Bosonization for 2D Interacting Fermion Systems: Non-Fermi Liquid Behavior

This note addresses the problem of constructing a proper bosonized description of the collective modes in strongly interacting (non-)Fermi liquids which is specific to two spatial dimensions. Although, in a mild form, this subtlety exists in the Fermi liquid as well, the discussion focuses on the effects of long-ranged and/or retarded interactions which can completely destroy the fermionic quasiparticles. The present analysis also provides a further insight into the nature an...

(Revised, with postscript figures appended, corrections and added comments.) We develop and describe new approaches to the problem of interacting Fermions in spatial dimensions greater than one. These approaches are based on generalizations of powerful tools previously applied to problems in one spatial dimension. We begin with a review of one-dimensional interacting Fermions. We then introduce a simplified model in two spatial dimensions to study the role that spin and perfe...

Understanding non-Fermi liquids in dimensions higher than one remains one of the most formidable challenges in modern condensed matter physics. These systems, characterized by an abundance of gapless degrees of freedom and the absence of well-defined quasiparticles, defy conventional analytical frameworks. Inspired by recent work on the bosonization of Fermi surfaces [Delacretaz, Du, Mehta, and Son, Physical Review Research, 4, 033131 (2022)], we present a procedure for boson...

We describe an analytical theory investigating the regime of validity of the Fermi liquid theory in interacting, via the long-range Coulomb coupling, two-dimensional Fermi systems comparing it with with the corresponding 3D systems. We find that the 2D Fermi liquid theory and 2D quasiparticles are robust up to high energies and temperatures of the order of Fermi energy above the Fermi surface, very similar to the corresponding three-dimensional situation. We calculate the pha...

We consider the Haldane bosonisation scheme in d spatial dimensions as applied to a realistic model of interacting fermions in d=2 and unequivocally demonstrate failure of this scheme in d > 1, specifically in d=2. In addition to tracing back this failure to its origin, we show that {\sl nothing} as regards the true metallic state of the model under consideration is known with any degree of certainty.

We investigate the effects of the Coulomb two-body interaction on Fermi liquids via bosonization. The Coulomb interaction is singular in the limit of low momentum transfer, and recent interest in the possibility that some singular interactions might destroy the Fermi liquid state motivate us to reexamine it. We calculate the exact boson correlation function to show that the Fermi liquid state is retained in the case of Coulomb interactions. Spin and charge degrees of freedom ...

We discuss interacting fermion models in two dimensions, and, in particular, such that can be solved exactly by bosonization. One solvable model of this kind was proposed by Mattis as an effective description of fermions on a square lattice. We review recent work on a specific relation between a variant of Mattis' model and such a lattice fermion system, as well as the exact solution of this model. The background for this work includes well-established results for one-dimensi...

We analyze the universal transport behavior in 1D and 2D fermionic systems by following the unified framework provided by bosonization. The role played by the adiabatic transition between interacting and noninteracting regions is emphasized.

The general 2-dimensional fermion system with repulsive interactions (typified by the Hubbard Model) is bosonized, taking into account the finite on-shell forward scattering phase shift derived in earlier papers. By taking this phase shift into account in the bosonic commutation relations a consistent picture emerges showing the charge-spin separation and anomalous exponents of the Luttinger liquid.

We discuss an approach to higher dimensional bosonization of interacting fermion s based on a picture of fluctuating Fermi surface. Compared with the linearized"constructive" approach developed in Refs.[9-11] this method allows an account of the Fermi surface curvature due to nongaussian terms in the bosonized Lagrangian. On the basis of this description we propose a procedure of calculating density response functions beyond the random phase approximation. We also formulate a...