TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.6.154
TI  - Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
PY  - 2024/06/17
UR  - https://scipost.org/SciPostPhys.16.6.154
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 6
SP  - 154
A1  - Seiberg, Nathan
AU  - Seifnashri, Sahand
AU  - Shao, Shu-Heng
AB  - We discuss the exact non-invertible Kramers-Wannier symmetry of 1+1d lattice models on a tensor product Hilbert space of qubits. This symmetry is associated with a topological defect and a conserved operator, and the latter can be presented as a matrix product operator. Importantly, unlike its continuum counterpart, the symmetry algebra involves lattice translations. Consequently, it is not described by a fusion category. In the presence of this defect, the symmetry algebra involving parity/time-reversal is realized projectively, which is reminiscent of an anomaly. Different Hamiltonians with the same lattice non-invertible symmetry can flow in their continuum limits to infinitely many different fusion categories (with different Frobenius-Schur indicators), including, as a special case, the Ising CFT. The non-invertible symmetry leads to a constraint similar to that of Lieb-Schultz-Mattis, implying that the system cannot have a unique gapped ground state. It is either in a gapless phase or in a gapped phase with three (or a multiple of three) ground states, associated with the spontaneous breaking of the lattice non-invertible symmetry.
ER  -

@Article{10.21468/SciPostPhys.16.6.154,
	title={{Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space}},
	author={Nathan Seiberg and Sahand Seifnashri and Shu-Heng Shao},
	journal={SciPost Phys.},
	volume={16},
	pages={154},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.6.154},
	url={https://scipost.org/10.21468/SciPostPhys.16.6.154},
}