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

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 ${\alpha }^{\prime }\text{−}{\mathrm{NaV}}_2{\mathrm{O}}_5$ may possibly be a consequence of this type of spin-charge coupling.

Figure 1

Temperature dependence of the staggered susceptibility for pseudospins ${\chi }_{\mathrm{T}}\left(\pi \right)$ calculated for the coupled spin-pseudospin Hamiltonian.

Figure 2

Dynamical pseudospin structure factor $S_{\mathrm{T}}(q,\omega )$ for the coupled spin-pseudospin model calculated at $k_{\mathrm{B}}T=0.1J_2$. The results at $J_2∕J_1=0$ are for the quantum Ising model. The peak at $\omega =0$ for $J_2∕J_1>0$ in the uppermost panel of (a) and (b) is spurious, which is due to the error of the maximum entropy method.

Figure 3

Dynamical spin structure factor $S_{\mathrm{S}}(q,\omega )$ for the coupled spin-pseudospin model calculated at $k_{\mathrm{B}}T=0.1J_2$.

Figure 4

Dispersion relations of the spin (open symbols) and pseudospin (solid symbols) excitations calculated at $k_{\mathrm{B}}T=0.1J_2$. Note that the same data at $g=2$ (at $g=1$) are plotted in (a) and (b) [in (c) and (d)] in different energy scales $J_1$ and $J_2$. The dotted line in (a) and (c) is the dispersion relation for the quantum Ising model Eq. (5), and that in (b) and (d) is the scaled dispersion relation for the 1D antiferromagnetic Heisenberg model Eq. (9).

Figure 5

Temperature dependence of the pseudospin quantum fluctuation $⟨T_i^{+}{T}_{i+1}^{-}+\mathrm{H.c.}⟩$ calculated exactly for a dimer model of our spin-pseudospin Hamiltonian Eq. (1).

Figure 6

Temperature dependence of the uniform spin susceptibility ${\chi }_{\mathrm{S}}$ calculated for the coupled spin-pseudospin Hamiltonian. The solid and dotted curves are the uniform susceptibility for the system of noninteracting $S=1∕2$ spins and that for the 1D antiferromagnetic Heisenberg model, respectively.

Figure 7

Effective exchange coupling constant $J_{\mathrm{eff}}\left(T\right)$ estimated from the fitting of the calculated uniform spin susceptibility to the Bonner-Fisher curve.[28] Note that the same data are plotted as a function of $k_{\mathrm{B}}T∕J_1$ (left panels) and of $k_{\mathrm{B}}T∕J_2$ (right panels), whereby a scaling behavior is seen in the latter. The arrows indicate the crossover temperature $T^{*}$. The solid lines are the guide to the eye.

Figure 8

Temperature dependence of the specific heat $C$ calculated for our coupled spin-pseudospin Hamiltonian.