Hilbert-Space Fragmentation from Strict Confinement

TitleHilbert-Space Fragmentation from Strict Confinement
Publication TypeJournal Article
Year of Publication2020
AuthorsYang, Z-C, Liu, F, Gorshkov, AV, Iadecola, T
JournalPhys. Rev. Lett.
Date Published5/22/2020

We study one-dimensional spin-1/2 models in which strict confinement of Ising domain walls leads to the fragmentation of Hilbert space into exponentially many disconnected subspaces. Whereas most of the previous works emphasize dipole moment conservation as an essential ingredient for such fragmentation, we instead require two commuting U(1) conserved quantities associated with the total domain-wall number and the total magnetization. The latter arises naturally from the confinement of domain walls. Remarkably, while some connected components of the Hilbert space thermalize, others are integrable by Bethe ansatz. We further demonstrate how this Hilbert-space fragmentation pattern arises perturbatively in the confining limit of Z2 gauge theory coupled to fermionic matter, leading to a hierarchy of time scales for motion of the fermions. This model can be realized experimentally in two complementary settings.