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 novel metallic state that emerges 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 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 quasi-local 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. 1The richness of exotic zero-temperature states in condensed matter systems [1,2] can be attributed to quantum fluctuations driven by kinetic energy and interaction which can not be simultaneously minimized due to the uncertainty principle. In conventional metals, kinetic energy plays the dominant role, and interactions only dress electrons into quasiparticles which survive as coherent excitations in the absence of instabilities [3,4]. The existence of well defined quasiparticle excitations is the cornerstone of Landau Fermi liquid theory [5], which successfully explains a large class of metals. However, the Fermi liquid theory breaks down at the verge of spontaneous formation of order in metals [6][7][8]. Near continuous quantum phase transitions, new metallic states can arise as quantum fluctuations of order parameter destroy the coherence of quasiparticles through interactions that persist down to the zero energy limit [9,10]. Systematic understanding of the resulting strange metallic states is still lacking, although there exist some examples whose universal behaviors in the low energy limit can be understood within controlled theoretical frameworks [11][12][13][14][15].Antiferromagnetic (AF) quantum phase transition commonly arises in strongly correlated systems including electron doped cuprates [16], iron pnictides [17] and heavy fermion compounds [18].In two space dimensions, it has been shown that the interaction between the AF mode and itinerant electrons qualitatively modify the dynamics of the system at the critical point [19,20]. A recent numerical simulation shows a strong enhancement of superconducting correlations near the AF critical point [21]. However, the precise nature of the putative strange metallic state has not been understood yet due t...

We study the quantum phases driven by interaction in a semimetal with a quadratic band touching at the Fermi level. By combining the density matrix renormalization group (DMRG), analytical power expanded Gibbs potential method, and the weak coupling renormalization group, we study a spinless fermion system on a checkerboard lattice at half-filling, which has a quadratic band touching in the absence of interaction.In the presence of strong nearest-neighbor (V1) and next-nearest-neighbor (V2) interactions, we identify a site nematic insulator phase, a stripe insulator phase, and a phase separation region, in agreement with the phase diagram obtained analytically in the strong coupling limit (i.e. in the absence of fermion hopping). In the intermediate interaction regime, we establish a quantum anomalous Hall phase in the DMRG as evidenced by the spontaneous time-reversal symmetry breaking and the appearance of a quantized Chern number C = 1. For weak interaction, we utilize the power expanded Gibbs potential method that treats V1 and V2 on equal footing, as well as the weak coupling renormalization group. Our analytical results reveal that not only the repulsive V1 interaction, but also the V2 interaction (both repulsive and attractive), can drive the quantum anomalous Hall phase. We also determine the phase boundary in the V1-V2 plane that separates the semimetal from the quantum anomalous Hall state. Finally, we show that the nematic semimetal, which was proposed for |V2| V1 at weak coupling in a previous study, is absent, and the quantum anomalous Hall state is the only weak coupling instability of the spinless quadratic band touching semimetal.

We study Weyl-loop semi-metals with short range interactions, focusing on the possible interaction driven instabilities. We introduce an ò expansion regularization scheme by means of which the possible instabilities may be investigated in an unbiased manner through a controlled weak coupling renormalization group (RG) calculation. The problem has enough structure that a 'functional' RG calculation (necessary for an extended Fermi surface) can be carried out analytically. The leading instabilities are identified, and when there are competing degenerate instabilities a Landau-Ginzburg calculation is performed to determine the most likely phase. In the particle-particle channel, the leading instability is found to be to a fully gapped chiral superconducting phase which spontaneously breaks time reversal symmetry, in agreement with general symmetry arguments suggesting that Weyl loops should provide natural platforms for such exotic forms of superconductivity. In the particle hole channel, there are two potential instabilities-to a gapless Pomeranchuk phase which spontaneously breaks rotation symmetry, or to a fully gapped insulating phase which spontaneously breaks mirror symmetry. The dominant instability in the particle hole channel depends on the specific values of microscopic interaction parameters.