Quantum phase transitions of metals in two spatial dimensions. I. Ising-nematic order

Abstract

We present a renormalization group theory for the onset of Ising-nematic order in a Fermi liquid in two spatial dimensions. This is a quantum phase transition, driven by electron interactions, which spontaneously reduces the point-group symmetry from square to rectangular. The critical point is described by an infinite set of 2+1 dimensional local field theories, labeled by points on the Fermi surface. Each field theory contains a real scalar field representing the Ising order parameter, and fermionic fields representing a time-reversed pair of patches on the Fermi surface. We demonstrate that the field theories obey compatibility constraints required by our redundant representation of the underlying degrees of freedom. Scaling forms for the response functions are proposed, and supported by computations up to three loops. Extensions of our results to other transitions of two-dimensional Fermi liquids with broken point-group and/or time-reversal symmetry are noted.Our results extend also to the problem of a Fermi surface coupled to a U(1) gauge field.

Fermi surfaces and gauge-gravity duality

“…In particular, the d = 3 model of Gubser and Rocha [10] is a promising model for future study. The problem of a Fermi surface coupled to a gauge field appears to be under control in d = 3: the results of the self-consistent one-loop theory [75][76][77] are expected to be robust to higher order corrections [41,42]. Such a theory only gives marginal corrections to the FL results: the low T specific heat behaves as T log T .…”

“…Such fluctuations are frequently controlled via a 1/N expansion, where each fermion is endowed with an additional flavor index which can take N values. Recent work [41][42][43] has shown that the naive 1/N expansion breaks down in d = 2 because of Fermi surface singularities that appear in higher loop graphs. The d = 2 case is therefore stronglycoupled, and the ultimate fate of the theory has not been fully resolved: these are difficult questions we will not address here.…”

Superconductivity from repulsive interaction

“…Refs. [ There are several features in the phase diagram, like the pseudogap in hole-doped cuprates, which are still not fully understood, although a substantial progress has been made over the last few years on the issue of the interplay between pseudogap and superconductivity [108,109,110] By all accounts, the symmetry of the superconducting state does not change between small doping, where pseudogap physics is relevant, and doping above the optimal one. For these larger dopings, ARPES and quantum oscillation experiments show a large FS (see Fig.…”

“…In this situation, SC instability definitely comes ahead of SDW magnetism. There may be other instabilities produced by strong spin fluctuations, like bond CDW [108,109,110], which compete with SC and, by construction, also occur before SDW order sets in In RG treatment (pRG or fRG), SDW magnetism and SC instability (and other potential instabilities) compete with each other, and which one develops first needs to be analyzed. So far, we only found that SC vertex changes sign and becomes attractive.…”

Fermi surface reconstruction in hole-dopedt−Jmodels without long-range antiferromagnetic order

“…10,11 In fact, many of the unresolved theoretical problems in strongly correlated electron materials, from heavy-Fermion compounds to high-T c cuprates, are related to the fate of electronic excitations close to antiferromagnetic quantum critical points. 12 It has been been argued, however, that the critical point between a metal with a large Fermi surface and an antiferromagnetic metal with small Fermi pockets may be replaced by a new intermediate phase, the so called fractionalized Fermi liquid (FL*) 13,14 , which exhibits small pockets similar to the antiferromagnetic metal, but breaks no symmetries: summaries of these arguments, and of previous theoretical work, can be found in two recent reviews. 15,16 The simplest picture of the FL* phase appears in the context of Kondo lattice models coupling a lattice of localized f moments and a conduction band of itinerant c electrons.…”