Multiple crossovers in interacting quantum wires

We study tunneling of electrons into and between interacting wires in the spin-incoherent regime subject to a magnetic field. The tunneling currents follow power laws of the applied voltage with exponents that depend on whether the electron spins at the relevant length scales are polarized or disordered. The crossover length (or energy) scale is exponential in the applied field. In a finite-size wire multiple crossovers can occur.

Figure 1

Hubbard chain with infinite on-site repulsion $U$ that allows sites to be singly occupied only. (a) Moving charge carriers (holes in the electron occupation) shift also the spin configuration such that the spin state at a given site may change. The relative position of the spins remains fixed, however. (b) The spin state at a given site does not fluctuate in a spin-polarized Hubbard chain, when the spin configuration is translationally invariant. (c) Also the spin configuration at the site that is at the end of the chain cannot be changed by the charge dynamics.

Figure 2

(Color online) Comparison between the logarithms of the sum $S$ (solid line) and its approximation Eq. (24) (dashed line) at $E_{\mathrm{Z}}=10k_{B}T$. The approximation improves as $w$ grows large.