Schrödinger Fermi liquids

Abstract

A class of strongly interacting many-body fermionic systems in $2+1$-dimensional nonrelativistic conformal field theory is examined via the gauge-gravity duality correspondence. The five-dimensional charged black hole with asymptotic Schr\"odinger isometry in the bulk gravity side introduces parameters of background density and finite particle number into the boundary field theory. We propose the holographic dictionary, and realize a quantum phase transition of this fermionic liquid with fixed particle number by tuning the background density $\ensuremath{\beta}$ at zero temperature. On the larger $\ensuremath{\beta}$ side, we find the signal of a sharp quasiparticle pole on the spectral function $A(k,\ensuremath{\omega})$, indicating a well-defined Fermi surface. On the smaller $\ensuremath{\beta}$ side, we find only a hump with no sharp peak for $A(k,\ensuremath{\omega})$, indicating the disappearance of the Fermi surface. The dynamical exponent $z$ of quasiparticle dispersion goes from being Fermi-liquid-like $z\ensuremath{\simeq}1$ scaling at larger $\ensuremath{\beta}$ to a non-Fermi-liquid scaling $z\ensuremath{\simeq}3/2$ at smaller $\ensuremath{\beta}$. By comparing the structure of Green's function with Landau Fermi liquid theory and Senthil's scaling ansatz, we further investigate the behavior of this quantum phase transition.