Orbital antiferromagnetic currents in a frustrated fermionic ladder

We consider a spinless t-\(t'\) ionic Hubbard chain at 1/2 filling and large hopping ratio \(t'/t\). In this limit, the model adequately maps onto a weakly coupled triangular ladder with a potential interchain bias. The low-energy properties of the system are formed due to the interplay of geometrical frustration, correlations and charge imbalance. We derive the effective field-theoretical model to study universal properties of the model in the scaling limit. We show that at full dynamical frustration, the ground state of the ladder represents a repulsive version of the Luther–Emery liquid with dominant orbital antiferromagnetic correlations exhibiting the slowest power law decay in the ground state. Pairing correlations also display algebraic order but are subdominant. At an incomplete dynamical frustration, a finite commensurability gap is dynamically generated, and the fluctuating OAF transforms to a long-range ordered state with a spontaneously broken time-reversal symmetry. The mass gap in the spectrum of relative density fluctuations gets suppressed upon increasing the potential bias.