Diamagnetism of doped two-leg ladders and probing the nature of their commensurate phases

TL;DR

This paper investigates the magnetic orbital effects in doped two-leg ladders, revealing complex phase transitions, the robustness of superconducting phases, and characterizing insulating phases at specific fillings through combined analytical and numerical methods.

Contribution

It provides a detailed phase diagram of doped two-leg ladders under magnetic fields, identifying new phase transitions and characterizing insulating phases at specific doping levels.

Findings

Spin gap destruction and reentrance at critical fluxes.

Robust superconducting phase with algebraic current correlations.

Distinct insulating phases at delta=1/4 and delta=1/2.

Abstract

We study the magnetic orbital effect of a doped two-leg ladder in the presence of a magnetic field component perpendicular to the ladder plane. Combining both low-energy approach (bosonization) and numerical simulations (density-matrix renormalization group) on the strong coupling limit (t-J model), a rich phase diagram is established as a function of hole doping and magnetic flux. Above a critical flux, the spin gap is destroyed and a Luttinger liquid phase is stabilized. Above a second critical flux, a reentrance of the spin gap at high magnetic flux is found. Interestingly, the phase transitions are associated with a change of sign of the orbital susceptibility. Focusing on the small magnetic field regime, the spin-gapped superconducting phase is robust but immediately acquires algebraic transverse (i.e. along rungs) current correlations which are commensurate with the 4k_F density correlations. In addition, we have computed the zero-field orbital susceptibility for a large range of doping and interactions ratio J/t : we found strong anomalies at low J/t only in the vicinity of the commensurate fillings corresponding to delta = 1/4 and 1/2. Furthermore, the behavior of the orbital susceptibility reveals that the nature of these insulating phases is different: while for delta = 1/4 a 4k_F charge density wave is confirmed, the delta = 1/2 phase is shown to be a bond order wave.