Haldane limits via Lagrangian embeddings

Bykov, Dmitri

doi:10.1016/j.nuclphysb.2011.10.005

Cited by 34 publications

(57 citation statements)

References 24 publications

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“…Only for a specific fine tuning of the couplings can Lorentz invariance be restored. These tuned models were the ones considered by Bykov in [39] and [40].…”

Section: Flavour Wave Theorymentioning

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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“…Only for a specific fine tuning of the couplings can Lorentz invariance be restored. These tuned models were the ones considered by Bykov in [39] and [40].…”

Section: Flavour Wave Theorymentioning

confidence: 99%

Generalization of the Haldane conjecture to SU(n) chains

et al. 2020

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“…Also, this restriction of symmetry is important to discuss the application of 2-flavor Schwinger model ( SU (2) level-1 Wess-Zumino-Witten (WZW) model) to (1 + 1)-dimensional anti-ferromagnetic quantum spin chain in the context of Haldane conjecture [67][68][69][70]. Its generalization to N -flavor case is important when we consider the generalization of Haldane conjecture to SU (N ) anti-ferromagnetic spin chain [54,[71][72][73][74]. We can readily find the anomaly of G sub .…”

Section: Discrete 'T Hooft Anomaly and Four-fermion Interactionmentioning

confidence: 99%

“…, e 2πi(N −1)/N ). This is related to the fermion field with the periodic boundary condition as 71) and the fermion kinetic term is given as…”

Section: Flavor-twisted Compactificationmentioning

confidence: 99%

Fractional θ angle, ’t Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model

Misumi

Tanizaki

Ünsal

2019

J. High Energ. Phys.

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This work examines non-perturbative dynamics of a 2-dimensional QFT by using discrete 't Hooft anomaly, semi-classics with circle compactification and bosonization. We focus on charge-q N -flavor Schwinger model, and also Wess-Zumino-Witten model. We first apply the recent developments of discrete 't Hooft anomaly matching to theories on R 2 and its compactification to R × S 1 L . We then compare the 't Hooft anomaly with dynamics of the models by explicitly constructing eigenstates and calculating physical quantities on the cylinder spacetime with periodic and flavor-twisted boundary conditions. We find different boundary conditions realize different anomalies. Especially under the twisted boundary conditions, there are N q vacua associated with discrete chiral symmetry breaking. Chiral condensates for this case have fractional θ dependence e iθ/N q , which provides the N q-branch structure with soft fermion mass. We show that these behaviors at a small circumference cannot be explained by usual instantons but should be understood by "quantum" instantons, which saturate the BPS bound between classical action and quantum-induced effective potential. The effects of the quantum-instantons match the exact results obtained via bosonization within the region of applicability of semi-classics. We also argue that large-N limit of the Schwinger model with twisted boundary conditions satisfy volume independence. arXiv:1905.05781v3 [hep-th]

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“…As shown in [2], this cohomology group can be described rather directly if one notes that there exists a Lagrangian embedding…”

Section: Topological Termsmentioning

confidence: 99%

“…Moreover, in this case it is a nearly Kähler manifold (see Section 4.4 below). Interestingly, it is precisely this metric that arose via the so-called Haldane limit of a spin chain in [2].…”

Section: Invariant Metrics and Formsmentioning

confidence: 99%

Integrable properties of σ-models with non-symmetric target spaces

Bykov

2015

Nuclear Physics B

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It is well known that σ -models with symmetric target spaces are classically integrable. With the example of the model with target space the flag manifold U(3) U(1) 3 -a non-symmetric space -we show that the introduction of torsion allows to cast the equations of motion in the form of a zero-curvature condition for a one-parameter family of connections, which can be a sign of integrability of the theory. We also elaborate on geometric aspects of the proposed model.

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Haldane limits via Lagrangian embeddings

Cited by 34 publications

References 24 publications

Generalization of the Haldane conjecture to SU(n) chains

Generalization of the Haldane conjecture to SU(n) chains

Fractional θ angle, ’t Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model

Integrable properties of σ-models with non-symmetric target spaces

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