TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.4.098
TI  - Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries
PY  - 2024/04/09
UR  - https://www.scipost.org/SciPostPhys.16.4.098
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 4
SP  - 098
A1  - Seifnashri, Sahand
AB  - We study 't Hooft anomalies of global symmetries in 1+1d lattice Hamiltonian systems. We consider anomalies in internal and lattice translation symmetries. We derive a microscopic formula for the "anomaly cocycle" using topological defects implementing twisted boundary conditions. The anomaly takes value in the cohomology group $H^3(G,U(1)) × H^2(G,U(1))$. The first factor captures the anomaly in the internal symmetry group $G$, and the second factor corresponds to a generalized Lieb-Schultz-Mattis anomaly involving $G$ and lattice translation. We present a systematic procedure to gauge internal symmetries (that may not act on-site) on the lattice. We show that the anomaly cocycle is the obstruction to gauging the internal symmetry while preserving the lattice translation symmetry. As an application, we construct anomaly-free chiral lattice gauge theories. We demonstrate a one-to-one correspondence between (locality-preserving) symmetry operators and topological defects, which is essential for the results we prove. We also discuss the generalization to fermionic theories. Finally, we construct non-invertible lattice translation symmetries by gauging internal symmetries with a Lieb-Schultz-Mattis anomaly.
ER  -

@Article{10.21468/SciPostPhys.16.4.098,
	title={{Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries}},
	author={Sahand Seifnashri},
	journal={SciPost Phys.},
	volume={16},
	pages={098},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.4.098},
	url={https://scipost.org/10.21468/SciPostPhys.16.4.098},
}