Abstract

​In the first part of the talk I will introduce the basic idea of fractonic systems and show that the combination of charge and dipole conservation leads to an extensive fragmentation of the Hilbert space, which, in turn, can lead to a breakdown of thermalization. As a concrete example, we investigate the out-of-equilibrium dynamics of one-dimensional spin-1 models that conserve charge (total Sz) and its associated dipole moment, and show that for any finite range of interactions, the system exhibits nonthermal eigenstates appearing throughout the entire spectrum. In particular, we will consider a minimal model including only three-site terms and find that the infinite temperature autocorrelation saturates to a finite value—showcasing nonthermal behavior. This absence of thermalization is a consequence of the strong fragmentation of the Hilbert space into exponentially many invariant subspaces in the local Sz basis, arising from the interplay of dipole conservation and local interactions. We will then label these subspaces introducing the notion of `statistically localized integrals of motion’ (SLIOM) and study the effects of those in the dynamics. SLIO Ms are not spatially localized in the operator sense, but appear localized to sub-extensive regions when their expectation value is taken in typical states with a finite density of particles. We illustrate this general concept on several Hamiltonians, both with and without dipole conservation, and derive the presence of statistically localized strong zero modes. If time allows, I will motivate experimental realizations of these ideas.

The talk would be based on the following works: Phys. Rev. X 10 , 011047 [arXiv:1904.04266]; Phys. Rev. B 101 , 125126 [arXiv:1910.06341]