Field theories of strongly correlated, two-dimensional metals : phases and criticality

This thesis details quantum-field-theoretical analyses of four distinct strongly correlated metallic systems in two spatial dimensions. It begins by examining two driving mechanisms proposed in the literature for the exotic charge-density-wave phase in monolayer vanadium diselenide. The spectral-function-fitting method used to analyse the first proves quite indeterminate, leading to only speculative conclusions. The second mechanism is tested by producing mean-field phase diagrams of the system, yielding an appreciable region of phase space in which it does drive the charge-density wave. In the next chapter, the square-lattice Hubbard model with first-, second- and third-nearest-neighbour hoppings is considered. Phase diagrams are predicted using the few-patch parquet renormalization group and compared with those produced by a colleague using another method, and with those from another patch scheme in the literature. It is concluded that few-patch parquet-renormalization-group schemes are not sophisticated enough to correctly describe many features of this system, and likely other systems. The second half of the thesis studies non-Fermi liquids. First, the non-Fermi liquid resulting from coupling finite-density fermions to a U (1) gauge field is examined. The functional renormalization group, with a soft frequency regulator for the fermions, is used, and gauge-symmetry constraints are imposed. The resulting bosonic dynamical exponent is zA = 2, and the fermionic self-energy scales as Σ (ω, kF) ~ √ω at small frequency. Enforcement of the symmetry constraints leaves the results largely unchanged, but does make the bosonic mass term irrelevant about criticality. In the final research chapter, the non-equilibrium modes of two-dimensional non-Fermi liquids in incipient itinerant ferromagnets are analysed. Linearized quantum Boltzmann equations are solved to find the spectra of charge- and spin-density modes. Whether collective modes are present is found to depend on both universal and non-universal information, in ways previously overlooked. Preliminary results are also given for the spectra when coupling to a classical magnetic field is reincluded.