimization method, we conclusively show that the U(1) Dirac SL is remarkably stable towards dimerizing into all 6-, 12-and 36-site unit cell VBCs. This stability is also preserved on addition of a next-nearest-neighbor super-exchange coupling of both antiferromagnetic and ferromagnetic (FM) type. However, we find that a 36-site unit cell VBC is stabilized on addition of a very small next-nearest-neighbor FM super-exchange coupling, i.e. |J 2 | ≈ 0.045, and this VBC is the same in terms of space-group symmetry as that obtained in an effective quantum dimer model study. It breaks reflection symmetry, has a nontrivial flux pattern and is a strong dimerization of the uniform RVB SL.

show abstract

“…Quantum Monte Carlo calculations face the sign problem. Sizes accessible by exact diagonalization [2, [35][36][37][38][39][40][41][42][43][44][45][46][47][48] are currently limited to 48. Other approaches diagonalized the valence bond basis or applied the contractor renormalization group (CORE) method, or the coupled cluster method (CCM) [49][50][51][52][53][54][55].…”

mentioning

confidence: 99%

Nature of the Spin-Liquid Ground State of theS=1/2Heisenberg Model on the Kagome Lattice

2012

View full text Add to dashboard Cite

We perform a density-matrix renormalization group (DMRG) study of the S=1/2 Heisenberg antiferromagnet on the kagome lattice to identify the conjectured spin liquid ground state. Exploiting SU(2) spin symmetry, which allows us to keep up to 16,000 DMRG states, we consider cylinders with circumferences up to 17 lattice spacings and find a spin liquid ground state with an estimated per site energy of -0.4386(5), a spin gap of 0.13(1), very short-range decay in spin, dimer and chiral correlation functions, and finite topological entanglement γ consistent with γ=log(2)2, ruling out gapless, chiral, or nontopological spin liquids in favor of a topological spin liquid of quantum dimension 2, with strong evidence for a gapped topological Z(2) spin liquid.

show abstract

Ground states and excitations of a one-dimensionalkagomé-like antiferromagnet

Cited by 38 publications

References 39 publications

Heisenberg antiferromagnet with anisotropic exchange on the kagomé lattice: Description of the magnetic properties of volborthite

Heisenberg antiferromagnet with anisotropic exchange on the kagomé lattice: Description of the magnetic properties of volborthite

Valence-bond crystals in the kagomé spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study

Nature of the Spin-Liquid Ground State of theS=1/2Heisenberg Model on the Kagome Lattice

Contact Info

Product

Resources

About