Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU$(N)$ Hubbard models
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| Format: | Preprint |
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2023
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| _version_ | 1866910296858165248 |
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| author | Mikkelsen, Mathias Danshita, Ippei |
| author_facet | Mikkelsen, Mathias Danshita, Ippei |
| contents | 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 $ρ$. 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 $ρ=1$ at intermediate and large lattice sizes on the basis of numeric and semi-analytic arguments. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2301_09807 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU$(N)$ Hubbard models Mikkelsen, Mathias Danshita, Ippei Quantum Gases Strongly Correlated Electrons 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 $ρ$. 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 $ρ=1$ at intermediate and large lattice sizes on the basis of numeric and semi-analytic arguments. |
| title | Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU$(N)$ Hubbard models |
| topic | Quantum Gases Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2301.09807 |