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arXiv:cond-mat/0512310 · Physical Review B

Spin and charge excitations in the anisotropic Hubbard ladder at quarter filling with charge-ordering instability

Y. Ohta, T. Nakaegawa, Satoshi Ejima

Published Jan 3, 2006• 5 citations
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Abstract

Quantum Monte Carlo and density-matrix renormalization group methods are used to study the coupled spin-pseudospin Hamiltonian in one-dimension (1D) that models the charge-ordering instability of the anisotropic Hubbard ladder at quarter filling. We calculate the temperature dependence of the uniform spin susceptibility and specific heat as well as the spin and charge excitation spectra of the system. We thereby show that there is a parameter and temperature region where the spin degrees of freedom are separated from the charge degrees of freedom and behave like a 1D antiferromagnetic Heisenberg model, and that, outside this parameter region and above a crossover temperature, the spin excitations are largely affected by the charge fluctuations. We argue that observed anomalous spin dynamics in the disorder phase of a typical charge-ordered material ${\ensuremath{\alpha}}^{\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{NaV}}_{2}{\mathrm{O}}_{5}$ may possibly be a consequence of this type of spin-charge coupling.

DOI
10.1103/physrevb.73.045101

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Quantum Monte Carlo and density-matrix renormalization group methods are used to study the coupled spin-pseudospin Hamiltonian in one-dimension (1D) that models the charge-ordering instability of the anisotropic Hubbard ladder at quarter filling. We calculate the temperature dependence of the uniform spin susceptibility and specific heat as well as the spin and charge excitation spectra of the system. We thereby show that there is a parameter and temperature region where the spin degrees of freedom are separated from the charge degrees of freedom and behave like a 1D antiferromagnetic Heisenberg model, and that, outside this parameter region and above a crossover temperature, the spin excitations are largely affected by the charge fluctuations. We argue that observed anomalous spin dynamics in the disorder phase of a typical charge-ordered material \ensuremathα\ensuremath′\ensuremath-NaV2O5{\ensuremath{\alpha}}^{\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{NaV}}_{2}{\mathrm{O}}_{5}\ensuremathα\ensuremath′\ensuremath-NaV2​O5​ may possibly be a consequence of this type of spin-charge coupling.
Quantum Monte Carlo (QMC) and density-matrix renormalization group (DMRG) methods are used to study the coupled spin-pseudospin Hamiltonian in one-dimension (1D) that models the charge-ordering instability of the anisotropic Hubbard ladder at quarter filling. We calculate the temperature dependence of the uniform spin susceptibility and specific heat as well as the spin and charge excitation spectra of the system. We show that there is a parameter and temperature region where the spin degrees of freedom are separated from the charge degrees of freedom and behave like a 1D antiferromagnetic Heisenberg model, and that, outside this parameter region and above a crossover temperature, the spin excitations are largely affected by the charge fluctuation. We argue that observed anomalous spin dynamics in the disorder phase of a typical charge-ordered material α′α'α′-NaV2_22​O5_55​ may possibly be a consequence of this type of spin-charge coupling.
By following the ideas of Emery and Noguera, a recent study revealed the dynamics of the charge sector of a one-dimensional quarter-filled electronic system with extended Hubbard interactions to be that of an effective pseudospin transverse-field Ising model (TFIM) in the strong-coupling limit. With the twin motivations of studying the co-existing charge and spin order found in strongly correlated chain systems and the effects of interchain couplings, we investigate the phase diagram of coupled effective (TFIM) systems. A bosonization and renormalization group (RG) analysis for a two-leg TFIM ladder yields a rich phase diagram showing Wigner/Peierls charge order and Néel/dimer spin order. In a broad parameter regime, the orbital antiferromagnetic phase is found to be stable. An intermediate gapless phase of finite width is found to lie in between two charge-ordered gapped phases. Kosterlitz-Thouless transitions are found to lead from the gapless phase to either of the charge-ordered phases. A detailed analysis is also carried out for the dimensional crossover physics when many such pseudospin systems are coupled to one another. Importantly, the analysis reveals the key role of critical quantum fluctuations in driving the strong dispersion in the transverse directions, as well as a T = 0 deconfinement transition. Our work is potentially relevant for a unified description of a class of strongly correlated, quarter-filled chain and ladder systems.
