Figure 1
(a)
for
(red solid line) and 80 (blue dotted line) at
for
when
. (b)
in the LHB (red lines) for (b-1)
,
; (b-2)
,
; and (b-3)
,
. In (b-1), the blue dashed-dotted line denotes the contribution of dominant modes, while the green region shows the contribution of continua except the dominant modes. In (b-2,3), the light blue regions denote the contribution from
. Arrows indicate
of Eq. (
1). (c) Dispersion relations of the upper edge of the
continuum (red dotted line) and the
mode with
(brown solid line) for
at
. The green dotted line and the dot at
show those of
. (d)
for
at
. Blue squares with the light blue region denote the contribution from
, which is the momentum distribution function in the ground state
. Green diamonds denote the contribution from
; red crosses and pink open circles denote that of the LHB for
and that of the UHB. The vertical yellow line indicates
. Brown solid circles denote the total weight at each
, which satisfies the sum rule within numerical accuracy. (e) Doping dependence of spectral weight
. Solid lines show
of the LHB for
at
(red circles) and 8 (blue squares). Red and blue triangles denote
for
at
and 8. The green dashed line and orange dashed-dotted line indicate
and (
, respectively. Open symbols denote data for
. (f)
for
at
.
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