A symmetry-breaking analysis for non-Fermi liquids induced by order fluctuations in correlated electron systems

Correlated electron systems display multi-order fluctuations, which are thought of the origin for non-Fermi liquids. Here, we present a symmetry-breaking analysis for establishing this relationship. Specifically, we establish a sequence of symmetry-breakings under increasing temperature with varying orders such as density wave, nematicity and loop current in cuprates. In particular, we propose that the underlying order for strange metal (SM) is vortex fluctuation, as a fluctuating loop current excited by thermal fluctuations and field. Furthermore, a theory for scattering rate by multi-order fluctuations is constructed based on a symmetry analysis of multi-dimensional Hamiltonian with elements determined by length order function (i.e. orders' periodicity). It then yields a formula for resistivity, i.e., ρ=ρ_a+(ρ_b²+α²T²+β²B²)^1/2, capturing the scaling transition from T² in pseudogap phase to T in SM phase, as well as anomalous magnetoresistance near quantum critical point. We report the validation evidence of dozens of cuprate samples. The most remarkable outcome is the revelation of the role of a length order function in linking macroscopic resistivity to microscopic fluctuating orders, which is essential for understanding anomalous transport in correlated electron systems.