Speaker: Carolyn Zhang (Harvard)
Title: Non-onsiteable symmetries and symmetry-protected quantum cellular automata (and beyond)
Abstract:
We study the correspondence between non-onsiteable symmetries in $d$ spatial dimensions and symmetry-protected quantum cellular automata in one higher dimension, using this correspondence to obtain "fixed point" examples of non-onsiteable (but non-anomalous) finite symmetries in 2+1d. We then discuss an example of a $U(1)$ protected locality-preserving unitary in 3+1d that necessarily involves exponential tails; it is not a QCA because it cannot be made to preserve strict locality. This $U(1)$ QCA leads to a class of 2+1d non-onsiteable (but non-anomalous) $U(1)$ symmetries that may lie beyond the recent cohomological classification of such symmetries.