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

Seiberg, Nathan; Shao, Shu-Heng

doi:10.21468/SciPostPhys.16.3.064

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

Journal Article · Fri Mar 01 00:00:00 EST 2024 · SciPost Physics

DOI:https://doi.org/10.21468/SciPostPhys.16.3.064· OSTI ID:2317717

Seiberg, Nathan; Shao, Shu-Heng

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.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0009988

OSTI ID:: 2317717

Journal Information:: SciPost Physics, Journal Name: SciPost Physics Vol. 16 Journal Issue: 3; ISSN 2542-4653

Publisher:: Stichting SciPostCopyright Statement

Country of Publication:: Netherlands

Language:: English

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