Magnetic-field-induced criticality in superconducting two-leg ladders

We study magnetic-field-induced critical singularities in the superconducting phase of the hole-doped Hubbard model of repulsively interacting electrons, defined on a two-leg ladder. We argue that, provided the low-energy spin excitations in doped ladders carry electric charge, the low-temperature thermodynamic quantities, such as the specific-heat coefficient and magnetic susceptibility, will show logarithmic singularities in the quantum critical regime. This behavior is in drastic contrast to the magnetic-field-induced criticality in undoped Mott insulator ladders, which is governed by the zero-scale-factor universality with its hallmark square-root singularities.

Figure 1

Cartoon of the lowest-energy spin excitations in the doped Hubbard ladders with on-site interaction $U$ and hopping amplitudes $t$. Open circles denote lattice sites, and solid circles represent electrons. In-plane magnetic field $h$ couples only to electron spins. On the last plaquette there is a hole-pair depicted, and in (a) spinon-holons are depicted on first and third rungs, while in (b) the bound state of the magnon and hole pair is located on the second plaquette.