Possibility to detect the bound state of the Heisenberg ferromagnetic chain at intermediate temperature

TL;DR

This study uses advanced numerical methods to explore the temperature-dependent detectability of bound states in Heisenberg ferromagnetic chains, revealing optimal conditions for experimental observation near intermediate temperatures.

Contribution

It provides the first detailed analysis of the temperature dependence of bound states in Heisenberg ferromagnets using the Thermal DMRG algorithm, highlighting conditions for experimental detection.

Findings

Bound state in spin-1/2 chains appears at intermediate temperatures with significant spectral weight.

In spin-1 chains, bound states compete with anti-bound states, affecting spectral signatures.

Presence of biquadratic interactions enhances the visibility of bound or anti-bound states.

Abstract

Motivated by the lack of direct evidence with inelastic neutron scattering of the well documented bound state of Heisenberg ferromagnets, we use the time-dependent Thermal Density Matrix Renormalization Group algorithm to study the temperature dependence of the dynamical spin structure factor of Heisenberg ferromagnetic spin chains. For spin-1/2, we show that the bound state appears as a well defined excitation with significant spectral weight in the temperature range $J/12 \lesssim T \lesssim J/3$, pointing to the possibility of detecting it with inelastic neutron scattering near $k=\pi$ provided the temperature is neither too low nor too high - at low temperature, the spectral weight only grows as $T^{3/2}$, and at high temperature the bound state peak merges with the two-magnon continuum. For spin-1, the situation is more subtle because the bound state with two neighboring spin flips competes with an anti-bound state with two spin-flips on the same site. As a consequence, the relative spectral weight of the bound state is smaller than for spin-1/2, and a weak resonance due to the anti-bound state appears in the continuum. A clearer signature of the bound state (resp. anti-bound state) can be obtained if a negative (resp. positive) biquadratic interaction is present.