Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU$(N)$ Hubbard models
| Autor: | Mikkelsen, Mathias, Danshita, Ippei |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Phys. Rev. A 107, 043313 (2023) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevA.107.043313 |
| Popis: | It is well established that the noise correlations measured by time-of-flight imaging in cold-atom experiments, which correspond to the density-density correlations in the momentum space of trapped atomic gases, can probe the spin structure factor deep in the Mott-insulating regime of SU(2) Hubbard models. We explicitly derive the mathematical relation between the noise correlations and the spin structure factor in the strong-interaction limit of SU$(N)$ Hubbard models at any integer filling $\rho$. By calculating the ground states of one-dimensional SU$(N)$ Fermi-Hubbard models for $2\leq N\leq 6$ with use of the density-matrix renormalization-group method, we confirm the relation numerically in the regime of strong interactions $U \gg t$, where $U$ and $t$ denote the onsite interaction and the hopping energy. We show that the deviation between the actual noise correlations and those obtained from the spin structure factor scales as approximately $(t/U)^2$ for $\rho=1$ at intermediate and large lattice sizes on the basis of numeric and semi-analytic arguments. Comment: 11 pages, 3 figures. Fixed sign error in eqs. (14,16,17,18). This error had no effect on any of the numerical results or conclusions |
| Databáze: | arXiv |
| Externí odkaz: |
|