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Title: Majorana chain and Ising model - (non-invertible) translations, anomalies, and emanant symmetries

Abstract

We study the symmetries of closed Majorana chains in 1+1d, including the translation, fermion parity, spatial parity, and time-reversal symmetries. The algebra of the symmetry operators is realized projectively on the Hilbert space, signaling anomalies on the lattice, and constraining the long-distance behavior. In the special case of the free Hamiltonian (and small deformations thereof), the continuum limit is the 1+1d free Majorana CFT. Its continuum chiral fermion parity (-1)^{F_L} ( − 1 ) F L emanates from the lattice translation symmetry. We find a lattice precursor of its mod 8 ’t Hooft anomaly. Using a Jordan-Wigner transformation, we sum over the spin structures of the lattice model (a procedure known as the GSO projection), while carefully tracking the global symmetries. In the resulting bosonic model of Ising spins, the Majorana translation operator leads to a non-invertible lattice translation symmetry at the critical point. The non-invertible Kramers-Wannier duality operator of the continuum Ising CFT emanates from this non-invertible lattice translation of the transverse-field Ising model.

Authors:
;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
2317717
Grant/Contract Number:  
SC0009988
Resource Type:
Published Article
Journal Name:
SciPost Physics
Additional Journal Information:
Journal Name: SciPost Physics Journal Volume: 16 Journal Issue: 3; Journal ID: ISSN 2542-4653
Publisher:
Stichting SciPost
Country of Publication:
Netherlands
Language:
English

Citation Formats

Seiberg, Nathan, and Shao, Shu-Heng. Majorana chain and Ising model - (non-invertible) translations, anomalies, and emanant symmetries. Netherlands: N. p., 2024. Web. doi:10.21468/SciPostPhys.16.3.064.
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Seiberg, Nathan, & Shao, Shu-Heng. Majorana chain and Ising model - (non-invertible) translations, anomalies, and emanant symmetries. Netherlands. https://doi.org/10.21468/SciPostPhys.16.3.064
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Seiberg, Nathan, and Shao, Shu-Heng. Fri . "Majorana chain and Ising model - (non-invertible) translations, anomalies, and emanant symmetries". Netherlands. https://doi.org/10.21468/SciPostPhys.16.3.064.
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@article{osti_2317717,
title = {Majorana chain and Ising model - (non-invertible) translations, anomalies, and emanant symmetries},
author = {Seiberg, Nathan and Shao, Shu-Heng},
abstractNote = {We study the symmetries of closed Majorana chains in 1+1d, including the translation, fermion parity, spatial parity, and time-reversal symmetries. The algebra of the symmetry operators is realized projectively on the Hilbert space, signaling anomalies on the lattice, and constraining the long-distance behavior. In the special case of the free Hamiltonian (and small deformations thereof), the continuum limit is the 1+1d free Majorana CFT. Its continuum chiral fermion parity (-1)^{F_L} ( − 1 ) F L emanates from the lattice translation symmetry. We find a lattice precursor of its mod 8 ’t Hooft anomaly. Using a Jordan-Wigner transformation, we sum over the spin structures of the lattice model (a procedure known as the GSO projection), while carefully tracking the global symmetries. In the resulting bosonic model of Ising spins, the Majorana translation operator leads to a non-invertible lattice translation symmetry at the critical point. The non-invertible Kramers-Wannier duality operator of the continuum Ising CFT emanates from this non-invertible lattice translation of the transverse-field Ising model.},
doi = {10.21468/SciPostPhys.16.3.064},
journal = {SciPost Physics},
number = 3,
volume = 16,
place = {Netherlands},
year = {Fri Mar 01 00:00:00 EST 2024},
month = {Fri Mar 01 00:00:00 EST 2024}
}
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