We investigate the ground-state phase diagram of the quarter-filled Hubbard ladder with nearest-neighbor Coulomb repulsion VVV using the density matrix renormalization-group technique. The ground state is homogeneous at small V,V,V, a ``checkerboard'' charge-ordered insulator at large VVV and not too small on site Coulomb repulsion U, and is phase separated for moderate or large VVV and small U. The zero-temperature transition between the homogeneous and the charge-ordered phase is found to be second order. In both the homogeneous and the charge-ordered phases the existence of a spin gap mainly depends on the ratio of interchain to intrachain hopping. In the second part of the paper we construct an effective Hamiltonian for the spin degrees of freedom in the strong-coupling, charge-ordered regime that maps the system onto a frustrated spin chain. The opening of a spin gap is thus connected with spontaneous dimerization.
We study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum---with low-energy peaks resembling spinonic excitations---already at intermediate on-site repulsion as small as $U/t\ensuremath{\sim}2--3$, although ratios of peak intensities at different momenta continue evolving with increasing U/tU/tU/t converging only slowly to the Heisenberg limit. We discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of U/tU/tU/t of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.
We calculate spin and charge excitation spectra of the one-dimensional (1D) quarter-filled Hubbard model with nearest-neighbor ttt and next-nearest-neighbor ${t}^{\ensuremath{'}}$ hopping integrals using the dynamical density-matrix renormalization group technique. We consider a case where ttt (>0)(>0)(>0) is much smaller than ${t}^{\ensuremath{'}}$ (>0)(>0)(>0). First, we examine the accuracy of our method based on comparison between our result and exact noninteracting spectrum. Next, we investigate the spectra with the on-site Coulomb interaction. We find that the spin and charge excitation spectra are essentially the same as those of the 1D quarter-filled Hubbard (and $t\text{\ensuremath{-}}J$) model for the two 1D chains along the hopping integral ${t}^{\ensuremath{'}}$. However, the hopping integral ttt $(<{t}^{\ensuremath{'}})$ plays a crucial role in the short-range correlations and low-energy excitaions; ferromagnetic correlation between electrons on neighboring sites is enhanced and pairing correlation between the electrons is induced. Consequently, a spin-triplet superconducting state may be derived.
We present density matrix renormalization group calculations of the ground-state properties of quarter-filled ladders including static electron-lattice coupling. Isolated ladders and two coupled ladders are considered, with model parameters obtained from band-structure calculations for ${\ensuremath{\alpha}}^{\ensuremath{'}}\text{\ensuremath{-}}\mathrm{Na}{\mathrm{V}}_{2}{\mathrm{O}}_{5}$. The relevant Holstein coupling to the lattice causes static out-of-plane lattice distortions, which appear concurrently with a charge-ordered state and which exhibit the same zigzag pattern observed in experiments. The inclusion of electron-lattice coupling drastically reduces the critical nearest-neighbor Coulomb repulsion Vc{V}_{c}Vc​ needed to obtain the charge-ordered state. No spin gap is present in the ordered phase. The charge ordering is driven by the Coulomb repulsion and the electron-lattice interaction. With electron-lattice interaction, coupling two ladders has virtually no effect on Vc{V}_{c}Vc​ or on the characteristics of the charge-ordered phase. At V=0.46eVV=0.46\phantom{\rule{0.3em}{0ex}}\mathrm{eV}V=0.46eV, a value consistent with previous estimates, the lattice distortion, charge gap, charge-order parameter, and the effective spin coupling are in good agreement with experimental data for NaV2O5\mathrm{Na}{\mathrm{V}}_{2}{\mathrm{O}}_{5}NaV2​O5​.