Fig. 6

Disentangling features of Mott and Hund physics in a DMFT + NRG study of the 3HHM: static local susceptibilities. The local spin and orbital susceptibilities are shown as functions of T for M1 (orange) and M0 (brown) in (a, b), and for H1 (blue) and W0 (purple) in (c, d), with Tχ depicted in the upper panels (a, c) and χ in the lower panels (b, d). a, c For temperatures well above \(T_{{\mathrm{orb}}}^{{\mathrm{onset}}}\) or \(T_{{\mathrm{spin}}}^{{\mathrm{onset}}}\), respectively, Tχ_orb and Tχ_spin approach plateaus, indicative of a Curie law, as expected for unscreened spin or orbital degrees of freedom. The observed plateau heights are roughly comparable to the values expected⁴⁶ for free local moments with occupancy strictly equal to 2 and, for M1 and H1 (M0 and W0), spin equal to 1 (and 0), for which \(T\chi _{{\mathrm{spin}}}^{{\mathrm{free}}} = {\textstyle{1 \over 3}}\langle \hat S^2\rangle = 2/3{\kern 1pt} (2/5)\) and \(T\chi _{{\mathrm{orb}}}^{{\mathrm{free}}} = {\textstyle{1 \over 8}}\langle \hat T^2\rangle = 1/6\,(4/15)\) indicated by filled and empty squares on the right vertical axes, respectively. (Deviations of the observed plateaus from these local moment values reflect admixtures of states with different occupancy or spin, see Supplementary Fig. 3.) For M1 in (a), the Curie law ceases to hold for both χ_orb and χ_spin below about \(T_{\mathrm{M}} \simeq 0.2\) (filled orange arrows). For H1 in (c), χ_spin deviates from a Curie-like behavior below about \(T \simeq 0.4\) (filled blue arrow), while χ_orb does not follow a Curie law in the temperature range displayed. For M0 in (a) and W0 in (c), deviations from Curie behavior set in at similar temperatures for χ_spin and χ_orb, since χ_spin = 1.5χ_orb for J = 0 (M0: small brown double arrow, W0: outside temperatures range of plot). Thus the onset of screening shows spin-orbital separation for H1, but not for M1 (due to its proximity to the Mott transition), and also not for M0 and W0 (since these have J = 0). b, d For both M1 and H1, χ_spin saturates at very low Fermi-liquid temperatures (not displayed here, but clearly deducible from the underlying zero-temperature NRG data^9,10). By contrast, χ_orb is approximately temperature independent below T = 0.01 (open orange arrow) for M1 in (b) and below T = 0.03 (open blue arrow) for H1 in (d). For M0 in (b) and W0 in (d), χ_orb and χ_spin become temperature independent at similar temperatures. Thus, the completion of screening shows tendencies of spin–orbital separation for M1 and H1 (since J ≠ 0), but not for M0 and W0 (since J = 0). Moreover, \(T_{{\mathrm{spin}}}^{{\mathrm{cmp}}}\) and hence T_FL is much smaller for J ≠ 0 than for J = 0