Fermi liquids in two-space dimensions

Sudhakar Yarlagadda, Susumu Kurihara

G. Baskaran

Jungsoo Kim, Dermot Coffey

Denis Dalidovich, Sung-Sik Lee

We devise a dimensional regularization scheme for quantum field theories with a Fermi surface to study scaling behavior of non-Fermi liquid states in a controlled approximation. Starting from two space dimensions, the co-dimension of the Fermi surface is extended to a general value while its dimension is fixed. When the Fermi surface is coupled with a critical boson centered at zero momentum, the interaction becomes marginal at a critical space dimension ${d}_{c}=5/2$. A deviation from the critical dimension is used as a small parameter for a systematic expansion. We apply this method to the theory where two patches of the Fermi surface are coupled with a critical boson, and show that the Ising-nematic critical point is described by a stable non-Fermi liquid state slightly below the critical dimension. Critical exponents are computed up to the two-loop order.

David Lidsky, J. Shiraishi, Yasuhiro Hatsugai +1 more

We generalize the model of Hatsugai and Kohmoto and find ground states which do not show the properties of Fermi liquids. We work in two space dimensions, but it is straightforward to generalize to higher dimensions. The ground state is highly degenerate and there is no discontinuity in the momentum distribution; i.e., there is no Fermi surface. The Green's function generically has a branch cut.