One of the key factors that determine the fates of quantum many-body systems in the zero temperature limit is the competition between kinetic energy that delocalizes particles in space and interaction that promotes localization. While one dominates over the other in conventional metals and insulators, exotic states can arise at quantum critical points where none of them clearly wins. Here we present a class of metallic states that emerge at an antiferromagnetic (AF) quantum critical point in the presence of one-dimensional Fermi surfaces embedded in space dimensions three and below. At the critical point, interactions between particles are screened to zero in the low-energy limit and at the same time the kinetic energy is suppressed in certain spatial directions to the leading order in a perturbative expansion that becomes asymptotically exact in three dimensions. The resulting dispersionless and interactionless state exhibits distinct quasilocal strange metallic behaviors due to a subtle dynamical balance between screening and infrared singularity caused by spontaneous reduction of effective dimensionality. The strange metal, which is stable near three dimensions, shows enhanced fluctuations of bond density waves,
d-wave pairing, and pair density waves.
We present a functional renormalization group analysis of a quantum critical point in two-dimensional metals involving Fermi surface reconstruction due to the onset of spin-density wave order. Its critical theory is controlled by a fixed point in which the order parameter and fermionic quasiparticles are strongly coupled and acquire spectral functions with a common dynamic critical exponent. We obtain results for critical exponents and for the variation in the quasiparticle spectral weight around the Fermi surface. Our analysis is implemented on a two-band variant of the spin-fermion model which will allow comparison with sign-problem-free quantum Monte Carlo simulations.
We devise a dimensional regularization scheme for quantum field theories with a Fermi surface to study scaling behavior of non-Fermi liquid states in a controlled approximation. Starting from two space dimensions, the co-dimension of the Fermi surface is extended to a general value while its dimension is fixed. When the Fermi surface is coupled with a critical boson centered at zero momentum, the interaction becomes marginal at a critical space dimension
dc=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 the Fermi surface are 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 up to the two-loop order.