Chiral nonFermi liquids
Abstract
A nonFermi liquid state without timereversal and parity symmetries arises when a chiral Fermi surface is coupled with a soft collective mode in two space dimensions. The full Fermi surface is described by a direct sum of chiral patch theories, which are decoupled from each other in the lowenergy limit. Each patch includes lowenergy excitations near a set of points on the Fermi surface with a common tangent vector. General patch theories are classified by the local shape of the Fermi surface, the dispersion of the critical boson, and the symmetry group, which form the data for distinct universality classes. We prove that a large class of chiral nonFermi liquid states exists as stable critical states of matter. For this, we use a renormalization group scheme where lowenergy excitations of the Fermi surface are interpreted as a collection of (1+1)dimensional chiral fermions with a continuous flavor labeling the momentum along the Fermi surface. Due to chirality, the Wilsonian effective action is strictly UV finite. This allows one to extract the exact scaling exponents although the theories flow to strongly interacting field theories at low energies. In general, the lowenergy effective theory of the full Fermi surface includes patch theories of more than one universality classes. As a result, physical responses include multiple universal components at low temperatures. We also point out that, in quantum field theories with extended Fermi surface, a noncommutative structure naturally emerges between a coordinate and a momentum which are orthogonal to each other. We show that the invalidity of patch description for Fermi liquid states is tied with the presence of UV/IR mixing associated with the emergent noncommutativity. On the other hand, UV/IR mixing is suppressed in nonFermi liquid states due to UV insensitivity, and the patch description is valid.
 Publication:

Physical Review B
 Pub Date:
 July 2014
 DOI:
 10.1103/PhysRevB.90.045121
 arXiv:
 arXiv:1310.7543
 Bibcode:
 2014PhRvB..90d5121S
 Keywords:

 71.10.Hf;
 74.40.Kb;
 11.10.Gh;
 NonFermiliquid ground states electron phase diagrams and phase transitions in model systems;
 Renormalization;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 37 pages, 25 figures