Seminarium Fizyki Materii Skondensowanej

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 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 $Z_2$ symmetry of Fermi liquids . I will present benchmarks for the method in d=1 and compare with``accepted'' results in d=2, where no exact results are known. I will also draw on comparisons with cold-atom experiments for the compressibility.