The density correlations of some singular Fermi liquids with anomalous properties such as resistivity varying linearly with $T$ at low temperatures and a $TlogT$ contribution to the entropy and thermopower are expected to be quite different from that in Landau Fermi liquids. A possible statistical mechanical model for the quantum-critical fluctuations in diverse systems with such properties is the 2D dissipative quantum XY model. Exact relations between the density correlations and singular irreducible vertices due to coupling of fermions to the topological excitations of the 2D dissipative quantum XY model are used to derive results which have become measurable only recently because of advances in experimental techniques. The density correlations are unusual at all momenta $\mathbf{q}$ and energy $\omega$, from the hydrodynamic limit to that for large momenta and energy. The hydrodynamic limit together with the continuity equation gives the linear in $T$ resistivity. The density correlations are almost independent of frequency up to a high-frequency cutoff for $q_{ZB}\gtrsim q\gg \omega /v_F$; $q_{ZB}$ is the Brillouin zone boundary and $v_F$ is the Fermi velocity. The results should be applicable to loop-current quantum criticality in cuprates, and to 2D Fe-based compounds near their antiferromagnetic quantum criticality. The relation of the results to the temperature and frequency dependent conductivity and to Raman response is also discussed.

• Received 19 April 2017
• Revised 26 June 2017

DOI:https://doi.org/10.1103/PhysRevB.96.075122