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arXiv:0709.0656 · Physical Review B

Hidden Fermi liquid: The secret of high- Tc cuprates

Philip Warren Anderson

Published Nov 6, 2008• 45 citations
arXivHTMLPDF

Abstract

I present a formalism for dealing directly with the effects of the Gutzwiller projection implicit in the $t\text{\ensuremath{-}}J$ model which is widely believed to underlie the phenomenology of the high-${T}_{c}$ cuprates. I suggest that a true BCS condensation from a Fermi-liquid state takes place but in the unphysical space prior to projection. The theory which results upon projection does not follow conventional rules of diagram theory and in fact in the normal state is a $Z=0$ non-Fermi liquid. Anomalous properties of the ``strange metal'' normal state are predicted and compared to experiments.

DOI
10.1103/physrevb.78.174505

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We present a formalism for dealing directly with the effects of the Gutzwiller projection implicit in the t-J model which is widely believed to underlie the phenomenology of the high-T(c) cuprates. We suggest that a true Bardeen-Cooper-Schrieffer condensation from a Fermi liquid state takes place, but in the unphysical space prior to projection. At low doping, however, instead of a hidden Fermi liquid one gets a 'hidden' non-superconducting resonating valence bond state which develops hole pockets upon doping. The theory which results upon projection does not follow conventional rules of diagram theory and in fact in the normal state is a Z = 0 non-Fermi liquid. Anomalous properties of the 'strange metal' normal state are predicted and compared against experimental findings.

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Fractionalized Fermi liquids ($\mathrm{FL}^{\!*}$), elusive metallic states characterized by fractionalized quasiparticles alongside conventional ones and defying Luttinger's theorem, are prime candidates for the pseudogap regime of underdoped cuprates. We show that a $\mathrm{FL}^{\!*}$ phase emerges in the single-band $t$-$J$ model through a simple ghost-Gutzwiller Ansatz, optimized at the cost of a mean-field calculation. The resulting temperature-doping phase diagram encompasses a low-doping $\mathrm{FL}^{\!*}$, a $d$-wave superconducting dome, and an overdoped conventional Fermi liquid, thereby reproducing key qualitative features of cuprate phenomenology.

arXiv:2607.12410•Jul 14, 2026•0 citations
I present a formalism for dealing directly with the effects of the Gutzwiller projection implicit in the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model which is widely believed to underlie the phenomenology of the high-Tc{T}_{c}Tc​ cuprates. I suggest that a true BCS condensation from a Fermi-liquid state takes place but in the unphysical space prior to projection. The theory which results upon projection does not follow conventional rules of diagram theory and in fact in the normal state is a Z=0Z=0Z=0 non-Fermi liquid. Anomalous properties of the ``strange metal'' normal state are predicted and compared to experiments.
We present a formalism for dealing directly with the effects of the Gutzwiller projection implicit in the t-J model which is widely believed to underlie the phenomenology of the high-T(c) cuprates. We suggest that a true Bardeen-Cooper-Schrieffer condensation from a Fermi liquid state takes place, but in the unphysical space prior to projection. At low doping, however, instead of a hidden Fermi liquid one gets a 'hidden' non-superconducting resonating valence bond state which develops hole pockets upon doping. The theory which results upon projection does not follow conventional rules of diagram theory and in fact in the normal state is a Z = 0 non-Fermi liquid. Anomalous properties of the 'strange metal' normal state are predicted and compared against experimental findings.
Low-lying one-particle anomalous excitations are studied for Gutzwiller-projected strongly correlated BCS states. It is found that the one-particle anomalous excitations are highly coherent, and the numerically calculated spectrum can be reproduced quantitatively by a renormalized BCS theory, thus strongly indicating that the nature of low-lying excitations described by the projected BCS states is essentially understood within a renormalized Bogoliubov quasiparticle picture. This finding resembles the well-known fact that a Gutzwiller-projected Fermi gas is a Fermi liquid. The present results are consistent with numerically exact calculations of the two-dimensional $t\text{\ensuremath{-}}J$ model as well as recent photoemission experiments on high-TC{T}_{\mathrm{C}}TC​ cuprate superconductors.
Abstract. The normal state metallic behavior above the superconducting transition temperature (Tsc) remains one of the least understood properties since its discovery in cuprates by Bednorz and Müller [1]. Apart from the pseudogap (T ∗) phenomenon above Tsc, there is this T-linear resistivity that was first recognized by Anderson [2] as strange simply because it does not obey the low-temperature T 2 electron-electron scattering rate predicted from the Fermi liquid theory. Here, we prove that the finite temperature continu-ous quantum phase transition (CTQPT) is responsible for the transition from a strange metal to a Fermi liquid for a given chemical composition. Our proof follows the Green function formalism and the energy-level spacing renormal-ization group method. Interestingly, the CTQPT stated above can be related to the proof derived by Parameswaran, Shankar and Sondhi [3], in which, the one-to-one correspondence between the Fermi gas and Fermi liquid is indeed a special case. The theory is further exploited to give unambiguous explanations as to why and how doping gives rise to spectral weight transfer observed in the soft X-ray absorption spectroscopic measurements for the La-Sr-Cu-O system. PACS: 74.72.-h, 71.10.Hf, 74.25.F-, 74.25.Jb 1.
A variety of low-temperature, normal-state properties of optimally and overdoped cuprate superconductors, including the DC and optical transport responses, are sufficiently anomalous that they might seem to be inconsistent with any quasiparticle description. However, we show by explicit construction that the most salient phenomena can be accounted for in a system with localized "strange scatterers" embedded into a Fermi liquid with a conventional quasiparticle description. Such scatterers could originate from "two-level systems" associated with an electronic glassy state with short-range charge-order correlations.
Fractionalized Fermi liquids (FL ⁣∗\mathrm{FL}^{\!*}FL∗), elusive metallic states characterized by fractionalized quasiparticles alongside conventional ones and defying Luttinger's theorem, are prime candidates for the pseudogap regime of underdoped cuprates. We show that a FL ⁣∗\mathrm{FL}^{\!*}FL∗ phase emerges in the single-band ttt-JJJ model through a simple ghost-Gutzwiller Ansatz, optimized at the cost of a mean-field calculation. The resulting temperature-doping phase diagram encompasses a low-doping FL ⁣∗\mathrm{FL}^{\!*}FL∗, a ddd-wave superconducting dome, and an overdoped conventional Fermi liquid, thereby reproducing key qualitative features of cuprate phenomenology.