On the Equivalence between Spin and Charge Dynamics of the Fermi Hubbard Model

TL;DR

This paper proves a theorem demonstrating the conditions under which spin and charge transport in the Fermi Hubbard model are equivalent, linking recent experimental measurements through a symmetry-based theoretical framework.

Contribution

It introduces a theorem showing the equivalence of spin and charge transport in the Fermi Hubbard model using particle-hole transformation and a dynamical symmetry.

Findings

Theoretical proof of spin-charge transport equivalence.

Potential for experimental verification with cold atom systems.

Connection between recent experimental measurements and underlying symmetries.

Abstract

Utilizing the Fermi gas microscope, recently the MIT group has measured the spin transport of the Fermi Hubbard model starting from a spin-density-wave state, and the Princeton group has measured the charge transport of the Fermi Hubbard model starting from a charge-density-wave state. Motivated by these two experiments, we prove a theorem that shows under certain conditions, the spin and charge transports can be equivalent to each other. The proof makes use of the particle-hole transformation of the Fermi Hubbard model and a recently discovered symmetry protected dynamical symmetry. Our results can be directly verified in future cold atom experiment with the Fermi gas microscope.