Abstract
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 towards 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 $t$-$J$ 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 non-interacting band at zero electron density loses its spectral weight and gradually disappears towards 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 $t$-$J$ 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.
Highlights
It is generally true that electrons in an interacting system are more difficult to move than those in a noninteracting system
Recent studies on electronic excitation near the Mott transition in the one-dimensional (1D), two-dimensional (2D), and ladder Hubbard and t-J models [5,6,7,8,9,10,11,12,13] have indicated that an electronic mode in the Hubbard gap loses its spectral weight and exhibits the magnetic dispersion relation shifted by the Fermi momentum in the small-doping limit
The validity of the results is confirmed by their comparison with the results obtained using the non-Abelian dynamical density-matrix renormalization-group (DDMRG) method for the chain [Fig. 1(c)] [8] and ladder [Fig. 1(f)] [12], those obtained using the cluster perturbation theory (CPT) for the plane [Fig. 1(i)] [9], and those of the effective theory near half filling for t⊥ t and J⊥ J for the bilayer [Fig. 1(l)] [12]
Summary
It is generally true that electrons in an interacting system are more difficult to move than those in a noninteracting system. The numerical results demonstrate that an electronic mode that is continuously deformed from a noninteracting band at zero electron density gradually loses its spectral weight and exhibits essentially the momentum-shifted magnetic dispersion relation in the small-doping limit, even if the ground state is assumed to be a Fermi-liquid-like state that exhibits gradual disappearance of the quasiparticle weight toward the Mott transition. This suggests that this characteristic of the Mott transition [5,6,7,8,9,10,11,12,13] is not highly sensitive to the ground-state properties, but would be general and fundamental in the Mott transition. The Mott transition can be better understood in terms of this characteristic [5,6,7,8,9,10,11,12,13], rather than conventional single-particle pictures, such as the divergence of the effective mass or disappearance of the carrier density [3], regardless of whether the ground state is like a Fermi liquid or not
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