Deconfinement in the presence of a Fermi surface

Abstract

U(1) gauge theory of non-relativistic fermions interacting via compact U(1) gauge fields in the presence of a Fermi surface appears as an effective field theory in low dimensional quantum antiferromagnetism and heavy fermion liquids. We investigate deconfinement of fermions near the Fermi surface in the effective U(1) gauge theory. Our present analysis benchmarks the recent investigation of quantum electrodynamics in two space and one time dimensions ($QED_3$) by Hermele et al. [Phys. Rev. B {\bf 70}, 214437 (2004)]. Utilizing a renormalization group analysis, we show that the effective U(1) gauge theory with a Fermi surface has a stable charged fixed point. Remarkably, the renormalization group equation for an internal charge $e$ (the coupling strength between non-relativistic fermions and U(1) gauge fields) reveals that the conductivity $\sigma$ of fermions near the Fermi surface plays the same role as the flavor number $N$ of massless Dirac fermions in $QED_3$. This leads us to the conclusion that if the conductivity of fermions is sufficiently large, instanton excitations of U(1) gauge fields can be suppressed owing to critical fluctuations of the non-relativistic fermions at the charged fixed point. As a result a critical field theory of non-relativistic fermions interacting via noncompact U(1) gauge fields is obtained at the charged fixed point

Spin-gapped incoherent metal with preformed pairing in the doped antiferromagnetic Mott insulator

“…Since gauge fluctuations are dissipative due to the presence of the Fermi surface, strong damping in gauge fluctuations may give rise to the stability of the mean-field analysis. [25] Actually, one of the present authors has discussed that average gauge fluctuations are proportional to 1/σ f , implying that such fluctuations will be suppressed in the infinite limit of the fermion conductivity σ f and allowing the mean-field analysis stable against gauge fluctuations. [25] This important issue is intensively discussed in section V.…”

“…The presence of gapless excitations can give rise to deconfinement, [25,[32][33][34] thus such a disordered phase ( z σ = 0 → Ω = 0) may be stabilized. However, the existence of such a deconfinement phase depends on how many flavors of gapless matters there are.…”

Antiferromagnetic metal to heavy-fermion metal quantum phase transition in the Kondo lattice model: A strong-coupling approach

“…[3] Because an additional Berry phase term appears in the effective σ model, the two Berry phase terms cancel each other and the contribution of Berry phase vanishes. [6] In the following, although we develop a formulation different from the above standard approach, we can also exclude the Berry phase term. An important issue of this study is how to introduce physics of the Fermi surface of the conduction electrons in the strong coupling approach.…”

“…[16, [23][24][25][26][27][28] Non-Fermi liquid phase corresponds to the deconfined phase which gapless fermion (η σ ) excitations make stable against instanton excitations. [16, 23] The present quantum critical point is identified as the deconfined quantum critical point [24] that can be stable due to critical boson (z σ ) excitations [25] and gapless fermion excitations. [16,23] On the other hand, Fermi liquid corresponds to the confinement phase.…”

“…[5][6][7] Then, the Kondo lattice model can be rewritten in terms of the spin-fractionalized bosons z iσ and renormalized conduction fermions ψ iσ . Integrating out the fermion fields ψ iσ and performing the gradient expansion in the resulting logarithmic action, this conventional strong coupling theory leads to an effective action of the z iσ bosons, which is well known in the context of the nonlinear σ model.…”