We obtain a controlled description of a strongly correlated regime of electronic behavior. We begin by arguing that there are two ways to characterize the electronic degree of freedom, either by the canonical fermion algebra or the graded Lie algebra $\mathfrak{su}(2|2)$ . The first underlies the Fermi liquid description of correlated matter, and we identify a regime governed by the latter. We exploit an exceptional central extension of $\mathfrak{su}(2|2)$ to employ a perturbative scheme recently developed by Shastry and obtain a series of successive approximations for the electronic Green's function. We then focus on the leading approximation, which reveals a splitting in two of the electronic dispersion. The Luttinger sum rule is violated, and a Mott metal-insulator transition is exhibited. We offer a perspective.We obtain a controlled description of a strongly correlated regime of electronic behavior. We begin by arguing that there are two ways to characterize the electronic degree of freedom, either by the canonical fermion algebra or the graded Lie algebra $\mathfrak{su}(2|2)$. The first underlies the Fermi liquid description of correlated matter, and we identify a regime governed by the latter. We exploit an exceptional central extension of $\mathfrak{su}(2|2)$ to employ a perturbative scheme recently developed by Shastry and obtain a series of successive approximations for the electronic Green's function. We then focus on the leading approximation, which reveals a splitting in two of the electronic dispersion. The Luttinger sum rule is violated, and a Mott metal-insulator transition is exhibited. We offer a perspective.

arXiv:1706.06499Physical review. B./Physical review. BMar 15, 20186 citations

Dynamical correlation in electron liquids

Gurinder S. Atwal

Jan 1, 20020 citations

\mathfrak{su}(2|2)

. The first underlies the Fermi liquid description of correlated matter, and we identify a regime governed by the latter. We exploit an exceptional central extension of

\mathfrak{su}(2|2)

to employ a perturbative scheme recently developed by Shastry and obtain a series of successive approximations for the electronic Green's function. We then focus on the leading approximation, which reveals a splitting in two of the electronic dispersion. The Luttinger sum rule is violated, and a Mott metal-insulator transition is exhibited. We offer a perspective.