Conformal field theory approach to Fermi liquids and other highly entangled states

The Fermi surface may be usefully viewed as a collection of ($1+1$)-dimensional chiral conformal field theories. This approach permits straightforward calculation of many anomalous ground-state properties of the Fermi gas, including entanglement entropy and number fluctuations. The ($1+1$)-dimensional picture also generalizes to finite temperature and the presence of interactions. We argue that the low-energy entanglement structure of Fermi liquid theory is universal, depending only on the geometry of the interacting Fermi surface. We also describe three additional systems in $3+1$ dimensions where a similar mechanism leads to a violation of the boundary law for entanglement entropy.

Figure 1

A sketch of a circular real-space region $A$ of radius $L$. The Fermi velocity of a particular patch on the Fermi surface is shown superimposed on the circle. The effective length $L_{\mathrm{eff}}=2L\cos \theta$, which is just the chordal distance across the circle parallel to the Fermi velocity, is a function of angle $\theta$ relative to $v_F$.