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arXiv:2409.02316

(Pre-)Modern (Non-)Fermi liquids

Dmitri V. Khveshchenko

Published Sep 3, 2024• 1 citation
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Abstract

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 and properties of the collective bosonic modes in such systems.

DOI
10.48550/arxiv.2409.02316

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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 and properties of the collective bosonic modes in such systems.
This Letter 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 provides a further insight into the nature and properties of the collective bosonic modes in such systems.
This note addresses the effects of long-ranged and/or retarded interactions on the bosonic collective modes in the so-called 'strange metals'. Recently, there have been conflicting reports on the very existence of such stable collective excitations and their properties. Extending a number of approaches that were previously used in the analyses of the standard Fermi liquid one finds evidence for, both, conventional and novel behaviors of the non-Fermi-liquid counterparts of the zero-, shear-, and other 'sounds'.
We develop a general theory of fermion liquids in spatial dimensions greater than 1. The principal method, bosonization, is applied to the cases of short- and long-range longitudinal interactions and to transverse gauge interactions. All the correlation funtions of the system may be obtained with the use of a generating functional. Short-range and Coulomb interactions do not destroy the Landau-Fermi fixed point. Non-Fermi liquid fixed points are found, however, in the cases of a super-long-range longitudinal interaction in two dimensions and transverse gauge interactions in two and three spatial dimensions. We consider in some detail the (2+1)-dimensional problem of a Chern-Simons gauge action combined with a longitudinal two-body interaction V(q)\ensuremath{\propto}\ensuremath{\Vert}q${\mathrm{\ensuremath{\Vert}}}^{\mathit{y}\mathrm{\ensuremath{-}}1}$, which controls the density, and hence gauge, fluctuations. For y0 we find that the gauge interaction is irrelevant and the Landau fixed point is stable, while for y>0 the interaction is relevant and the fixed point cannot be accessed by bosonization. Of special importance is the case y=0 (Coulomb interaction), which describes the Halperin-Lee-Read theory of the half-filled Landau level. We obtain the full quasiparticle propagator, which is of a marginal Fermi-liquid form. Using Ward identities, we show that neither the inclusion of nonlinear terms in the fermion dispersion nor vertex corrections alters our results: the fixed point is accessible by bosonization. As the two-point fermion Green's function is not gauge invariant, we also invetigate the gauge-invariant density response function. Near momentum Q=2kF{\mathit{k}}_{\mathit{F}}kF​, in addition to the Kohn anomaly we find other nonanalytic behavior. In the appendies we present a numerical calculation of the spectral function for a Fermi liquid with Landau parameter f0{\mathit{f}}_{0}f0​\ensuremath{\ne}0. We also show how Kohn's theorem is satisfied within the bosonization framework.
We study the stability and single-particle properties of Fermi liquids in spatial dimensions greater than one via bosonization. For smooth nonsingular Fermi-liquid interactions we obtain Shankar's renormalization-group flows to second order in the BCS coupling and reproduce well-known results for quasiparticle lifetimes. We demonstrate by explicit calculation that spin-charge separation does not occur when the Fermi-liquid interactions are regular. We also explore the relationship between quantized bosonic excitations and zero-sound modes and present a concise derivation of both the spin and the charge collective-mode equations. Finally we discuss some aspects of singular Fermi-liquid interactions.
The authors provide a comprehensive theoretical investigation of the validity of the Fermi-liquid quasiparticle description in a two-dimensional electron gas interacting via the long-range Coulomb interaction. Contrary to popular belief, they find that quasiparticles are robust far above the Fermi momentum, perhaps providing a clue as to why the energy-band description works well far from the Fermi surface. The authors also find that there exists a small region around a critical wave vector where the quasiparticles become fragile due to their coupling to the collective modes. They also provide three-dimensional results.
In a recent paper by Schmeltzer [Phys. Rev. B 52, 7939 (1995)] it is claimed that a non-Fermi liquid behavior arises in a d-dimensional system of fermions interacting through a long-range potential of the form V(q)=g/|q${\mathrm{|}}^{\mathrm{d}+\mathrm{\ensuremath{\epsilon}}\ensuremath{-}|\mathrm{A}\mathrm{x}\mathrm{\ensuremath{-}}1}$ for 0\ensuremath{\leqslant}1. Schmeltzer arrives at this result using both renormalization group (RG) and bosonization. In this Comment we show that a proper application of the bosonization technique to this problem leads instead to a non-Fermi liquid behavior only for \ensuremath{\epsilon}-hat\ensuremath{\geqslant}d-1, in agreement with several previous analyses. We also give a direct physical interpretation of this result. Finally we comment on the application of RG to this problem.