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arXiv:0904.0454

Doublon-Holon binding in a half-filled band

Philip Phillips

Published Apr 3, 2009• 0 citations
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Abstract

The arguments presented in PRL. vol. 102, 056404 (2009) are discussed in the context of the vast literature on spectral weight transfer in doped Mott insulators. We show that the conclusions regarding spectral weight transfer in PRL. vol. 102, 056404 (2009) are, where novel, internally inconsistent and where correct, have been reached at least 18 years ago.

DOI
10.48550/arxiv.0904.0454

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Reply to Comment on "Evolution of electronic structure of doped Mott insulator - reconstruction of poles and zeros of Green's function" [arXiv:0904.0454] by P. Phillips

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In a recent Comment [arXiv:0904.0454] on our Letter [Phys. Rev. Lett. 102, 056404 (2009); arXiv:0809:0950], Phillips criticizes one specific issue discussed in our paper, concerning the spectral weight transfer, among our wide-ranging clarifications of the filling-control Mott transition. Here we show that all his criticisms have nothing to do with our contributions. Our nontrivial finding on this particular aspect is a very quick, non-linear increase in the spectral weight just above the chemical potential caused by tiny doping to the Mott insulator, which is indeed unprecedented in the literature. We call attention to its novelty in comparison with the perturbation theory, and reemphasize our picture for the quick weight transfer, that is, an avalanchine screening of doublon-holon binding energy.

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The arguments presented in PRL. vol. 102, 056404 (2009) are discussed in the context of the vast literature on spectral weight transfer in doped Mott insulators. We show that the conclusions regarding spectral weight transfer in PRL. vol. 102, 056404 (2009) are, where novel, internally inconsistent and where correct, have been reached at least 18 years ago.
In a recent Comment [arXiv:0904.0454] on our Letter [Phys. Rev. Lett. 102, 056404 (2009); arXiv:0809:0950], Phillips criticizes one specific issue discussed in our paper, concerning the spectral weight transfer, among our wide-ranging clarifications of the filling-control Mott transition. Here we show that all his criticisms have nothing to do with our contributions. Our nontrivial finding on this particular aspect is a very quick, non-linear increase in the spectral weight just above the chemical potential caused by tiny doping to the Mott insulator, which is indeed unprecedented in the literature. We call attention to its novelty in comparison with the perturbation theory, and reemphasize our picture for the quick weight transfer, that is, an avalanchine screening of doublon-holon binding energy.
We introduce a slave-fermion formulation in which to study the charge dynamics of the half-filled Hubbard model on the square lattice. In this description, the charge degrees of freedom are represented by fermionic holons and doublons and the Mott-insulating characteristics of the ground state are the consequence of holon–doublon bound-state formation. The bosonic spin degrees of freedom are described by the antiferromagnetic Heisenberg model, yielding long-ranged (Néel) magnetic order at zero temperature. Within this framework and in the self-consistent Born approximation, we perform systematic calculations of the average double occupancy, the electronic density of states, the spectral function and the optical conductivity. Qualitatively, our method reproduces the lower and upper Hubbard bands, the spectral-weight transfer into a coherent quasiparticle band at their lower edges and the renormalisation of the Mott gap, which is associated with holon–doublon binding, due to the interactions of both quasiparticle species with the magnons. The zeros of the Green function at the chemical potential give the Luttinger volume, the poles of the self-energy reflect the underlying quasiparticle dispersion with a spin-renormalised hopping parameter and the optical gap is directly related to the Mott gap. Quantitatively, the square-lattice Hubbard model is one of the best-characterised problems in correlated condensed matter and many numerical calculations, all with different strengths and weaknesses, exist with which to benchmark our approach. From the semi-quantitative accuracy of our results for all but the weakest interaction strengths, we conclude that a self-consistent treatment of the spin-fluctuation effects on the charge degrees of freedom captures all the essential physics of the antiferromagnetic Mott–Hubbard insulator. We remark in addition that an analytical approximation with these properties serves a vital function in developing a full understanding of the fundamental physics of the Mott state, both in the antiferromagnetic insulator and at finite temperatures and dopings.
We theoretically study photoemission spectra for photodoped one-dimensional Mott insulators that can host excitons, and show that their spectral characteristics differ qualitatively from those of photodoped semiconductors. In conventional semiconductors, photoemission spectra are well understood; free charge carriers generate spectral weight near the bottom of the conduction band, while the formation of excitons leads to replica features of the valence band appearing inside the band gap. In one-dimensional Mott insulators, on the other hand, strong correlations give rise to fractionalized elementary excitations-spinons, holons, and doublons-which fundamentally modify the photoemission response. We find that when photodoped carriers, i.e., doublons and holons, remain unbound, the photoemission spectrum directly reflects the dispersion of spinons, i.e., magnetic elementary excitations. In contrast, when a doublon and a holon form an excitonic bound state, replica structures of the lower Hubbard band emerge inside the Mott gap, carrying contributions from both spinon and holon excitations. Importantly, the distribution of the in-gap signal depends sensitively on the degree of doublon-holon binding. The origin of these spectral features is clarified through a combination of exact diagonalization and the slave-particle approach. These results indicate that photoemission from photoinduced carriers and excitons in strongly correlated electron systems can provide information on magnetic properties and carrier-binding properties.