Fig. 4: QMC-SAC results compared with perturbative energy levels.
From: Fractional and composite excitations of antiferromagnetic quantum spin trimer chains
a–d Show results for Sred(q, ω) in the reduced BZ, while e−h show S(q, ω) in the full BZ as in Fig. 2. In a–d the magenta and red solid lines are respectively the lower boundary \({\omega }_{{{{\rm{l}}}}}={{{\rm{\pi }}}}{J}_{{{{\rm{eff}}}}}\left|\sin (q)\right|/2\) and upper boundary \({\omega }_{{{{\rm{u}}}}}={{{\rm{\pi }}}}{J}_{{{{\rm{eff}}}}}\left|\sin (q/2)\right|\) of the two-spinon continuum, the black solid lines represent the dispersion relations (see Eqs. 6−8) corresponding to the intermediate-energy spectrum. The green solid lines are the dispersion relations (see Eqs. 9−17) corresponding to the higher-energy spectrum. The dispersion relations in full BZ are obtained by unfolding the results in the reduced BZ. The boundaries between the linear and logarithmic color mappings are a–d U0 = 4 and e–h U0 = 5, respectively, as indicated on the color bars.
