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arXiv:1701.03808

Limitations of spin-fermion models in studying underdoped cuprates

Ferraz, Alvaro, E. A. Kochetov

Published Jan 13, 2017• 0 citations
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Abstract

A microscopic basis is provided for the spin-fermion model used to describe the physics of the underdoped cuprates. In this way, a spin-fermion coupling is shown to take care of the local no double occupancy constraint, which is ignored in the weakly coupled regime. This ingredient is proved to be essential to capture the physics of strong correlations, however. We elaborate further on our recent proposal for the strong-coupling version of the spin-fermion model that may prove to be the correct starting point to deal with the strong correlation physics displayed by the underdoped cuprates.

DOI
10.48550/arxiv.1701.03808

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A microscopic basis is provided for the spin-fermion model used to describe the physics of the underdoped cuprates. In this way, a spin-fermion coupling is shown to take care of the local no double occupancy constraint, which is ignored in the weakly coupled regime. This ingredient is proved to be essential to capture the physics of strong correlations, however. We elaborate further on our recent proposal for the strong-coupling version of the spin-fermion model that may prove to be the correct starting point to deal with the strong correlation physics displayed by the underdoped cuprates.
We study the stability of the spin gap phase in the U (1) slave-boson theory of the t - J model in connection with the underdoped cuprates. We approach the spin gap phase from the superconducting state and consider the quantum phase transition of the slave bosons at zero temperature by introducing vortices in the boson superfluid. At finite temperatures, the properties of the bosons are different from those in the strange-metal phase and lead to modified gauge field fluctuations. As a result, the spin gap phase can be stabilized in the quantum-critical (QC) and quantum-disordered (QD) regime of the boson system. We also show that the regime of QD bosons with the paired fermions can be regarded as a strong-coupling version of the recently proposed nodal liquid theory.
We review the intermediate coupling model for treating electronic correlations in the cuprates. Spectral signatures of the intermediate coupling scenario are identified and used to adduce that the cuprates fall in the intermediate rather than the weak or the strong coupling limits. A robust, ‘beyond local-density approximation’ framework for obtaining wide-ranging properties of the cuprates via a GW-approximation based self-consistent self-energy correction for incorporating correlation effects is delineated. In this way, doping- and temperature-dependent spectra, from the undoped insulator to the overdoped metal, in the normal as well as the superconducting state, with features of both weak and strong coupling can be modeled in a material-specific manner with very few parameters. Efficacy of the model is shown by considering available spectroscopic data on electron- and hole-doped cuprates from angle-resolved photoemission, scanning tunneling microscopy/spectroscopy, neutron scattering, inelastic light scattering, optical and other experiments. Generalizations to treat systems with multiple correlated bands such as the heavy-fermions, the ruthenates and the actinides are discussed.
The microscopical analysis of the unconventional and puzzling physics of the underdoped cuprates, as carried out lately by means of the composite operator method (COM) applied to the 2D Hubbard model, is reviewed and systematized. The 2D Hubbard model has been adopted as it has been considered the minimal model capable of describing the most peculiar features of cuprates held responsible for their anomalous behavior. COM is designed to endorse, since its foundation, the systematic emergence in any SCS of new elementary excitations described by composite operators obeying noncanonical algebras. In this case (underdoped cuprates—2D Hubbard model), the residual interactions—beyond a 2-pole approximation—between the new elementary electronic excitations, dictated by the strong local Coulomb repulsion and well described by the two Hubbard composite operators, have been treated within the noncrossing approximation. Given this recipe and exploiting the few unknowns to enforce the Pauli principle content in the solution, it is possible to qualitatively describe some of the anomalous features of high-Tc cuprate superconductors such as large versus small Fermi surface dichotomy, Fermi surface deconstruction (appearance of Fermi arcs), nodal versus antinodal physics, pseudogap(s), and kinks in the electronic dispersion. The resulting scenario envisages a smooth crossover between an ordinary weakly interacting metal sustaining weak, short-range antiferromagnetic correlations in the overdoped regime to an unconventional poor metal characterized by very strong, long-but-finite-range antiferromagnetic correlations leading to momentum-selective non-Fermi liquid features as well as to the opening of a pseudogap and to the striking differences between the nodal and the antinodal dynamics in the underdoped regime.
A partial charge-spin separation fermion-spin theory is developed to study the normal-state properties of the underdoped cuprates. In this approach, the physical electron is decoupled as a gauge invariant dressed holon and spinon, with the dressed holon behaving like a spinful fermion, and represents the charge degree of freedom together with the phase part of the spin degree of freedom, while the dressed spinon is a hard-core boson, and representing the amplitude part of the spin degree of freedom. The electron local constraint for single occupancy is satisfied. Within this approach, the charge and spin dynamics of the underdoped cuprates are studied based on the t-t'-J model. It is shown that the charge dynamics is mainly governed by the scattering from the dressed holons due to the dressed spinon fluctuation, while the scattering from the dressed spinons due to the dressed holon fluctuation dominates the spin dynamics.
We outline the basic ideas involved in a recently proposed [17] derivation of a gauge theory for underdoped cuprates in the “spin gap phase”, performed essentially step by step starting from the t — J model, considered as a model Hamiltonian for the CuO2 layers. The basic tool is the U(1) x SU(2) Chern-Simons bosonization, to which it is dedicated a somewhat detailed discussion. The basic output is a “spingap” not vanishing in any direction and an antiferromagnetic correlation length proportional to the inverse square root of doping concentration, in agreement with data deduced from the neutron experiments. The model also exhibits a small half-pocket Fermi surface around (±π/2, ±π/2) and a linear in temperature dependence of in-plane resistivity in certain temperature range.