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Register a new userLarge $N$ theory of critical Fermi surfaces
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We describe the large $N$ saddle point, and the structure of fluctuations about the saddle point, of a theory containing a sharp, critical Fermi surface in two spatial dimensions. The theory describes the onset of Ising order in a Fermi liquid, and closely related theories apply to other cases with critical Fermi surfaces. We employ random couplings in flavor space between the fermions and the bosonic order parameter, but there is no spatial randomness: consequently, the $G$-$Sigma$ path integral of the theory is expressed in terms of fields bilocal in spacetime. The critical exponents of the large $N$ saddle-point are the same as in the well-studied non-random RPA theory; in particular, the entropy density vanishes in the limit of zero temperature. We present a full numerical solution of the large $N$ saddle-point equations, and the results agree with the critical behavior obtained analytically. Following analyses of Sachdev-Ye-Kitaev models, we describe scaling operators which descend from fermion bilinears around the Fermi surface. This leads to a systematic consideration of the role of time reparameterization symmetry, and the scaling of the Cooper pairing and $2k_F$ operators which can determine associated instabilities of the critical Fermi surface. We find no violations of scaling from time reparameterizations. We also consider the same model but with spatially random couplings: this provides a systematic large $N$ theory of a marginal Fermi liquid with Planckian transport.
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We study critical Fermi surfaces in generic dimensions arising from coupling finite-density fermions with transverse gauge fields, by applying the dimensional regularization scheme developed previously [Phys. Rev. B 92, 035141 (2015)]. We consider the cases of $U(1)$ and $U(1)times U(1)$ transverse gauge couplings, and extract the nature of the renormalization group (RG) flow fixed points as well as the critical scalings. Our analysis allows us to treat a critical Fermi surface of a generic dimension $m$ perturbatively in an expansion parameter $epsilon =left (2-m right ) /left (m+1 right).$ One of our key results is that although the two-loop corrections do not alter the existence of an RG flow fixed line for certain $U(1)times U(1)$ theories, which was identified earlier for $m=1$ at one-loop order, the third-order diagrams do. However, this fixed line feature is also obtained for $m>1$, where the answer is one-loop exact due to UV/IR mixing.
At certain quantum critical points in metals an entire Fermi surface may disappear. A crucial question is the nature of the electronic excitations at the critical point. Here we provide arguments showing that at such quantum critical points the Fermi surface remains sharply defined even though the Landau quasiparticle is absent. The presence of such a critical Fermi surface has a number of consequences for the universal phenomena near the quantum critical point which are discussed. In particular the structure of scaling of the universal critical singularities can be significantly modified from more familiar criticality. Scaling hypotheses appropriate to a critical fermi surface are proposed. Implications for experiments on heavy fermion critical points are discussed. Various phenomena in the normal state of the cuprates are also examined from this perspective. We suggest that a phase transition that involves a dramatic reconstruction of the Fermi surface might underlie a number of strange observations in the metallic states above the superconducting dome.
We compute the entanglement entropy of the Wilson-Fisher conformal field theory (CFT) in 2+1 dimensions with O($N$) symmetry in the limit of large $N$ for general entanglement geometries. We show that the leading large $N$ result can be obtained from the entanglement entropy of $N$ Gaussian scalar fields with their mass determined by the geometry. For a few geometries, the universal part of the entanglement entropy of the Wilson-Fisher CFT equals that of a CFT of $N$ massless scalar fields. However, in most cases, these CFTs have a distinct universal entanglement entropy even at $N=infty$. Notably, for a semi-infinite cylindrical region it scales as $N^0$, in stark contrast to the $N$-linear result of the Gaussian fixed point.
We construct examples of translationally invariant solvable models of strongly-correlated metals, composed of lattices of Sachdev-Ye-Kitaev dots with identical local interactions. These models display crossovers as a function of temperature into regimes with local quantum criticality and marginal-Fermi liquid behavior. In the marginal Fermi liquid regime, the dc resistivity increases linearly with temperature over a broad range of temperatures. By generalizing the form of interactions, we also construct examples of non-Fermi liquids with critical Fermi-surfaces. The self energy has a singular frequency dependence, but lacks momentum dependence, reminiscent of a dynamical mean field theory-like behavior but in dimensions $d<infty$. In the low temperature and strong-coupling limit, a heavy Fermi liquid is formed. The critical Fermi-surface in the non-Fermi liquid regime gives rise to quantum oscillations in the magnetization as a function of an external magnetic field in the absence of quasiparticle excitations. We discuss the implications of these results for local quantum criticality and for fundamental bounds on relaxation rates. Drawing on the lessons from these models, we formulate conjectures on coarse grained descriptions of a class of intermediate scale non-fermi liquid behavior in generic correlated metals.
The fractional quantum Hall (FQH) effect was discovered in two-dimensional electron systems subject to a large perpendicular magnetic field nearly four decades ago. It helped launch the field of topological phases, and in addition, because of the quenching of the kinetic energy, gave new meaning to the phrase correlated matter. Most FQH phases are gapped like insulators and superconductors; however, a small subset with even denominator fractional fillings nu of the Landau level, typified by nu = 1/2, are found to be gapless, with a Fermi surface akin to metals. We discuss our results, obtained numerically using the infinite Density Matrix Renormalization Group (iDMRG) scheme, on the effect of non-isotropic distortions with discrete N-fold rotational symmetry of the Fermi surface at zero magnetic field on the Fermi surface of the correlated nu = 1/2 state. We find that while the response for N = 2 (elliptical) distortions is significant (and in agreement with experimental observations with no adjustable parameters), it decreases very rapidly as N is increased. Other anomalies, like resilience to breaking the Fermi surface into disjoint pieces, are also found. This highlights the difference between Fermi surfaces formed from the kinetic energy, and those formed of purely potential energy terms in the Hamiltonian.
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