Systematic study of multi-magnon binding energies in the FM-AFM <i>J</i> ₁ - <i>J</i> ₂ chain

Abstract We present a systematic study of multi-magnon bound states (MBSs) in the spin- <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mfrac> <m:mrow> <m:mn>1</m:mn> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:mfrac> </m:math> $\frac{1}{2}$ FM-AFM J 1 - J 2 chain under magnetic fields using the density-matrix renormalization group method. As a quantitative measure of stability, we compute the magnon binding energy E b ( M , p ) for bound clusters of size p over wide ranges of the frustration ratio J 2 /| J 1 | and the normalized magnetization M / M s . Near saturation, we benchmark our data against the analytic two-magnon result and map out a clear hierarchy of p -magnon states, whose phase boundaries follow an empirical scaling J 2,c ( p ; p + 1)/| J 1 | ≈ 0.34 p −2.3 for large p . We further quantify the relation between the most stable p and the zero-field pitch angle θ , verifying the conjectured inequality 1/ p &gt; θ / π &gt; 1/( p + 1) up to p ≲ 9. The binding energy shows pronounced suppression as J 2 /| J 1 | → 1/4 + and, for some frustration values, attains a maximum below full saturation, indicating that partial depolarization enhances bound-magnon mobility. Close to the FM instability, E b ( M s , p ) exhibits an empirical power-law vanishing consistent with a quantum-Lifshitz scenario. Our results provide a comprehensive, experimentally relevant map of MBS stability across field and frustration, offering concrete guidance for inelastic probes in quasi-one-dimensional magnets.