Ground State Properties of SU(4) Attractive Hubbard Model on a Honeycomb Lattice

Tianxing Ma, Lufeng Zhang, Hai‐Qing Lin

Jize Zhao, Kazuo Ueda, Xiaoqun Wang

Rahul Hingorani, J. Oitmaa, Rajiv R. P. Singh

We use finite-temperature strong coupling expansions to calculate thermodynamic properties of the honeycomb-lattice SU(4) Hubbard model. We present numerical results for various properties including chemical potential, compressibility, entropy and specific heat as a function of temperature and density at several $U/t$ values. We study the onset of charge incompressibility and Mott gaps as the temperature is lowered at integer densities. In the incompressible Mott regime, the expansions are recast into a high-temperature expansion for a generalized spin model with SU(4) symmetry, which is then used to study the convergence of strong coupling expansions in $t/U$. We discuss lessons that can be drawn from high-temperature properties of a simple Hubbard model regarding twisted bilayer graphene and other magic-angle flat-band systems.

Thomas C. Lang, Fakher F. Assaad, Zi Yang Meng +2 more

Masahiko G. Yamada, Masaki Oshikawa, George Jackeli

While the enhancement of spin-space symmetry from the usual SU(2) to SU(N) is promising for finding nontrivial quantum spin liquids, its realization in magnetic materials remains challenging. Here, we propose a new mechanism by which SU(4) symmetry emerges in the strong spin-orbit coupling limit. In d^{1} transition metal compounds with edge-sharing anion octahedra, the spin-orbit coupling gives rise to strongly bond-dependent and apparently SU(4)-breaking hopping between the J_{eff}=3/2 quartets. However, in the honeycomb structure, a gauge transformation maps the system to an SU(4)-symmetric Hubbard model. In the strong repulsion limit at quarter filling, as realized in α-ZrCl_{3}, the low-energy effective model is the SU(4) Heisenberg model on the honeycomb lattice, which cannot have a trivial gapped ground state and is expected to host a gapless spin-orbital liquid. By generalizing this model to other three-dimensional lattices, we also propose crystalline spin-orbital liquids protected by this emergent SU(4) symmetry and space group symmetries.

Alessandro Giuliani

In these lectures I consider the half-filled two-dimensional (2D) Hubbard model on the honeycomb lattice and I review the rigorous construction of its ground state properties by making use of constructive fermionic Renormalization Group methods.