Haldane Quantum Spin Chains

Renard, Jean‐Pierre; Regnault, L.P.

doi:10.1002/9783527620548.ch2

Cited by 16 publications

(21 citation statements)

References 166 publications

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“…Haldane argued that, in fact, the model was massless for θ = π, an unexpected result, which might have implications for QCD at θ = π. Ironically, the surprise to the condensed matter community was the massive behaviour for integer s and the surprise to the high energy community was the massless behaviour for θ = π! In the following years, Haldane's results have been confirmed experimentally, with the measurement of gaps for quasi-1D spin-1 chains [9], and numerically for chains of s = 1 and higher [10][11][12][13][14][15]. The field theory prediction has also been confirmed numerically [16][17][18][19][20][21] by Monte Carlo calculations, although the topological term presents severe challenges since the Boltzmann factor is not positive-definite for θ 0.…”

Section: Introductionmentioning

confidence: 72%

Generalization of the Haldane conjecture to SU(3) chains

Wamer¹,

Lajkó²,

Mila³

et al. 2017

Nuclear Physics B

118

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We apply field theory methods to SU(3) chains in the symmetric representation, with p boxes in the Young tableau, mapping them into a flag manifold nonlinear σ-model with a topological angle θ = 2πp/3. Generalizing the Haldane conjecture, we argue that the models are gapped for p = 3m but gapless for p = 3m ± 1 (for integer m), corresponding to a massless phase of the σ-model at θ = ±2π/3. We confirm this with Monte Carlo calculations on the σ-model. Figure 4: Breaking translational symmetry of the system by weakening the nearest neighbour bonds between sublattices 1 and 3. The R 13 mirror symmetry and a three site translational symmetry still remains.

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Section: Introductionmentioning

confidence: 72%

Generalization of the Haldane conjecture to SU(3) chains

Wamer¹,

Lajkó²,

Mila³

et al. 2017

Nuclear Physics B

118

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show abstract

“…In the past three decades, a plethora of experimental work has explored the existence of the Haldane gap and fractional edge excitations in materials containing quasi-one-dimensional (1D) S = 1 chains of transition metal ions 15 , employing ensemble probes such as neutron scattering, electron spin resonance and thermodynamic property measurements. However, magnetic anisotropy of transition metal ions and a finite interchain magnetic exchange, inherently present in these materials, are detrimental for the emergence of the Haldane phase.…”

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confidence: 99%

“…3 and Supplementary Figs. [7][8][9][10][11][12][13][14][15][16][17][18], and eight cTSCs with N = 5, 6, 12, 13, 14, 15, 16 and 47 (Fig. 4 and Supplementary Figs.…”

mentioning

confidence: 99%

Observation of fractional edge excitations in nanographene spin chains

Mishra

Catarina

et al. 2021

Nature

149

162

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Fractionalization is a phenomenon in which strong interactions in a quantum system drive the emergence of excitations with quantum numbers that are absent in the building blocks.Outstanding examples are excitations with charge e/3 in the fractional quantum Hall effect 1,2 , solitons in one-dimensional conducting polymers 3,4 and Majorana states in topological superconductors 5 . Fractionalization is also predicted to manifest itself in lowdimensional quantum magnets, such as one-dimensional antiferromagnetic S = 1 chains.

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“…See Figure 5 for the case n = p = 3. Additionally, for p not a multiple of n, with r := n/ gcd(n, p), Hamiltonians are constructed with r-fold degenerate ground states that are invariant under translations by r sites (see Figures 3,4). All of these models have short range correlations, and are expected to have gapped ground states, based on arguments of spinon confinement.…”

Section: B Aklt Constructionsmentioning

confidence: 99%

Generalization of the Haldane conjecture to SU(n) chains

et al. 2020

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Recently, SU(3) chains in the symmetric and self-conjugate representations have been studied using field theory techniques. For certain representations, namely rank-p symmetric ones with p not a multiple of 3, it was argued that the ground state exhibits gapless excitations. For the remaining representations considered, a finite energy gap exists above the ground state. In this paper, we extend these results to SU(n) chains in the symmetric representation. For a rank-p symmetric representation with n and p coprime, we predict gapless excitations above the ground state. If p is a multiple of n, we predict a unique ground state with a finite energy gap. Finally, if p and n have a greatest common divisor 1 < q < n, we predict a ground state degeneracy of n/q, with a finite energy gap. To arrive at these results, we derive a non-Lorentz invariant flag manifold sigma model description of the SU(n) chains, and use the renormalization group to show that Lorentz invariance is restored at low energies. We then make use of recently developed anomaly matching conditions for these Lorentz-invariant models. We also review the Lieb-Shultz-Mattis-Affleck theorem, and extend it to SU(n) models with longer range interactions. arXiv:1910.08196v2 [cond-mat.str-el]

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Haldane Quantum Spin Chains

Cited by 16 publications

References 166 publications

Generalization of the Haldane conjecture to SU(3) chains

Generalization of the Haldane conjecture to SU(3) chains

Observation of fractional edge excitations in nanographene spin chains

Generalization of the Haldane conjecture to SU(n) chains

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