Integrals of motion in dipole-conserving models

P. Łydżba,1 P. Prelovšek,1 M. Mierzejewski2

1Institute of Theoretical Physics, Wroclaw University of Science and Technology, 50-370 Wroclaw, Poland

2Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia

The Hilbert space fragmentation, for which the Hamiltonian shatters into exponentially many blocks in the site occupation basis, can result in the breakdown of thermalization. In this presentation, we focus on the pair-hopping (PH) model, a paradigmatic model of the Hilbert-space fragmentation. Furthermore, it can be derived as an effective model of the Stark chain, imposing strict conservation of the dipole moment. Notably, the non-vanishing autocorrelation functions in the PH model, as reported in [1], suggests the existence of local or quasilocal integrals of motion (IOMs). Hence, we propose a numerical algorithm that establishes all IOMs linear in a given set of operators. We employ it to demonstrate that the density modes in the PH model are frozen and become strict IOMs in the thermodynanic limit. Nevertheless, these modes become subdiffusive after incorporating higher-order corrections the PH model. Finally, we make a connection with the Stark model. We demonstrate that although both energy and dipole moment are conserved in the thermodynamic limit [2], the Stark chain supports only one IOM.

1. P. Sala et al., Physical Review X 10 (2020)
2. S. Nandy et al., arXiv:2310.01862 (2023)