We devise a dimensional regularization scheme for quantum field theories with
Fermi surface to study scaling behaviour of non-Fermi liquid states in a
controlled approximation. Starting from a Fermi surface in two space
dimensions, the co-dimension of Fermi surface is extended to a general value
while the dimension of Fermi surface is fixed. When Fermi surface is coupled
with a critical boson centered at zero momentum, the interaction becomes
marginal at a critical space dimension d_c=5/2. A deviation from the critical
dimension is used as a small parameter for a systematic expansion. We apply
this method to the theory where two patches of Fermi surface is coupled with a
critical boson, and show that the Ising-nematic critical point is described by
a stable non-Fermi liquid state slightly below the critical dimension. Critical
exponents are computed upto the two-loop order.Comment: 46 pages, 10 figures; v3) typos correcte
The conventional theory of metals is in crisis. In the past 15 years, there has been an unexpected sprouting of metallic states in low-dimensional systems, directly contradicting conventional wisdom. For example, bosons are thought to exist in one of two ground states: condensed in a superconductor or localized in an insulator. However, several experiments on thin metal-alloy films have observed that a metallic phase disrupts the direct transition between the superconductor and the insulator. We analyze the experiments on the insulator-superconductor transition and argue that the intervening metallic phase is bosonic. All relevant theoretical proposals for the Bose metal are discussed, particularly the recent idea that the metallic phase is glassy. The implications for the putative vortex-glass state in the copper oxide superconductors are examined.
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