Unconventional metallic states which do not support well defined single-particle excitations can arise near quantum phase transitions as strong quantum fluctuations of incipient order parameters prevent electrons from forming coherent quasiparticles. Although antiferromagnetic phase transitions occur commonly in correlated metals, understanding the nature of the strange metal realized at the critical point in layered systems has been hampered by a lack of reliable theoretical methods that take into account strong quantum fluctuations. We present a non-perturbative solution to the lowenergy theory for the antiferromagnetic quantum critical metal in two spatial dimensions. Being a strongly coupled theory, it can still be solved reliably in the low-energy limit as quantum fluctuations are organized by a new control parameter that emerges dynamically. We predict the exact critical exponents that govern the universal scaling of physical observables at low temperatures.

We study the antiferromagnetic quantum critical metal in 3 − ǫ space dimensions by extending the earlier one-loop analysis [Sur and Lee, Phys. Rev. B 91, 125136 (2015)] to higher-loop orders. We show that the ǫ-expansion is not organized by the standard loop expansion, and a two-loop graph becomes as important as one-loop graphs due to an infrared singularity caused by an emergent quasilocality. This qualitatively changes the nature of the infrared (IR) fixed point, and the ǫ-expansion is controlled only after the two-loop effect is taken into account. Furthermore, we show that a ratio between velocities emerges as a small parameter, which suppresses a large class of diagrams. We show that the critical exponents do not receive corrections beyond the linear order in ǫ in the limit that the ratio of velocities vanishes. The ǫ-expansion gives critical exponents which are consistent with the exact solution obtained in 0 < ǫ ≤ 1.

We study the field theory for the SU(Nc) symmetric antiferromagnetic quantum critical metal with a one-dimensional Fermi surface embedded in general space dimensions between two and three. The asymptotically exact solution valid in this dimensional range provides an interpolation between the perturbative solution obtained from the -expansion near three dimensions and the nonperturbative solution in two dimensions. We show that critical exponents are smooth functions of the space dimension. However, physical observables exhibit subtle crossovers that make it hard to access subleading scaling behaviors in two dimensions from the low-energy solution obtained above two dimensions. These crossovers give rise to noncommutativities, where the low-energy limit does not commute with the limits in which the physical dimensions are approached. arXiv:1805.05252v2 [cond-mat.str-el]