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arXiv:0904.2318

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

志朗 酒井, Yukitoshi Motome, Masatoshi Imada

Published Apr 15, 2009• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.0904.2318

Related papers

Evolution of Electronic Structure of Doped Mott Insulators: Reconstruction of Poles and Zeros of Green’s Function

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We study the evolution of metals from Mott insulators in the carrier-doped 2D Hubbard model using a cluster extension of the dynamical mean-field theory. While the conventional metal is simply characterized by the Fermi surface (pole of the Green function G), interference of the zero surfaces of G with the pole surfaces becomes crucial in the doped Mott insulators. Mutually interfering pole and zero surfaces are dramatically transferred over the Mott gap, when lightly doped holes synergetically loosen the doublon-holon binding. The heart of the Mott physics such as the pseudogap, hole pockets, Fermi arcs, in-gap states, Lifshitz transitions, and non-Fermi liquids appears as natural consequences of this global interference in the frequency space.

arXiv:0809.0950•Physical Review Letters•Feb 4, 2009•206 citations

Doublon-Holon binding in a half-filled band

Philip Phillips

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.

arXiv:0904.0454•Apr 3, 2009•0 citations

Exact integration of the high energy scale in doped Mott insulators

Ting-Pong Choy, Robert G. Leigh, Philip Phillips +1 more

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Reply to ``Comment on `On the Luttinger theorem concerning number of particles in the ground states of systems of interacting fermions','' arXiv:0711.3093v1, by A. Rosch

Behnam Farid

We reply to the Comment by Achim Rosch [1] (arXiv:0711.3093v1) who challenges our finding in Ref. [2] (arXiv:0711.0952v1) with regard to the validity of the Luttinger theorem in the cases of Mott insulating N-particle ground states (even) when the chemical potential used in applying this theorem coincides with the zero-temperature limit of the chemical potential satisfying the equation of state corresponding to N particles. Rosch further argues that the strong-coupling expression for the single-particle Green function presented in Ref. [3] (arXiv:cond-mat/0602656v2) and analyzed in Ref. [2] does not imply destruction of the Mott insulating state at half-filling as a result of an arbitrary weak hopping contribution that breaks particle-hole symmetry and therefore suggests that our conclusion in Ref. [2] to the contrary were incorrect. Here we show the shortcomings of Rosch's arguments.

arXiv:0711.3195•Nov 20, 2007•0 citations

Breakdown of Fermi Liquid Theory in Doped Mott Insulators by Dynamical Spectral Weight Transfer

Philip Phillips, Ting-Pong Choy, Robert G. Leigh

We show that doped Mott insulators exhibit a collective degree of freedom, not made out of the elemental excitations, because the number of single-particle addition states at low energy per electron per spin is greater than one. The presence of such a collective degree of freedom which is not a consequence of proximity to a phase transition is a consequence of dynamical spectral weight transfer from high to low energies. This physics is captured by the charge $2e$ boson that emerges by explicitly integrating out the high-energy scale in the Hubbard model. The charge $2e$ boson binds to a hole, thereby mediating new charge $e$ states at low energy. It is the presence of such charge $e$ states which have no counterpart in the non-interacting system that provides the general mechanism for the breakdown of Fermi liquid theory in doped Mott insulators. The relationship between the charge $2e$ boson formulation and the standard perturbative treatment is explained.

