Singlet-RVB Solid Phase of SU(4) Fermi Gas with Population Imbalance in a Tetramerized Optical Lattice

In the area of cold atomic systems, recently a great deal of effort is being made to realize higher-symmetric quantum many-body systems and find novel physical properties. Alkaline-earth(-like) fermionic atoms have nuclear spin I, e.g., I = 5/2 for ¹⁷³Yb, and with these atomic species we can prepare ideal SU(N ≤ 2I + 1)-symmetric systems [1, 2]. In this work, we study the quantum magnetism of the SU(4) Mott insulator in a tetramerized optical lattice, in which atoms with four nuclear-spin components strongly interact with each other. We investigate quantum phases induced by the external field that favors the populations of two components against the other two. This is a natural extension of the physics of spin-dimer materials such as TlCuCl₃ [3, 4] under strong magnetic field to SU(4)-symmetric systems. We study the ground state of the Hamiltonian using an extended linear flavor-wave theory [5] based on four-site plaquettes. We unveil the ground-state phase diagram in the plane of external field vs. interplaquette exchange coupling. Our main finding is a nontrivial quantum phase, which has a checkerboard-like arrangement of the SU(4) singlet and four-site RVB states [6, 7].



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[2] C. Hofrichter et al., PRX 6, 021030 (2016).

[3] T. Nikuni et al., PRL 84, 5868 (2000).

[4] F. Yamada et al., JPSJ 77, 013701 (2008).

[5] N. Papanicolaou, Nucl. Phys. B 240, 281 (1984); ibid. 305, 367 (1988).

[6] M. Miyazaki et al., AIP Adv. 11, 025202 (2021).

[7] M. Miyazaki et al., JPSJ 91, 073702 (2022).