Tuning the Drude weight of Dirac-Weyl fermions in one-dimensional ring traps

We study the response to an applied flux of an interacting system of Dirac-Weyl fermions confined in a one-dimensional (1D) ring. Combining analytical calculations with density-matrix renormalization group results, we show that tuning of the interactions leads to a unique many-body system that displays either a suppression or an enhancement of the Drude weight—the zero-frequency peak in the ac conductivity—with respect to the noninteracting value. An asymmetry in the interaction strength between same- and different-pseudospin Dirac-Weyl fermions leads to Drude weight enhancement. Vice versa, symmetric interactions lead to Drude weight suppression. Our predictions can be tested in mixtures of ultracold fermions in 1D ring traps.

Figure 1

A sketch of the Creutz ladder model (1) for fermions endowed with a pseudospin degree of freedom $\sigma =\uparrow ,\downarrow$. The right inset illustrates all the single-particle terms in the Hamiltonian (1), while the left inset illustrates the Dirac-Weyl crossing in the energy-quasimomentum dispersion ${\varepsilon }_s\left(k\right)$ for $t=m=g$ and both $s=\pm$ bands.

Figure 2

First- and second-order perturbation theory diagrams. (a) Hartree diagram; (b) Fock diagram; (c) and (d) second-order Hugenholtz diagrams [48]. Solid lines denote bare propagators in all diagrams. Dashed lines in (a) and (b) denote interparticle interactions.

Figure 3

Drude weight $D$ of a 1D interacting Creutz ladder model (with a Dirac-Weyl crossing for the choice $m=g=t)$ measured in units of the noninteracting value $D_0$ and plotted as a function of filling $\rho =N/L$. (a) Drude weight suppression for finite values of $U/t$ and no nearest-neighbor interactions $\left(V=\tilde{V}=0\right)$. (b) Drude weight enhancement for $U/t=0$ and finite values of the nearest-neighbor interaction terms, keeping $V=2\tilde{V}$. Data in this plot refer to a chain with $L=32$ sites and $2\le N\le 32$. At half filling, $D$ always tends to 0 in the thermodynamic limit $L\to \infty$ (see text). The values of $D$ at all other fillings shown in these panels are instead fully converged at the aforementioned system sizes.

Figure 4

Stability of the Drude weight enhancement of an interacting Creutz ladder model $\left(m=g=t\right)$ with respect to the value of the Hubbard on-site interaction $U/t$. The nearest-neighbor interaction parameters are fixed at $V/t=4$ and $\tilde{V}/t=2$. Data in this plot refer to a 1D ring with $L=64$ sites. The enhancement disappears only for $U\gg V,\tilde{V}$.