Bosonization and density-matrix renormalization group studies of Fulde-Ferrell-Larkin-Ovchinnikov phase and irrational magnetization plateaus in coupled chains

TL;DR

This paper combines analytical and numerical methods to study coupled fermionic chains under magnetic fields, revealing complex phases including irrational magnetization plateaus and extended Fulde-Ferrell-Larkin-Ovchinnikov states, with implications for superconductivity.

Contribution

It provides a systematic comparison of bosonization and DMRG results, identifying novel magnetization plateaus and superconducting phases in coupled chains under magnetic fields.

Findings

Existence of doping-dependent irrational magnetization plateaus.

Identification of extended FFLO phases in Hubbard and t-J models.

Prediction of polarized triplet pairing at high magnetic fields.

Abstract

We review the properties of two coupled fermionic chains, or ladders, under a magnetic field parallel to the lattice plane. Results are computed by complementary analytical (bosonization) and numerical (density-matrix renormalization group) methods which allows a systematic comparison. Limiting cases such as coupled bands and coupled chains regimes are discussed. We particularly focus on the evolution of the superconducting correlations under increasing field and on the presence of irrational magnetization plateaus. We found the existence of large doping-dependent magnetization plateaus in the weakly-interacting and strong-coupling limits and in the non-trivial case of isotropic couplings. We report on the existence of extended Fulde-Ferrell-Larkin-Ovchinnikov phases within the isotropic t-J and Hubbard models, deduced from the evolution of different observables under magnetic field. Emphasis is put on the variety of superconducting order parameters present at high magnetic field. We have also computed the evolution of the Luttinger exponent corresponding to the ungaped spin mode appearing at finite magnetization. In the coupled chain regime, the possibility of having polarized triplet pairing under high field is predicted by bosonization.