Aspects of the ground state of the U=∞U=\infty Hubbard ladder

We consider two aspects of the ground state of the $U=\infty$ Hubbard ladder: ferromagnetism and the metal-insulator transition at quarter-filling. First, we present rigorous results for the $U=\infty$ Hubbard ladder in the limit of the large inter-chain hopping ($t_{\perp}/t\to\infty$). In this limit, the total spin $S$ of the ground state is shown to be zero for the electron density $n\le 0.5$ and its maximum ($S=S_{max}$) for $n>0.5$. The charge gap at quarter-filling is $2t_{\perp}$. We extend these results to finite $t_{\perp}/t$ by means of the density-matrix renormalization group method. We estimate the phase boundaries with respect to spontaneous magnetization and the charge gap at quarter-filling for finite $t_{\perp}/t$. Applying the extended Aharonov-Bohm method, we give numerical evidence that the critical ratio $t_{\perp}/t$, above which the charge gap opens, is less than 0.001. Ferromagnetism in the t-J ladder is briefly discussed.Comment: 24 pages, RevTex, 11 figures, to appear in Phys.Rev.

Quasiparticles of spatially anisotropic triangular antiferromagnets in a magnetic field

The spectral properties of the spin-1/2 Heisenberg antiferromagnet on an anisotropic triangular lattice in a magnetic field are investigated using a weak-interchain-coupling approach combined with exact solutions of a chain. Dominant modes induced by interchain interactions in a magnetic field behave as quasiparticles which show distinctive features such as anomalous incommensurate ordering and high-energy modes. In terms of them, various unusual features observed in the anisotropic triangular antiferromagnet Cs_2CuCl_4 in a magnetic field are quantitatively explained in a unified manner.Comment: 4 pages, 3 figure

Relation between high-energy quasiparticles of quasi-one-dimensional antiferromagnets in a magnetic field and a doublon of a Hubbard chain

In spin-1/2 one-dimensional Heisenberg antiferromagnets and anisotropic triangular Heisenberg antiferromagnets, high-energy states carrying considerable spectral weights have been observed in a magnetic field using inelastic neutron scattering. Such high-energy properties cannot be explained in terms of either Nambu-Goldstone bosons due to spontaneous breaking of continuous symmetries or quasiparticles in a Tomonaga-Luttinger liquid. Here, we show that the mechanism causing the high-energy states is analogous to that of the upper Hubbard band in the one-dimensional Hubbard model, by theoretically tracing the origin of the high-energy states back to string solutions of the Bethe ansatz.Comment: 6 pages, 1 figur

Ground State Properties of the Two-Dimensional t-J Model

The two-dimensional $t$-$J$ model in the ground state is investigated by the power Lanczos method. The pairing-pairing correlation function for $d_{x^2-y^2}$-wave symmetry is enhanced in the realistic parameter regime for high-$T_c$ superconductors. The charge susceptibility $\chi_c$ shows divergent behavior as $\chi_c\propto\delta^{-1}$ near half-filling for the doping concentration $\delta$, indicating that the value of the dynamical exponent $z$ is four under the assumption of hyperscaling. The peak height of the spin structure factor $S_{max}(Q)$ also behaves as $S_{max}(Q) \propto\delta^{-1}$ near half-filling, which leads to the divergence of the antiferromagnetic correlation length $\xi_m$ as $\xi_m \propto\delta^{-1/2}$. The boundary of phase separation is estimated on the basis of the Maxwell construction. Numerical results are compared with experimental features observed in high-$T_c$ cuprates.Comment: 15 pages, RevTex, 12 PostScript figures, to appear in Phys.Rev.

Spectral properties near the Mott transition in the two-dimensional t-J model

The single-particle spectral properties of the two-dimensional t-J model in the parameter regime relevant to cuprate high-temperature superconductors are investigated using cluster perturbation theory. Various anomalous features observed in cuprate high-temperature superconductors are collectively explained in terms of the dominant modes near the Mott transition in this model. Although the behavior of the dominant modes in the low-energy regime is similar to that in the two-dimensional Hubbard model, significant differences appear near the Mott transition for the high-energy electron removal excitations which can be considered to primarily originate from holon modes in one dimension. The overall spectral features are confirmed to remain almost unchanged as the cluster size is increased from 4x4 to 6x6 sites by using a combined method of the non-abelian dynamical density-matrix renormalization group method and cluster perturbation theory.Comment: 7 pages, 2 figure

Spectral properties near the Mott transition in the two-dimensional Hubbard model with next-nearest-neighbor hopping

The single-particle spectral properties near the Mott transition in the two-dimensional Hubbard model with next-nearest-neighbor hopping are investigated by using cluster perturbation theory. Complicated spectral features of this model are simply interpreted, by considering how the next-nearest-neighbor hopping shifts the spectral weights of the two-dimensional Hubbard model. Various anomalous features observed in hole-doped and electron-doped cuprate high-temperature superconductors are explained in a unified manner as properties near the Mott transition in a two-dimensional system whose spectral weights are shifted by next-nearest-neighbor hopping.Comment: 10 pages, 5 figure

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

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-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.Comment: 7 pages, 1 figur

Magnetic and Electronic Properties of the New Ferrimagnet Sr8CaRe3Cu4O24

Magnetic and electronic properties of the recently-discovered material Sr8CaRe3Cu4O24 were investigated by means of a quantum Monte Carlo simulation, the Green function method and the LSDA+U (local spin-density approximation plus the Hubbard-U term) method. The LSDA+U calculation shows that the ground state is an insulator with magnetic moment M=1.01\muB/f.u., which is consistent with experimental results. The magnetic sites were specified and an effective model for the magnetic properties of this compound derived. The resultant effective model is a three-dimensional Heisenberg model with spin-alternation. Finite-temperature properties of this effective model are investigated by the quantum Monte Carlo method (continuous-time loop algorithm) and the Green function method. The numerical results are consistent with experimental results, indicating that the model is suitable for this material. Using the analysis of the effective model, some predictions for the material are made.Comment: 5 pages, 6 figure

Mott transition and electronic excitation of the Gutzwiller wavefunction

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.Comment: 10 pages, 3 figures; to appear in Phys. Rev.

Dynamically dominant excitations of string solutions in the spin-1/2 antiferromagnetic Heisenberg chain in magnetic fields

Using Bethe-ansatz solutions, we uncover a well-defined continuum in dynamical structure factor $S^{+-}(k,\omega)$ of the spin-1/2 antiferromagnetic Heisenberg chain in magnetic fields. It comes from string solutions which continuously connect the mode of the lowest-energy excitations in the zero-field limit and that of bound states of overturned spins from the ferromagnetic state near the saturation field. We confirm the relevance to real materials through comparisons with experimental results.Comment: 4 pages, 5 figures; to appear in Phys. Rev. Lett