arXiv:0802.3405•Feb 22, 2008•1 citation
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 study the evolution of metals from Mott insulators in the carrier-doped 2D Hubbard model using a cluster extension of the dynamical mean-field theory. While the conventional metal is simply characterized by the Fermi surface (pole of the Green function G), interference of the zero surfaces of G with the pole surfaces becomes crucial in the doped Mott insulators. Mutually interfering pole and zero surfaces are dramatically transferred over the Mott gap, when lightly doped holes synergetically loosen the doublon-holon binding. The heart of the Mott physics such as the pseudogap, hole pockets, Fermi arcs, in-gap states, Lifshitz transitions, and non-Fermi liquids appears as natural consequences of this global interference in the frequency space.
We expand on our earlier work [R. G. Leigh et al., Phys. Rev. Lett. 99, 46404 (2007)] in which we constructed the exact low energy theory of a doped Mott insulator by explicitly integrating (rather than projecting) out the degrees of freedom far away from the chemical potential. The exact low energy theory contains degrees of freedom that cannot be obtained from projective schemes. In particular, a charge $\ifmmode\pm\else\textpm\fi{}2e$ bosonic field that is not made out of elemental excitations emerges at low energies. Such a field accounts for dynamical spectral weight transfer across the Mott gap. At half-filling, we show that two such excitations emerge which play a crucial role in preserving the Luttinger surface along which the single-particle Green's function vanishes. In addition, the interactions with the bosonic fields defeat the artificial local SU(2) symmetry that is present in the Heisenberg model. We also apply this method to the Anderson-U impurity and show that in addition to the Kondo interaction, bosonic degrees of freedom appear as well. Finally, we show that as a result of the bosonic degree of freedom, the electron at low energies is in a linear superposition of two excitations---one arising from the standard projection into the low energy sector and the other from the binding of a hole and the boson.
Since the discovery of half-filled cuprate to be a Mott insulator, the excitation spectra above the chemical potential for the unoccupied states has attracted much research attention. There were many theoretical works using different numerical techniques to study this problem, but many have reached different conclusions. One of the reasons is the lack of very detailed high-resolution experimental results for the theories to be compared with. Recently, the scanning tunneling spectroscopy [P. Cai et al., Nat. Phys. 12, 1047 (2016); C. Ye et al., Nat. Commun. 4, 1365 (2013)] on lightly doped Mott insulator with an antiferromagnetic order found the presence of in-gap states with energy of order half an eV above the chemical potential. The measured spectral properties with doping are not quite consistent with earlier theoretical works. Although the experiment has disorder and localization effect, but for the energy scale we will study here, a model without disorder is sufficed to illustrate the underlying physics. We perform a diagonalization method on top of the variational Monte Carlo calculation to study the evolution of antiferromagnetic Mott state with doped hole concentration in the Hubbard model. Our results found in-gap states that behave similarly with ones reported by STS. These in-gap states acquire a substantial amount of dynamical spectral weight transferred from the upper Hubbard band. The in-gap states move toward chemical potential with increasing spectral weight as doping increases. Our result also provides information about the energy scale of these in-gap states in relation with the Coulomb coupling strength UUU.
We reply to the Comment by Achim Rosch [1] (arXiv:0711.3093v1) who challenges our finding in Ref. [2] (arXiv:0711.0952v1) with regard to the validity of the Luttinger theorem in the cases of Mott insulating N-particle ground states (even) when the chemical potential used in applying this theorem coincides with the zero-temperature limit of the chemical potential satisfying the equation of state corresponding to N particles. Rosch further argues that the strong-coupling expression for the single-particle Green function presented in Ref. [3] (arXiv:cond-mat/0602656v2) and analyzed in Ref. [2] does not imply destruction of the Mott insulating state at half-filling as a result of an arbitrary weak hopping contribution that breaks particle-hole symmetry and therefore suggests that our conclusion in Ref. [2] to the contrary were incorrect. Here we show the shortcomings of Rosch's arguments.
We show that doped Mott insulators exhibit a collective degree of freedom, not made out of the elemental excitations, because the number of single-particle addition states at low energy per electron per spin is greater than one. The presence of such a collective degree of freedom which is not a consequence of proximity to a phase transition is a consequence of dynamical spectral weight transfer from high to low energies. This physics is captured by the charge 2e2e2e boson that emerges by explicitly integrating out the high-energy scale in the Hubbard model. The charge 2e2e2e boson binds to a hole, thereby mediating new charge eee states at low energy. It is the presence of such charge eee states which have no counterpart in the non-interacting system that provides the general mechanism for the breakdown of Fermi liquid theory in doped Mott insulators. The relationship between the charge 2e2e2e boson formulation and the standard perturbative treatment is explained.