Canted magnetism and $\mathbb{Z}_2$ fractionalization in metallic states of the Lieb lattice Hubbard model near quarter filling
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2025
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| _version_ | 1866912490122641408 |
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| author | Nikolaenko, Alexander Bonetti, Pietro M. Kale, Anant Lebrat, Martin Greiner, Markus Sachdev, Subir |
| author_facet | Nikolaenko, Alexander Bonetti, Pietro M. Kale, Anant Lebrat, Martin Greiner, Markus Sachdev, Subir |
| contents | A recent experiment has examined ultracold, fermionic, spin-1/2 $^6$Li atoms in the Lieb lattice at different Hubbard repulsion $U$ and filling fractions $ν$ (Lebrat et al. arXiv:2404.17555). At $ν=1/2$ and small $U$, they observe an enhanced compressibility on the $p_{x,y}$ sites, pointing to a flat band near the Fermi energy. At $ν=1/2$ and large $U$ they observe an insulating ferrimagnet. Both small and large $U$ observations at $ν=1/2$ are consistent with theoretical expectations. Surprisingly, near $ν=1/4$ and large $U$, they again observe a large $p_{x,y}$ compressibility, pointing to a flat $p_{x,y}$ band of fermions across the Fermi energy. Our Hartree-Fock computations near $ν=1/4$ find states with canted magnetism (and related spiral states) at large $U$, which possess nearly flat $p_{x,y}$ bands near the Fermi level. We employ parton theories to describe quantum fluctuations of the magnetic order found in Hartree-Fock. We find a metallic state with $\mathbb{Z}_2$ fractionalization possessing gapless, fermionic, spinless `chargons' carrying $\mathbb{Z}_2$ gauge charges which have a nearly flat $p_{x,y}$ band near their Fermi level: this fractionalized metal is also consistent with observations. Our DMRG study does not indicate the presence of magnetic order, and so supports a fractionalized ground state. Given the conventional ferrimagnetic insulator at $ν=1/2$, the $\mathbb{Z}_2$ fractionalized metal at $ν=1/4$ represents a remarkable realization of doping-induced fractionalization. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_12235 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Canted magnetism and $\mathbb{Z}_2$ fractionalization in metallic states of the Lieb lattice Hubbard model near quarter filling Nikolaenko, Alexander Bonetti, Pietro M. Kale, Anant Lebrat, Martin Greiner, Markus Sachdev, Subir Strongly Correlated Electrons Quantum Gases A recent experiment has examined ultracold, fermionic, spin-1/2 $^6$Li atoms in the Lieb lattice at different Hubbard repulsion $U$ and filling fractions $ν$ (Lebrat et al. arXiv:2404.17555). At $ν=1/2$ and small $U$, they observe an enhanced compressibility on the $p_{x,y}$ sites, pointing to a flat band near the Fermi energy. At $ν=1/2$ and large $U$ they observe an insulating ferrimagnet. Both small and large $U$ observations at $ν=1/2$ are consistent with theoretical expectations. Surprisingly, near $ν=1/4$ and large $U$, they again observe a large $p_{x,y}$ compressibility, pointing to a flat $p_{x,y}$ band of fermions across the Fermi energy. Our Hartree-Fock computations near $ν=1/4$ find states with canted magnetism (and related spiral states) at large $U$, which possess nearly flat $p_{x,y}$ bands near the Fermi level. We employ parton theories to describe quantum fluctuations of the magnetic order found in Hartree-Fock. We find a metallic state with $\mathbb{Z}_2$ fractionalization possessing gapless, fermionic, spinless `chargons' carrying $\mathbb{Z}_2$ gauge charges which have a nearly flat $p_{x,y}$ band near their Fermi level: this fractionalized metal is also consistent with observations. Our DMRG study does not indicate the presence of magnetic order, and so supports a fractionalized ground state. Given the conventional ferrimagnetic insulator at $ν=1/2$, the $\mathbb{Z}_2$ fractionalized metal at $ν=1/4$ represents a remarkable realization of doping-induced fractionalization. |
| title | Canted magnetism and $\mathbb{Z}_2$ fractionalization in metallic states of the Lieb lattice Hubbard model near quarter filling |
| topic | Strongly Correlated Electrons Quantum Gases |
| url | https://arxiv.org/abs/2502.12235 |