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arXiv:1406.0911 · International Conference on Strongly Correlated Electron Systems (SCES)

Relationship between Single-Particle Excitation and Spin Excitation at the Mott Transition

Masanori Kohno

Published Jun 16, 2014• 13 citations
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Abstract

An intuitive interpretation of the relationship between the dispersion relation of the single-particle excitation in a metal and that of the spin excitation in a Mott insulator is presented, based on the results for the one- and two-dimensional Hubbard models obtained by using the Bethe ansatz, dynamical density-matrix renormalization group method, and cluster perturbation theory. The dispersion relation of the spin excitation in the Mott insulator is naturally constructed from that of the single-particle excitation in the zero-doping limit in both one- and two-dimensional Hubbard models, which allows us to interpret the doping-induced states as the states that lose charge character toward the Mott transition. The characteristic feature of the Mott transition is contrasted with the feature of a Fermi liquid and that of the transition between a band insulator and a metal.

DOI
10.7566/jpscp.3.013020

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An intuitive interpretation of the relationship between the dispersion relation of the single-particle excitation in a metal and that of the spin excitation in a Mott insulator is presented, based on the results for the one- and two-dimensional Hubbard models obtained by using the Bethe ansatz, dynamical density-matrix renormalization group method, and cluster perturbation theory. The dispersion relation of the spin excitation in the Mott insulator is naturally constructed from that of the single-particle excitation in the zero-doping limit in both one- and two-dimensional Hubbard models, which allows us to interpret the doping-induced states as the states that lose charge character toward the Mott transition. The characteristic feature of the Mott transition is contrasted with the feature of a Fermi liquid and that of the transition between a band insulator and a metal.
An intuitive interpretation of the relationship between the dispersion relation of the single-particle excitation in a metal and that of the spin excitation in a Mott insulator is presented, based on the results for the one- and two-dimensional Hubbard models obtained by using the Bethe ansatz, dynamical density-matrix renormalization group method, and cluster perturbation theory. The dispersion relation of the spin excitation in the Mott insulator is naturally constructed from that of the single-particle excitation in the zero-doping limit in both one- and two-dimensional Hubbard models, which allows us to interpret the doping-induced states as the states that lose charge character toward the Mott transition. The characteristic feature of the Mott transition is contrasted with the feature of a Fermi liquid and that of the transition between a band insulator and a metal.
By infinitesimal doping of a Mott insulator, states are induced in the Mott gap in the single- particle spectrum. To clarify the nature of these states, their relationships with the magnetically excited states of the Mott insulator are investigated. By using the commutator between the Hamiltonian and an electron creation operator of the t-J model, it is shown that the doping- induced states generally have considerable overlaps with the magnetically excited states of the Mott insulator. In addition, the electron-addition spectral weight of spin-1 states from the spin- 1/2 ground state is shown to be three times as large as that of spin-0 states in the t-J model. These results imply that the doping-induced states in the small-doping limit of a continuous Mott transition can generally be interpreted as essentially the magnetically excited states of the Mott insulator which exhibit the momentum-shifted magnetic dispersion relation primarily outside the free-electron Fermi surface in the electron-addition spectrum following the doping. This picture is supported by numerical results for the one- and two-dimensional t-J models.
In strongly correlated electron systems, the emergence of states in the Mott gap in the single-particle spectrum following the doping of the Mott insulator is a remarkable feature that cannot be explained in a conventional rigid-band picture. Here, based on an analysis of the quantum numbers and the overlaps of relevant states, as well as through a demonstration using the ladder and bilayer $t\text{\ensuremath{-}}J$ models, it is shown that in a continuous Mott transition due to hole doping, the magnetically excited states of the Mott insulator generally emerge in the electron-addition spectrum with the dispersion relation shifted by the Fermi momentum in the momentum region where the lower Hubbard band is not completely filled. This implies that the dispersion relation of a free-electron-like mode in the electron-addition spectrum eventually transforms into essentially the momentum-shifted magnetic dispersion relation of the Mott insulator, while its spectral weight gradually disappears toward the Mott transition. This feature reflects the spin-charge separation of the Mott insulator.
The single-particle spectral properties near the Mott transition in the one-dimensional Hubbard model are investigated by using the dynamical density-matrix renormalization group method and the Bethe ansatz. The pseudogap, hole-pocket behavior, spectral-weight transfer, and upper Hubbard band are explained in terms of spinons, holons, antiholons, and doublons. The Mott transition is characterized by the emergence of a gapless mode whose dispersion relation extends up to the order of hopping t (spin exchange J) in the weak (strong) interaction regime caused by infinitesimal doping.
The Mott transition is usually considered as resulting from the divergence of the effective mass of the quasiparticle in the Fermi-liquid theory; the dispersion relation around the Fermi level is considered to become flat toward the Mott transition. Here, to clarify the characterization of the Mott transition under the assumption of a Fermi-liquid-like ground state, the electron-addition excitation from the Gutzwiller wavefunction in the $t\text{\ensuremath{-}}J$ model is investigated on a chain, ladder, square lattice, and bilayer square lattice in the single-mode approximation using a Monte Carlo method. The numerical results demonstrate that an electronic mode that is continuously deformed from a noninteracting band at zero electron density loses its spectral weight and gradually disappears toward the Mott transition. It exhibits essentially the magnetic dispersion relation shifted by the Fermi momentum in the small-doping limit as indicated by recent studies for the Hubbard and $t\text{\ensuremath{-}}J$ models, even if the ground state is assumed to be a Fermi-liquid-like state exhibiting gradual disappearance of the quasiparticle weight. This implies that, rather than as the divergence of the effective mass or disappearance of the carrier density that is expected in conventional single-particle pictures, the Mott transition can be better understood as freezing of the charge degrees of freedom while the spin degrees of freedom remain active, even if the ground state is like a Fermi liquid.
We analyze the single-particle and collective excitations near the metal to charge-transfer insulator transition, using the slave-boson technique. We show that the Mott transition can be interpreted as a softening of an auxiliary Bose excitation. In the insulating phase the energy of the boson at zero momentum is related to the jump in the chemical potential at zero doping. The dispersion of the collective modes gives rise to the structure of the incoherent Hubbard bands. A similar picture holds for the single-band Hubbard model.