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Journal of Physics Condensed Matter

Hidden Fermi liquid; the moral: a good effective low-energy theory is worth all of Monte Carlo with Las Vegas thrown in

Philip Warren Anderson, Philip A. Casey

Published Mar 30, 2010• 5 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/22/16/164201

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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.
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-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 investigate analytically a connection between the t-J model and the strongly correlated Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, with the effect of strong electron correlations accounted by the Gutzwiller projection. We show that in the immediate vicinity of half filling the projected 2D BCS Hamiltonian with strong pairing develops an antiferromagnetically (AF) ordered ground state. This result explicitly demonstrates that antiferromagnetism in this model appears as a natural consequence of the strong Coulomb repulsion in a low doped regime. At moderate doping the ground state of the Gutzwiller-projected BCS Hamiltonian becomes qualitatively similar to Anderson's resonating valence bond state which is known to fit nicely the properties of the t-J model in this regime. These two properties taken together indicate that the projected BCS Hamiltonian captures the essential low-energy physics of the t-J model in the whole underdoped region.
We investigate a connection between the $t\text{\ensuremath{-}}J$ model and the strongly correlated Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, with the effect of strong electron correlations accounted by the Gutzwiller projection. We show that in the immediate vicinity of half filling the projected two-dimensional BCS Hamiltonian with strong pairing develops an antiferromagnetically ordered ground state. This result explicitly demonstrates that antiferromagnetism in this model appears as a natural consequence of the strong Coulomb repulsion in a low doped regime. At moderate doping the ground state of the Gutzwiller-projected BCS Hamiltonian is, in finite-system studies, known to become qualitatively similar to Anderson's resonating valence bond state which, in turn, fits nicely with the properties of the $t\text{\ensuremath{-}}J$ model in that regime. Combined together, these two properties indicate that the projected BCS Hamiltonian at least qualitatively captures the essential low-energy physics of the $t\text{\ensuremath{-}}J$ model in the underdoped region.
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.
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.
Many strongly correlated systems exhibit strange metallic behavior in certain parameter regimes characterized by anomalous transport properties that are irreconcilable with a Fermi-liquid-like description in terms of quasiparticles. The Hubbard model is a standard theoretical starting point to examine the properties of such systems and also exhibits non-Fermi-liquid behavior in simulations. Here we analytically study the two-dimensional hole-doped Hubbard model in the large UUU limit, first identifying a doping-induced percolation transition in the low-energy sector occurring at a definite critical doping pc{p}_{c}pc​ depending on lattice structure. Using the critical properties near this transition we rewrite the Hubbard Hamiltonian and motivate a low-energy lattice-independent large-NNN model with distinct non-Fermi-liquid properties. We show that this model has linear-in-TTT resistivity with doping-dependent slope maximized at p=pcp={p}_{c}p=pc​ and power-law optical conductivity ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}2/3}$. Though the parameters used in developing this theory mean it cannot be directly applied to the cuprate superconductors, we nevertheless reproduce several important phenomena observed in their strange metal phase and also predict these same qualitative behaviors to manifest in other lattices near concrete hole dopings.