Loop current fluctuations and quantum critical transport

Non-Fermi liquids from kinetic constraints in tilted optical lattices

“…Indeed, turning on a background vector potential A a in H hop simply amounts to replacing φ a by φ a + A a . We can then completely eliminate the coupling of the fermions to A a through a shift of φ a (see also [33]). Since φ a is the Goldstone mode for the broken dipole symmetry, all other terms in the effective Hamiltonian can only involve gradients of φ a , and thus after the shift, the Hamiltonian can only depend on gradients of A a .…”

“…To demonstrate the NFL nature of L DF H , we note that it is essentially the same as the action that arises at the 'Hertz-Millis' theory [38,39] of the quantum critical point associated with the onset of loop current order in a metal [33] (but with the crucial restriction (7) coming from dipole conservation). Like in that case, fluctuations of φ a turn the system into an NFL.…”