Phase diagram of the frustrated spin ladder

TL;DR

This paper revises the phase diagram of a frustrated spin ladder, highlighting the role of marginal interactions and showing how changing inter-chain exchanges affects the stability of the columnar dimer phase, confirmed by numerical and analytical methods.

Contribution

It introduces a new understanding of the phase stability in frustrated spin ladders by analyzing the impact of inter-chain interactions and their ferromagnetic or antiferromagnetic nature.

Findings

Marginal inter-chain current-current interactions destabilize the intermediate phase.

Changing inter-chain exchanges to ferromagnetic expands the columnar dimer phase.

Numerical and analytical methods confirm the revised phase diagram.

Abstract

We re-visit the phase diagram of the frustrated spin-1/2 ladder with two competing inter-chain antiferromagnetic exchanges, rung coupling J_\perp and diagonal coupling J_\times. We suggest, based on the accurate renormalization group analysis of the low-energy Hamiltonian of the ladder, that marginal inter-chain current-current interaction plays central role in destabilizing previously predicted intermediate columnar dimer phase in the vicinity of classical degeneracy line J_\perp = 2J_\times. Following this insight we then suggest that changing these competing inter-chain exchanges from the previously considered antiferromagnetic to the ferromagnetic ones eliminates the issue of the marginal interactions altogether and dramatically expands the region of stability of the columnar dimer phase. This analytical prediction is convincingly confirmed by the numerical density matrix renormalization group and exact diagonalization calculations as well as by the perturbative calculation in the strong rung-coupling limit. The phase diagram for ferromagnetic J_\perp and J_\times is determined.