States induced in the single-particle spectrum by infinitesimal doping of a Mott insulator

Masanori Kohno

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.

J. Monecke

Masanori Kohno

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.

Lin Tian, Fumitaka Fujiwara, Tim Byrnes +1 more

Masatoshi Imada

Masanori Kohno

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.