Letter J. Phys. Soc. Jpn. S. Watanabe and K. Miyake 3 culated several U cases, we show the result for U = ∞ , since the result is essentially unchanged even for finite U , as far as U is larger than the bandwidth. First, we show the ground-state phase diagram deter- mined under the assumption of the paramagnetic states with p$_{↑}$ = p$_{↓}$ and δλ = 0 in Fig. 1(a). The first-order valence transition line (solid line with filled triangles) terminates at the QCP (filled circle) at ( ε QCP f , U QCP fc ) = ( − 0 . 3623 , 1 . 1778). For U$_{fc}$ > U QCP fc , ¯ n$_{f}$ shows a jump as a function of ε$_{f}$ , indicating the first-order transition be- tween the paramagnetic metals with ¯ n$_{f}$ close to 1 and ¯ n$_{f}$ < 1 in deep- ε$_{f}$ and shallow- ε$_{f}$ regions, respectively, since large U$_{fc}$ forces electrons to pour into either the f level or the conduction band. 20–22, 24 At the QCP, va- lence fluctuations diverge χ$_{v}$ = − ∂ ¯ n$_{f}$/∂ε$_{f}$ = ∞ , and for U$_{fc}$ < U QCP fc , χ$_{v}$ has a conspicuous peak at ε$_{f}$ represented by the dashed line with open circles in Fig. 1(a), indicat- ing strong valence fluctuations, as shown in Fig. 1(b). At the QCP, the characteristic energy scale of the sys- tem, the so-called Kondo temperature is given by T$_{K}$ ≡ ¯ ε$_{f}$ − µ = 2 . 93 × 10 − 3 with ¯ ε$_{f}$ = ε$_{f}$ + λ + U$_{fc}$ ¯ n$_{c}$ . When the AF states are taken into account, the AF order parameter defined as m$_{s}$ ≡ p 2 ↑ − p 2 ↓ decreases as ε$_{f}$ increases, as shown in Fig. 1(c) for U$_{fc}$ = 0 . 5. When the ground-state energies of this AF state and the para- magnetic state are comapared, the level crossing occurs at ε$_{f}$ = ε c $_{f}$. Then, this AF and paramagnetic phase tran- sition is identified to be of the first order. The phase boundary determined in this way is shown by the solid line with filled squares in Fig. 1(a). We find that the AF order terminates in the vicinity of the first-order valence transition line and the valence-crossover line. These re- sults imply that the suppression of the AF order occurs at the points with strong valence fluctuations. These results are favorably compared with CeRhIn$_{5}$. Applying pressure to Ce systems corresponds to increas- ing ε$_{f}$ , since negative ions approach the tail of 4f wave- function at the Ce site. Experimental fact of the sudden disappearance of the AF order at P = P$_{c}$ and simulta- neous emergence of the ρ$_{0}$ peak as well as ρ ∝ T near P = P$_{c}$ seem to be well described by the results shown in Fig. 1: The vicinity of ε c f for moderate U$_{fc}$ ( < U QCP fc ) with well-developed χ$_{v}$ seems to correspond to the vicinity of P = P$_{c}$ in CeRhIn$_{5}$. To analyze the Fermi-surface change shown by the dHvA measurement in CeRhIn$_{5}$, we apply the magnetic field to Eq. (1) as − h ∑ $_{i}$( S f z i + S c z i ). The dHvA effect 9 and A coefficient 11 were measured at H = 12 ∼ 17 T and H = 15 T, respectively. The magnetic field of H = 15 T is estimated to be h = 0 . 0046 t when the half bandwidth of the conduction band 4 t of Eq. (1) is compared with that of CeRhIn$_{5}$ by the band-structure calculation, about 1.5 eV. 27 Then, we show in Fig. 2 the contour plot of the energy band of Eq. (1) with ↓ spin located at the Fermi level µ for U$_{fc}$ = 0 . 5 at h = 0 . 005. In the AF state, the lower hybridized band of Eq. (1) is folded, giving rise to the hole region emerging at the mag- netic zone boundary connecting k = (0 , π ) and ( π, 0), as shown in Fig. 2(a). Here, in order to make a compar- ison with the “small” Fermi surface, which consists of only conduction electrons, we plot the Fermi surface of the conduction band ε$_{k}$ at the filling ¯ n$_{c}$ = 0 . 8 as the dashed line in Fig. 2(a). This Fermi surface corresponds to that when the hybridization between f and conduction electrons is switched off, V = 0 in Eq. (1); Since f elec- trons for ¯ n$_{f}$ = 1 are located at the localized f level for V = 0, extra electrons in n = 0 . 9, i.e., ¯ n$_{c}$ = 0 . 8 are in the conduction band. We see that the Fermi surface of the AF state for V = 0 . 2 is nearly the same as the “small” Fermi surface represented by the dashed line. This cor- responds to the experimental fact that the dHvA signals of CeRhIn$_{5}$ are very similar to those of LaRhIn$_{5}$ in the AF-ordered phase for P ≤ P$_{c}$ . 9, 13 The shape of the Fermi surface close to the “small” Fermi surface remains until ε$_{f}$ reaches the AF- paramagnetic boundary ε c f = − 0 . 283, as shown in Fig. 2(b), which corresponds to CeRhIn$_{5}$ at P < ∼ P$_{c}$ . When ε$_{f}$ exceeds ε c $_{f}$, the Fermi surface drastically changes, as shown in Fig. 2(c) for ε$_{f}$ = − 0 . 280; The folding of the lower hybridized band disappears and the “large” Fermi surface recovers, which is clearly different from the “small” Fermi surface shown in Figs. 2(a) and (b). This “large” Fermi surface remains in the paramag- netic phase, as shown in Fig. 2(d) for ε$_{f}$ = − 0 . 250. To facilitate the comparison with the dHvA result, we plot the Fermi wave number k$_{F}$ , defined by the distance between k = (0 , 0) and the intersection point of the Fermi surface and the line connecting k = (0 , 0) and ( π, π ), in Fig. 3(a). Here, for the AF-ordered state ε$_{f}$ < ε c $_{f}$, k$_{F}$ in the 1st Brillouin zone is plotted. We see that k$_{F}$ is almost unchanged as a function of ε$_{f}$ , which is nearly the same as k$_{F}$ of the conduction band at ¯ n$_{c}$ = 0 . 8, k c F represented by the solid line. Then, k$_{F}$ shows an abrupt jump at ε c $_{f}$. This Fig. 2. (color online) The contour plot of the energy band with ↓ spin located at the Fermi level µ for t = 1, V = 0 . 2, U = ∞ , U fc = 0 . 5, and n = 0 . 9 at h = 0 . 005: (a) ε f = − 0 . 40, (b) ε f = − 0 . 29, (c) ε f = − 0 . 28, and (d) ε f = − 0 . 25. The E$_{k}$$_{↓}$ > µ parts are represented by white regions. In (a) and (b), the dashed line indicates the Fermi surface of the conduction band, ε$_{k}$ for ¯ n c = 0 . 8.