Fermionic quantum criticality

Full text: The fermion-sign problem, i.e. the inability to deal theoretically with states of fermionic matter which are neither Fermi-liquids nor formed from bosonic bound states, is generally regarded as the fundamental problem of condensed matter physics. This problem becomes particularly acute dealing with quantum phase transitions involving a change of Fermi-surface. Resting on Ceperley's nodal constraint path-integral language we demonstrate that a scale-invariant Fermionic state necessarily involves a fractal nodal hypersurface and we demonstrate that Feynman's fermionic back flow wave function is of this kind when the backflow is in the hydrodynamical regime. In this formulation it is obvious that a fermionic quantum critical state is characterized by an extremely bad free energy, making possible a superconductor at high temperatures when attractive interactions open up the Cooper channel. (authors)