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arXiv:cond-mat/0010306 · Physical review. B, Condensed matter

Dynamics of fermions coupling to a U(1) gauge field in the limit e2→∞

Tai Kai Ng

Published Jun 4, 2001• 2 citations
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Abstract

In this paper we study the properties of a gas of fermions coupling to a U(1) gauge field at wave vectors $q<\ensuremath{\Lambda}\ensuremath{\ll}{k}_{F}$ at dimensions larger than 1, where $\ensuremath{\Lambda}\ensuremath{\ll}{k}_{F}$ is a high-momentum cutoff and ${k}_{F}$ is the Fermi wave vector. In particular, we shall consider the ${e}^{2}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, where charge and current fluctuations at wave vectors $q<\ensuremath{\Lambda}$ are forbidden. By generalizing a method reported in a previous paper [Phys. Rev. B 62, 7019 (2000)], we show that the system can be described as a ``marginal'' Fermi liquid of spin $1/2;$ chargeless fermions with vanishing wave functions overlap with the bare fermions in the system.

DOI
10.1103/physrevb.63.245109

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In this paper we study the properties of a gas of fermions coupling to a U(1) gauge field at wave vectors q<\ensuremathΛ\ensuremath≪kFq<\ensuremath{\Lambda}\ensuremath{\ll}{k}_{F}q<\ensuremathΛ\ensuremath≪kF​ at dimensions larger than 1, where \ensuremathΛ\ensuremath≪kF\ensuremath{\Lambda}\ensuremath{\ll}{k}_{F}\ensuremathΛ\ensuremath≪kF​ is a high-momentum cutoff and kF{k}_{F}kF​ is the Fermi wave vector. In particular, we shall consider the e2\ensuremath→\ensuremath∞{e}^{2}\ensuremath{\rightarrow}\ensuremath{\infty}e2\ensuremath→\ensuremath∞ limit, where charge and current fluctuations at wave vectors q<\ensuremathΛq<\ensuremath{\Lambda}q<\ensuremathΛ are forbidden. By generalizing a method reported in a previous paper [Phys. Rev. B 62, 7019 (2000)], we show that the system can be described as a ``marginal'' Fermi liquid of spin 1/2;1/2;1/2; chargeless fermions with vanishing wave functions overlap with the bare fermions in the system.
We discuss in this paper the low energy properties of a liquid of fermions coupling to a U(1) gauge field at wavevectors q<Λ≪k F at dimensions larger than one, where Λ≪k F is a high momentum cutoff and k F is the Fermi wave vector. In particular, we shall consider the e2→∞ limit where charge and current fluctuations at wave vectors q<Λ are forbidden, and the problem reduces to the problem of imposing constraint that no charge and current fluctuations are allowed in the liquid of fermions. Within a bosonization approximation, we show that the low energy properties of the system can be described as a Fermi liquid of chargeless quasiparticles which has vanishing wavefunction overlap with the bare fermion's in the system. The case of a two component system (t–J model) will also be discussed.
We study in this paper the properties of a gas of fermions interacting via a scalar potential $v(q)=4\ensuremath{\pi}{e}^{2}{/q}^{2}$ for $q<\ensuremath{\Lambda}\ensuremath{\ll}{k}_{F}$ at dimensions larger than 1, where $\ensuremath{\Lambda}\ensuremath{\ll}{k}_{F}$ is a high-momentum cutoff and kF{k}_{F}kF​ is the Fermi wave vector. In particular, we shall consider the ${e}^{2}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, where charge fluctuations at wave vectors $q<\ensuremath{\Lambda}$ are forbidden. Within a bosonization approximation, effective actions describing the low-energy physics of the system are constructed, where we show that the system can be described as a Fermi liquid formed by chargeless quasiparticles, which has vanishing wave function overlap with the bare fermions in the system.
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We study the low-energy effective theory for a non-Fermi-liquid state in 2+12+12+1 dimensions, where a transverse U(1) gauge field is coupled with a patch of Fermi surface with NNN flavors of fermion in the large NNN limit. In the low-energy limit, quantum corrections are classified according to the genus of the two-dimensional surface on which Feynman diagrams can be drawn without a crossing in a double line representation and all planar diagrams are important in the leading order. The emerging theory has the similar structure to the four-dimensional SU(N) gauge theory in the large NNN limit. Because of strong quantum fluctuations caused by the abundant low-energy excitations near the Fermi surface, low-energy fermions remain strongly coupled even in the large NNN limit. As a result, there are infinitely many quantum corrections that contribute to the leading frequency dependence of the Green's function of fermion on the Fermi surface. On the contrary, the boson self-energy is not modified beyond the one-loop level and the theory is stable in the large NNN limit. The nonperturbative nature of the theory also shows up in correlation functions of gauge-invariant operators.
A renormalization-group analysis combined with bosonization is performed for fermions interacting with repulsive long-range interaction of the form V(R)\ensuremath{\simeq}1/${\mathit{R}}^{(1\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\epsilon}}\mathrm{^})}$, 0^\ensuremath{\le}1; we find that in any dimension the system is a non-Fermi liquid with a quasiparticle weight which vanishes like ${\mathit{w}}^{\mathrm{\ensuremath{\epsilon}}\mathrm{^}/4}$ when w\ensuremath{\rightarrow}0. For \ensuremath{\epsilon}^\ensuremath{\rightarrow}0 a marginal Fermi liquid is obtained. A nonperturbative solution is obtained using the bosonization method in d\ensuremath{\ge}1 dimensions. Within the same formalism we investigate also the electron-phonon interaction in dimensions d=3-\ensuremath{\epsilon}. When the coupling constant is imaginary, one obtains a time-dependent potential similar to what is obtained for fermions coupled to transversed U(1) gauge bosons. A non-Fermi-liquid behavior is found for d\ensuremath{\le}3.