Giant Magnetoresistance in Hubbard Chains

We use numerically unbiased methods to show that the one-dimensional Hubbard model with periodically distributed on-site interactions already contains the minimal ingredients to display the phenomenon of magnetoresistance; i.e., by applying an external magnetic field, a dramatic enhancement on the charge transport is achieved. We reach this conclusion based on the computation of the Drude weight and of the single-particle density of states, applying twisted boundary condition averaging to reduce finite-size effects. The known picture that describes the giant magnetoresistance, by interpreting the scattering amplitudes of parallel or antiparallel polarized currents with local magnetizations, is obtained without having to resort to different entities; itinerant and localized charges are indistinguishable.

Figure 1

(a) Schematic representation of the superlattice with the picture for transport and magnetism (see the text), in the absence or presence of an external magnetic field $\overrightarrow{B}$. In (b) [(c)], we display the spin-resolved density of states of the superlattice ($L=16$) at zero temperature for $h=0$ ($h\ne 0$). In the absence of the field, the Mott gap renders an insulating behavior, while the latter, a metal induced by the field, has a much higher mobility for charges with spin aligned to $\overrightarrow{B}$, as highlighted by the difference in local density of states at the Fermi energy for finite population imbalances in (d). Shading surrounding the curves depicts the error bars after the twisted boundary condition averaging and dashed lines, the Fermi energies.

Figure 2

Local moment $⟨{\widehat{m}}_i^2{⟩}_U$ ($⟨{\widehat{m}}_i^2{⟩}_0$) and its dependence on the interaction strength in repulsive (free) sites, marked by full (empty) symbols in (a), for the superlattice with $h/t=0$. (Inset) The same for a homogeneous lattice; the dashed line denotes the Heisenberg limit of full localization. Site-dependent interactions break particle-hole symmetry and lead to an imbalance of the densities in both types of sites, as shown in (b). In (c), the spin correlations for nearest and next-nearest repulsive sites, taking a repulsive site as the reference, as a function of the external field magnitude with $U/t=4$. (Inset) The negative correlations for $h=0$. All results are presented for a lattice with $L=64$, using DMRG. (d) Dependence on the Zeeman field of the lowest energy state for different $S_z$ sectors of Eq. (1). The ground state is represented by the lower dashed-dotted curve enveloping the lines of each sector.

Figure 3

(a) Drude weight dependence on the Zeeman energy for the superlattice with interaction strength $U/t=4$ and different system sizes. These are obtained via Lanczos diagonalization after using Eq. (2) to obtain the curvatures of $E_{0}L$ vs $\mathrm{\Phi }$ curves; an example for zero field is presented in the inset. (b) The energy difference between periodic and antiperiodic boundary conditions for much larger system sizes obtained via DMRG as a function of the Zeeman energy.

Figure 4

System size scaling of the Drude weight in (a) the absence of a magnetic field and (b) for the value of $h$ that results in the largest $D$ for a given system size. (Insets) The respective scaling analyses for $\mathrm{\Delta }E(0,\pi )$, where the empty symbols denote the DMRG results, for larger systems.

Figure 5

Regime of parameters where the insulator-to-metal transition is observed (shaded area). Small (large) values of the field, result in a Mott (band) insulator. (Inset) The finite-size scaling of the saturation field, shown as an example. $h_{\text{sat}}$ can be similarly obtained via an analysis of an effective two-body problem [22].