<i>The Theory of Quantum Liquids, Vol. 1: Normal Fermi Liquids</i>

Pines, David; Nozières, Phillippe; Chang, Howard H. C.

doi:10.1063/1.3034512

Cited by 395 publications

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“…That allows one to express the excited-state quantities in terms of the corresponding deviations δN c ( q j ) and δN s1 ( q j ) of the c and s1 fermion momentum distribution functions, respectively, relative to the initial ground-state values. Alike in a Fermi liquid 39,40 , one can then construct an energy functional whose first-order terms in such deviations refer to the dominant processes and whose second-order terms in the same deviations are associated with the c and s1 fermion residual interactions. Such a functional refers to the square-lattice quantum liquid whose c and s1 fermion energy dispersions are studied in this paper.…”

Section: Quantum Numbers Of the Hubbard Model In The One-and Twomentioning

confidence: 99%

“…In Appendix A some basic information on the one-and two-electron subspace needed for the studies of this paper is provided. The quantum liquid of c and s1 fermions studied in the following is expected to play the same role for many-electron problems with short-range interactions on a square lattice as a Fermi liquid for 3D isotropic metals 39,40,45 .…”

Section: Introductionmentioning

confidence: 96%

“…The square-lattice quantum liquid studied in this paper is non-perturbative in terms of electron operators so that, in contrast to a 3D isotropic Fermi liquid 39,40 , rewriting its theory in terms of the standard formalism of manyelectron physics is an extremely complex problem. Fortunately, the description of the physics of such a quantum liquid simplifies when it is expressed in terms of the c and s1 fermion operators.…”

Section: Introductionmentioning

confidence: 99%

“…ii) It turns out that the quantum problem under consideration is non-perturbative in terms of electron operators so that, in contrast to a 3D isotropic Fermi liquid 39,40 , rewriting the square-lattice quantum liquid theory emerging from the general description used in the studies of this paper for the model in the one-and two-electron subspace in terms of the standard formalism of many-electron physics is an extremely complex problem. Fortunately, such a quantum liquid simplifies when expressed in terms of the c and s1 fermion operators.…”

Section: Introductionmentioning

confidence: 99%

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The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

Carmelo

2010

Nuclear Physics B

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The momentum bands, energy dispersions, and velocities of the charge c fermions and spin-neutral two-spinon s1 fermions of a square-lattice quantum liquid referring to the Hubbard model on such a lattice of edge length L in the one-and two-electron subspace are studied. The model involves the effective nearest-neighbor integral t and on-site repulsion U and can be experimentally realized in systems of correlated ultra-cold fermionic atoms on an optical lattice and thus our results are of interest for such systems. Our investigations profit from a general rotated-electron description, which is consistent with the model global SO(3)×SO(3)×U (1) symmetry. For the model in the oneand two-electron subspace the discrete momentum values of the c and s1 fermions are good quantum numbers so that in contrast to the original strongly-correlated electronic problem their interactions are residual. The use of our description renders an involved many-electron problem into a quantum liquid with some similarities with a Fermi liquid. For the Hubbard model on a square lattice in the one-and two-electron subspace a composite s1 fermion consists of a spin-singlet spinon pair plus an infinitely thin flux tube attached to it. In the U/4t → ∞ limit of infinite on-site interaction the c fermions become non-interacting spinless fermions and the s1 fermion occupancy configurations that generate the spin degrees of freedom of spin-density m = 0 ground states become within a suitable mean-field approximation for the fictitious magnetic field Bs1 ex 3 brought about by the correlations of the original N electron problem those of a full lowest Landau level with N/2 degenerate one-s1 fermion states of the two-dimensional quantum Hall effect. In turn, for U/4t finite the degeneracy of the N/2 one-s1-fermion states is removed by the emergence of a finite-energy-bandwidth s1 fermion dispersion yet the number of s1 band discrete momentum values remains being given by Bs1 L 2 /Φ0 and the s1 effective lattice spacing by as1 = ls1/ √ 2π where ls1 is the fictitious-magnetic-field length and in our units the fictitious-magnetic-field flux quantum reads Φ0 = 1. Elsewhere it is found that the use of the square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions investigated here contributes to the further understanding of the role of electronic correlations in the unusual properties of the hole-doped cuprate superconductors. This indicates that quantum-Hall-type behavior with or without magnetic field may be ubiquitous in nature.

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Section: Quantum Numbers Of the Hubbard Model In The One-and Twomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

Carmelo

2010

Nuclear Physics B

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“…Do we need to go beyond Landau's concept of the Fermi liquid? [3] What, if any, is the evidence for the presence or absence of quasiparticles in the excitation spectra of these complex oxides? The energy resolution of the new instruments is comparable to or better than the energy or temperature scale of superconductivity and the energy of many collective excitations.…”

Section: Introductionmentioning

confidence: 99%

Photoemission as a Probe of the Collective Excitations in Condensed Matter Systems

Johnson

Valla

Very High Resolution Photoelectron Spectroscopy

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Linear response and quasiparticle calculations as probes of the Kohn‐Sham eigenvalues in metals

Eguiluz

1996

Int J of Quantum Chemistry

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The Koh-Sham eigenvalues were formally introduced into density functional theory as Lagrange multipliers in the implementation of the minimum principle for the total energy of a many-electron system. No general results are available concerning the physical significance of these one-electron eigenvalues (with the exception of the highest occupied level, which equals the Fermi energy). Recent ab initio calculations of dynamical response in metals make explicit use of the Koh-Sham band structure, and associated wave functions, through the use of spectral representations. This opens up the possibility of examining the significance of the eigenvalues at an "empirical" level, i.e., through direct comparison with the results of spectroscopic measurements. A particularly interesting example is afforded by new inelastic x-ray scattering experiments on Al. For a special wave vector transfer, 90 = 1.5k,, the measured spectrum provides a direct mapping of the Kohn-Sham noninteracting spectrum. For a range of wave vectors about qo, the bare Kohn-Sham spectrum still reproduces all the main features of the measurements; this suggests that, in this metal, the Koh-Sham eigenvalues are good approximations to the quasiparticle energies. We also discuss the interplay between Kohr-Sham bands and the energy of the "anomalous" plasmon in Cs, whose dispersion bears a signature of the excited-state band structure. Finally, and in a more formal framework, we outline the results of a first-principles comparison between quasiparticle amplitudes and Kohn-Sham wave functions at a jellium surface; the latter turn out to be excellent approximations to the former.

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The Theory of Quantum Liquids, Vol. 1: Normal Fermi Liquids

Cited by 395 publications

References 0 publications

The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

Photoemission as a Probe of the Collective Excitations in Condensed Matter Systems

Linear response and quasiparticle calculations as probes of the Kohn‐Sham eigenvalues in metals

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