't Hooft Anomalies of Fermi Liquids and Luttinger's Theorem

Abstract: Lattice systems with translation symmetry and U(1) charge conservation have a filling fraction, defined as the charge per unit cell. In this talk I will explain how the filling fraction is captured by anomalous emergent symmetries in the continuum limit of such systems. This anomaly matching is a generalization of Luttinger's theorem for Fermi liquids, which says that the filling fraction equals the volume enclosed by the Fermi surface. Luttinger's theorem is obtained by analyzing an anomalous loop-group symmetry of the Fermi liquid, which generalizes the chiral anomaly of a Luttinger liquid in 1+1d. I will argue more generally that systems at irrational filling cannot have continuum limits with compact symmetry groups.

other condensed mattersoft condensed matterstatistical mechanicsstrongly correlated electronssuperconductivitygeneral relativity and quantum cosmologyHEP - theorymathematical physicschaotic dynamicsfluid dynamicsquantum physics

Audience: researchers in the topic

Kadanoff seminars