Trimerized ground state of the spin-1 Heisenberg antiferromagnet on the kagome lattice

Changlani, Hitesh J.; Läuchli, Andreas M.

doi:10.1103/physrevb.91.100407

Cited by 48 publications

(64 citation statements)

References 44 publications

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“…I, the S = 1 Heisenberg model on the kagome lattice has recently attracted strong attention. Older proposals for the ground state, including the hexagonal singlet solid [22] and the resonating AKLT loop state [23,24], appear to have been supplanted by a trimerized simplex-solid state [25][26][27], which has the best variational energy, E k 0 = −1.4116(4) [26]. This is a symmetry-broken state with trimerization order, which as above can be defined by the difference of the average energies between up-and down-triangle simplices, quoted in Ref.…”

Section: B S =mentioning

confidence: 99%

“…Recently, and in part with a view to solving this conundrum, more attention has also been paid to kagome Heisenberg antiferromagnets with higher spins [20,21]. Various proposals have been put forward for the spin-1 case, including the hexagonal singlet solid state [22], the resonating AKLT loop state [23,24], and the trimerized simplex-solid state [25][26][27], among which the last has the best variational energy [26,27]. For the S = 2 case, a coupled-cluster calculation suggested that the ground state has √ 3 × √ 3 antiferromagnetic order [28], whereas the infinite Projected Entangled Pair States (iPEPS) algorithm indicates a (topologically trivial) spin liquid with a spin gap and no symmetry breaking [21].…”

Section: Introductionmentioning

confidence: 99%

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Heisenberg antiferromagnet on the Husimi lattice

et al. 2016

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We perform a systematic study of the antiferromagnetic Heisenberg model on the Husimi lattice using numerical tensor-network methods based on Projected Entangled Simplex States (PESS). The nature of the ground state varies strongly with the spin quantum number, S. For S = 1/2, it is an algebraic (gapless) quantum spin liquid. For S = 1, it is a gapped, non-magnetic state with spontaneous breaking of triangle symmetry (a trimerized simplex-solid state). For S = 2, it is a simplex-solid state with a spin gap and no symmetry-breaking; both integer-spin simplex-solid states are characterized by specific degeneracies in the entanglement spectrum. For S = 3/2, and indeed for all spin values S ≥ 5/2, the ground states have 120-degree antiferromagnetic order. In a finite magnetic field, we find that, irrespective of the value of S, there is always a plateau in the magnetization at m = 1/3.

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Section: B S =mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Heisenberg antiferromagnet on the Husimi lattice

et al. 2016

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“…The physics of the spin-one cousin of the Heisenberg model on the kagome lattice has been focused on recently [3][4][5][6][7][8][9] . Interestingly, several works point towards a spontanenous trimerization of the system 7-9 , i.e.…”

Section: Introductionmentioning

confidence: 99%

Nonperturbative linked-cluster expansions for the trimerized ground state of the spin-one kagome Heisenberg model

Ixert¹,

Tischler

Schmidt

2015

Phys. Rev. B

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We use non-perturbative linked-cluster expansions to determine the ground-state energy per site of the spin-one Heisenberg model on the kagome lattice. To this end, a parameter is introduced allowing to interpolate between a fully trimerized state and the isotropic model. The ground-state energy per site of the full graph decomposition up to graphs of six triangles (18 spins) displays a complex behaviour as a function of this parameter close to the isotropic model which we attribute to divergencies of partial series in the graph expansion of quasi-1d unfrustrated chain graphs. More concretely, these divergencies can be traced back to a quantum critical point of the one-dimensional unfrustrated chain of coupled triangles. Interestingly, the reorganization of the non-perturbative linked-cluster expansion in terms of clusters with enhanced symmetry yields a ground-state energy per site of the isotropic two-dimensional model being in quantitative agreement with other numerical approaches in favor of a spontaneous trimerization of the system. Our findings are of general importance for any non-perturbative linked-cluster expansion on geometrically frustrated systems.

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“…Meanwhile, the high spin (S > 1/2) kagome physics has also gained great interest currently. For the spin-1 KHAF, the ground state was shown to be a nonmagnetic simplex valence bond crystal with geometric inversion symmetry breaking [13][14][15][16][17][18]. For the spin-S KHAF, the magnetization curves [19] up to S = 2 have been obtained with tensor network methods based on the infinite projected entangled pair states (iPEPS) [20,21].…”

Section: Introductionmentioning

confidence: 99%

Spin-ordered ground state and thermodynamic behaviors of the spin-32kagome Heisenberg antiferromagnet

Liu

2016

Phys. Rev. E

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Three different tensor network (TN) optimization algorithms are employed to accurately determine the ground state and thermodynamic properties of the spin-3/2 kagome Heisenberg antiferromagnet. We found that the √ 3 × √ 3 state (i.e., the state with 120 • spin configuration within a unit cell containing 9 sites) is the ground state of this system, and such an ordered state is melted at any finite temperature, thereby clarifying the existing experimental controversies. Three magnetization plateaus (m/m s = 1/3, 23/27, and 25/27) were obtained, where the 1/3-magnetization plateau has been observed experimentally. The absence of a zero-magnetization plateau indicates a gapless spin excitation that is further supported by the thermodynamic asymptotic behaviors of the susceptibility and specific heat. At low temperatures, the specific heat is shown to exhibit a T 2 behavior, and the susceptibility approaches a finite constant as T → 0. Our TN results of thermodynamic properties are compared with those from high temperature series expansion. In addition, we disclose a quantum phase transition between q = 0 state (i.e. the state with 120 • spin configuration within a unit cell containing three sites) and √ 3 × √ 3 state in a spin-3/2 kagome XXZ model at the critical point ∆ c = 0.54. This study provides reliable and useful information for further explorations on high spin kagome physics.

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Trimerized ground state of the spin-1 Heisenberg antiferromagnet on the kagome lattice

Cited by 48 publications

References 44 publications

Heisenberg antiferromagnet on the Husimi lattice

Heisenberg antiferromagnet on the Husimi lattice

Nonperturbative linked-cluster expansions for the trimerized ground state of the spin-one kagome Heisenberg model

Spin-ordered ground state and thermodynamic behaviors of the spin-32kagome Heisenberg antiferromagnet

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