Solving the Mott Problem

The Mott problem stands as a grand challenge largely because its solution is at the heart of high-temperature superconductivity in the cuprates. It is unfortunate that such materials are largely 2-dimensional and the only exact solutions are restricted to d=1 with Bethe ansatz and infinite dimensions.

I will present a method [1] valid in any dimension that recovers the Bethe ansatz results in $d=1$ and the $d=\infty$ solutions as well. At the heart of the method is the breaking of an overlooked $Z_2$ [2] symmetry of Fermi liquids . I will present benchmarks for the method in d=1 and compare with``accepted'' results in d=2 for the spectral function, occupancy as a function of momentum, the heat capcity and the spin susceptibility.

References:

1.) P.Mai, J. Zhao, G. Tenkila, N. A. Hackner, D. Kush, D. Pan, and P. W. Phillips, https://arxiv.org/abs/2401.08746

2.) E. Huang, G. La Nave, and P. W. Phillips, Nature Physics volume 18, pages511–516 (2022).