Ladders in a magnetic field: a strong coupling approach

TL;DR

This paper develops a strong coupling approach to map ladder spin systems in a magnetic field onto an XXZ model, enabling analysis of critical phases and frustration effects on magnetization plateaus.

Contribution

It introduces a systematic mapping method for ladder models in magnetic fields to an XXZ model, providing quantitative insights into critical behavior and frustration effects.

Findings

Mapping valid in the critical region from zero to saturation magnetization

Relates critical phase properties to exchange integrals

Estimates frustration needed for half-saturation plateau

Abstract

We show that non-frustrated and frustrated ladders in a magnetic field can be systematically mapped onto an XXZ Heisenberg model in a longitudinal magnetic field in the limit where the rung coupling is the dominant one. This mapping is valid in the critical region where the magnetization goes from zero to saturation. It allows one to relate the properties of the critical phase ($H_c^1$, $H_c^2$, the critical exponents) to the exchange integrals and provide quantitative estimates of the frustration needed to create a plateau at half the saturation value for different models of frustration.