The collective charge state (holon) in a periodical lattice is defined. The exact commutation relations for the holon operators correspond to the modified para-Fermi statistics of rank M ( M is the number of lattice sites at which the hole can be created), i.e. one state can be occupied by up to M holons. At small concentration, the holon gas can be treated as a bosonic system. In the general case, the holon gas is characterized by the immanent interaction and coupling among the different holon band states, even in the absence of dynamic interactions (the so-called kinematic interaction). In spite of the kinematic interaction, there is no statistical prohibition of Bose-Einstein condensation in the holon system. The possible extension of the approach developed to the coupled hole pairs in high- T c superconductors is discussed.The collective charge state (holon) in a periodical lattice is defined. The exact commutation relations for the holon operators correspond to the modified para-Fermi statistics of rank M ( M is the number of lattice sites at which the hole can be created), i.e. one state can be occupied by up to M holons. At small concentration, the holon gas can be treated as a bosonic system. In the general case, the holon gas is characterized by the immanent interaction and coupling among the different holon band states, even in the absence of dynamic interactions (the so-called kinematic interaction). In spite of the kinematic interaction, there is no statistical prohibition of Bose-Einstein condensation in the holon system. The possible extension of the approach developed to the coupled hole pairs in high- T c superconductors is discussed.

Journal of Physics Condensed MatterAug 2, 199913 citations

Classical holons

Joseph Wheatley

Physica C SuperconductivityFeb 1, 19901 citation

The quantum ideal gas

J. P. Casquilho, P. I. C. Teixeira

Cambridge University Press eBooksDec 23, 20140 citations

Statistics of holons in the quantum hard-core dimer gas

Steven Allan Kivelson

The nature of holons, and in particular, their statistics, are studied in the context of a two-dimensional quantum hard-core dimer gas. This model has been shown to embody the low-energy physics of the short-ranged resonating-valence-bond state. We find that, depending on detailed energetic considerations, the holons either bind a half flux quantum of "statistical flux," in which case they are fermions, or they are free, in which case they are bosons. The exchange energy is shown to favor a fermionic hole while the hole kinetic energy (which generally exceeds the exchange energy) favors bosonic holes. Finally, it is shown that even in the bosonic case, flux quantization is in units of $\frac{\mathrm{hc}}{2e}$ .The nature of holons, and in particular, their statistics, are studied in the context of a two-dimensional quantum hard-core dimer gas. This model has been shown to embody the low-energy physics of the short-ranged resonating-valence-bond state. We find that, depending on detailed energetic considerations, the holons either bind a half flux quantum of "statistical flux," in which case they are fermions, or they are free, in which case they are bosons. The exchange energy is shown to favor a fermionic hole while the hole kinetic energy (which generally exceeds the exchange energy) favors bosonic holes. Finally, it is shown that even in the bosonic case, flux quantization is in units of $\frac{\mathrm{hc}}{2e}$.

Physical review. B, Condensed matterJan 1, 1989102 citations

The quantum gases

C. Di Castro, Roberto Raimondi

Cambridge University Press eBooksAug 27, 20150 citations

Fermi liquid identities for the infinite- U multichannel Anderson model

Eran Lebanon, Piers Coleman

We show how the electron-gas methods of Luttinger, Ward, and Nozi\`eres can be applied to an $\mathrm{SU}(N)$ , multichannel generalization of the infinite- $U$ Anderson impurity model within a Schwinger boson treatment. Working to all orders in a $1∕N$ expansion, we show how the Friedel-Langreth relationship and the Yamada-Yosida-Yoshimori and the Shiba-Korringa relations can be derived under the assumption that the spinon and holon fields are gapped. One of the remarkable features of this treatment is that the Landau amplitudes depend on the exchange of low-energy virtual spinons and holons. We end the paper with a discussion on the extension of our approach to the lattice, where the spinon-holon gap is expected to close at a quantum critical point.We show how the electron-gas methods of Luttinger, Ward, and Nozi\`eres can be applied to an $\mathrm{SU}(N)$, multichannel generalization of the infinite-$U$ Anderson impurity model within a Schwinger boson treatment. Working to all orders in a $1∕N$ expansion, we show how the Friedel-Langreth relationship and the Yamada-Yosida-Yoshimori and the Shiba-Korringa relations can be derived under the assumption that the spinon and holon fields are gapped. One of the remarkable features of this treatment is that the Landau amplitudes depend on the exchange of low-energy virtual spinons and holons. We end the paper with a discussion on the extension of our approach to the lattice, where the spinon-holon gap is expected to close at a quantum critical point.

arXiv:cond-mat/0610027Physical Review BAug 14, 200710 citations

\frac{\mathrm{hc}}{2e}

We show how the electron-gas methods of Luttinger, Ward, and Nozi\`eres can be applied to an

\mathrm{SU}(N)

, multichannel generalization of the infinite-

U

Anderson impurity model within a Schwinger boson treatment. Working to all orders in a

1∕N

expansion, we show how the Friedel-Langreth relationship and the Yamada-Yosida-Yoshimori and the Shiba-Korringa relations can be derived under the assumption that the spinon and holon fields are gapped. One of the remarkable features of this treatment is that the Landau amplitudes depend on the exchange of low-energy virtual spinons and holons. We end the paper with a discussion on the extension of our approach to the lattice, where the spinon-holon gap is expected to close at a quantum critical point.