Generalization of the Haldane conjecture to SU(3) chains

Wamer, Kyle; Lajkó, Miklós; Mila, Frédéric; Affleck, Ian

doi:10.1016/j.nuclphysb.2017.09.015

Cited by 54 publications

(132 citation statements)

References 109 publications

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“…A more recent and advanced suggestion that any symmetric representation of the SU(3) spin with a single row of Young tableau boxes of length p not equal to a multiple of 3 should give a gapless spectrum [43,44] is consistent with our observation, since both ULS and pure trimer models are written in the fundamental representation of SU(3) with p = 1. This symmetry is presumably lowered to U(1)×U (1) angle θ moves away from π/2.…”

Section: Trimer Liquid Phasesupporting

confidence: 90%

Proposal of a spin-one chain model with competing dimer and trimer interactions

Katsura

Lee

et al. 2017

Phys. Rev. B

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A new kind of spin-1 chain Hamiltonian consisting of competing dimer and trimer projection operators is proposed. As the relative strengths and signs of the interactions are varied, the model exhibits a number of different phases including the gapped dimer phase and the gapless trimer phase with critical correlations described by a conformal field theory with central charge c = 2. A symmetry-protected topological phase also exists in this model, even though the microscopic interactions are not the simple adiabatic extensions of the well-known Heisenberg and the AffleckKennedy-Lieb-Tasaki model and contains both two-and three-particle permutations. A fourth phase is characterized by macroscopically degenerate ground states. While bearing almost a oneto-one resemblance to the phase diagram of the bilinear-biquadratic spin-1 chain Hamiltonian, our model is rooted on very different physical origin, namely the two competing tendencies of spin-1 particles to form singlets through either dimer or trimer formation.

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Section: Trimer Liquid Phasesupporting

confidence: 90%

Proposal of a spin-one chain model with competing dimer and trimer interactions

Katsura

Lee

et al. 2017

Phys. Rev. B

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“…In this article, we generalize Haldane's conjecture to SU(n) chains in the rank-p symmetric representations ( Figure 1, left), following the methodology presented in [12]. Our main result is the prediction of gapless excitations above the ground state when p and n have no common divisor greater than 1.…”

Section: Introductionmentioning

confidence: 78%

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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“…But if we take M 2 < 0 the scalar fields condense and we obtain the CP 1 model at θ = π. This flows to a conformal field theory which is the SU (2) 1 WZW model (see [23] for the references on this classic result). The symmetry of the infrared model is SO (4) in which the ultraviolet O(3) symmetry is contained.…”

Section: A Majorana Fermion In 2 + 1 Dimensionsmentioning

confidence: 98%

Anomaly matching in the symmetry broken phase: Domain walls, CPT, and the Smith isomorphism

2020

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Symmetries in Quantum Field Theory may have 't Hooft anomalies. If the symmetry is unbroken in the vacuum, the anomaly implies a nontrivial low-energy limit, such as gapless modes or a topological field theory. If the symmetry is spontaneously broken, for the continuous case, the anomaly implies low-energy theorems about certain couplings of the Goldstone modes. Here we study the case of spontaneously broken discrete symmetries, such as Z2 and T . Symmetry breaking leads to domain walls, and the physics of the domain walls is constrained by the anomaly. We investigate how the physics of the domain walls leads to a matching of the original discrete anomaly. We analyze the symmetry structure on the domain wall, which requires a careful analysis of some properties of the unbreakable CP T symmetry. We demonstrate the general results on some examples and we explain in detail the mod 4 periodic structure that arises in the Z2 and T case. This gives a physical interpretation for the Smith isomorphism, which we also extend to more general abelian groups. We show that via symmetry breaking and the analysis of the physics on the wall, the computations of certain discrete anomalies are greatly simplified. Using these results we perform new consistency checks on the infrared phases of 2 + 1 dimensional QCD. * which by construction leaves the boundary conditions invariant and therefore indeed acts on the wall! But observe that this is an anti-unitary symmetry, since CP ⊥ T is anti-unitary. Thus, the correct answer to the question about the fate of the spontaneously broken, unitary, Z 2 symmetry is that it becomes some anti-unitary symmetry acting on the wall.By the same argument, if we began with a spontaneously broken anti-unitary Z 2 symmetry, the domain wall would inherit a unitary Z 2 symmetry. In fact, we will derive a 4-periodic dimensional

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Generalization of the Haldane conjecture to SU(3) chains

Cited by 54 publications

References 109 publications

Proposal of a spin-one chain model with competing dimer and trimer interactions

Proposal of a spin-one chain model with competing dimer and trimer interactions

Generalization of the Haldane conjecture to SU(n) chains

Anomaly matching in the symmetry broken phase: Domain walls, CPT, and the Smith isomorphism

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