An obstruction to realizing anomalous symmetries in 1+1d lattice models

Realizing quantum field theories on lattice models is important for several reasons, ranging from enabling non-perturbative studies of field theories to quantum simulations. However, it is well known that not all quantum field theories can be realized on a lattice (for example, Nielsen-Ninomiya theorem).

 

In this talk, I will consider a very special aspect of this problem. Given a symmetry described by a group G with a specific choice of ’t Hooft anomaly, can it be realized in a quantum spin system, i.e., a lattice model whose Hilbert space is a tensor product of finite-dimensional Hilbert spaces associated with each site? I will describe an explicit constraint which shows that certain anomalous symmetries cannot be realized in such lattice models. 

 

This talk is based on https://arxiv.org/pdf/2602.13948 (also, https://arxiv.org/pdf/2401.02533 and https://arxiv.org/pdf/1409.5436).