We propose a lattice model for strongly interacting electrons with the potential to explain the main phenomenology of the strange metal phase in the cuprate high-temperature superconductors. Our model is motivated by the recently developed “tetrahedron” rank-3 tensor model that mimics much of the physics of the better-known Sachdev-Ye-Kitaev (SYK) model. Our electron model has the following advantageous properties: (1) it needs only one orbital per site on the square lattice. (2) It does not require any quenched random interaction. (3) It has local interactions and respects all the symmetries of the system. (4) The soluble limit of this model has a longitudinal dc resistivity that scales linearly with temperature within a finite temperature window. (5) Again, the soluble limit of this model has a fermion pairing instability in the infrared, which can lead to either superconductivity or a “pseudogap” phase. The linear-$T$ longitudinal resistivity and the pairing instability originate from the generic scaling feature of the SYK model and the tetrahedron tensor model.

• Received 9 April 2018
• Revised 11 September 2018

DOI:https://doi.org/10.1103/PhysRevB.98.165117