Mass generation by fractional instantons in SU(
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) chains

Wamer, Kyle; Affleck, Ian

doi:10.1103/physrevb.101.245143

Cited by 13 publications

(17 citation statements)

References 16 publications

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“…30,32 A gapless phase in the SU(N ) 1 universality class has been predicted for model (18) when p and N are coprime while a spectral gap is formed in other situations. 31,60,61 We thus expect that the perturbed CFT ( 14) is a massive field theory in the far-infrared regime since p = N here.…”

Section: Wzwn Model and Sigma Model On A Flag Manifoldmentioning

confidence: 95%

“…The generalization of the Haldane conjecture for SU(N ) is described by three different cases depending on the value of n Y with respect to N . [29][30][31] When n Y and N are coprime, both a semiclassical approach of model (1) in Refs. 30-32 and a CFT analysis 33,34 have shown that a quantum critical behavior in the SU(N ) 1 universality class with central charge c = N − 1 emerges.…”

Section: Introductionmentioning

confidence: 99%

“…The one-step translation symmetry T a0 of model ( 1) is spontaneously broken resulting in a ground-state degeneracy. 31,34 The last case, the most interesting for us, is when n Y = 0 mod N and a "Haldane gap" phase is expected. 29 For these representations, the continuous symmetry group of model ( 1) is the projective unitary group PSU(N ) and the N − 1 different SPT phases might be found in the lattice model (1).…”

Section: Introductionmentioning

confidence: 99%

“…In the N = 3 case, the operator(31) corresponds to an SU(3) spin which belongs to the adjoint representation with quadratic Casimir C 2 (adj) = 3. For N = 4, the quadratic Casimir (32) is 15/2 corresponding to the self-conjugate SU(4) representation 64 such that 64 ←→ .…”

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confidence: 99%

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Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach

Fromholz,

Lecheminant

2020

Preprint

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The nature of symmetry-protected topological phases of Heisenberg spin chains in totally symmetric representations of rank N of the SU(N ) group is investigated through a Majorana fermion study starting from an integrable point. The latter approach generalizes the one pioneered by Tsvelik [A. M. Tsvelik, Phys. Rev. B 42, 10 499 (1990)] to describe the low-energy properties of the Haldane phase of the spin-1 Heisenberg chain from three massive Majorana fermions. We find for all N the emergence of a non-degenerate gapped phase with edge states whose topological protection depends on the parity of N . While for N odd there is no such protection, the phase with even N is shown to be topologically protected. We find that the phase belongs to the same topological class as the phase with edge states living in self-conjugate fully antisymmetric representation of the SU(N ) group.

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Section: Wzwn Model and Sigma Model On A Flag Manifoldmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach

Fromholz,

Lecheminant

2020

Preprint

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“…In the process of completing this paper, we became aware of ref [80],. which gives a description of flag manifold sigma models, where fractional vortex instantons associated with νa ∈ Γw gaps out the theory.…”

mentioning

confidence: 99%

Strongly coupled QFT dynamics via TQFT coupling

Ünsal

2021

J. High Energ. Phys.

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We consider a class of quantum field theories and quantum mechanics, which we couple to ℤN topological QFTs, in order to classify non-perturbative effects in the original theory. The ℤN TQFT structure arises naturally from turning on a classical background field for a ℤN 0- or 1-form global symmetry. In SU(N) Yang-Mills theory coupled to ℤN TQFT, the non-perturbative expansion parameter is exp[−SI/N] = exp[−8π2/g2N] both in the semi-classical weak coupling domain and strong coupling domain, corresponding to a fractional topological charge configurations. To classify the non-perturbative effects in original SU(N) theory, we must use PSU(N) bundle and lift configurations (critical points at infinity) for which there is no obstruction back to SU(N). These provide a refinement of instanton sums: integer topological charge, but crucially fractional action configurations contribute, providing a TQFT protected generalization of resurgent semi-classical expansion to strong coupling. Monopole-instantons (or fractional instantons) on T3 × $$ {S}_L^1 $$ S L 1 can be interpreted as tunneling events in the ’t Hooft flux background in the PSU(N) bundle. The construction provides a new perspective to the strong coupling regime of QFTs and resolves a number of old standing issues, especially, fixes the conflicts between the large-N and instanton analysis. We derive the mass gap at θ = 0 and gaplessness at θ = π in $$ \mathbbm{CP} $$ CP 1 model, and mass gap for arbitrary θ in $$ \mathbbm{CP} $$ CP N−1, N ≥ 3 on ℝ2.

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An Improved Infinite Time-Evolving Block Decimation Algorithm Applied to SU(N) Antiferromagnetic Heisenberg Chains

Lin,

2024

J Low Temp Phys

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Mass generation by fractional instantons in SU( n ) chains

Cited by 13 publications

References 16 publications

Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach

Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach

Strongly coupled QFT dynamics via TQFT coupling

An Improved Infinite Time-Evolving Block Decimation Algorithm Applied to SU(N) Antiferromagnetic Heisenberg Chains

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