  The recent experimental observations of loop current in Sr$_{2}$IrO$_{4}$,
YBa$_{2}$Cu$_{3}$O$_{7}$, and Sr$_{14}$Cu$_{24}$O$_{41}$ have inspired a
theoretical study that broadly redefines loop current as a manifestation of
quantum liquid crystals. Using the density-matrix renormalization group method,
we investigate the emergence of spin loop-current (sLC) textures in
carrier-doped (i) excitonic insulators, (ii) orbital-selective Mott insulators,
and (iii) two-dimensional Mott insulators, modeled by a two-orbital Hubbard
model on a ladder lattice in (i) and (ii) and a single-orbital Hubbard model on
a square lattice in (iii). Calculating the spatial distribution of spin current
around a bond to which a pinning field is applied, we find conditions for
longer-ranged sLC correlations. In system (i), when using the model parameters
employed to describe the excitonic condensation, we find that a sLC texture
appears near half filling, associated with an excitonic condensation in a spin
channel. In system (ii), using typical sets of model parameters for
BaFe$_{2}$Se$_{3}$, we find that a sLC texture appears at electron fillings
where a block-type antiferromagnetism develops. In system (iii), introducing a
next-nearest-neighbor hopping $t'\sim -0.25$ (in units of the nearest-neighbor
hopping) suggested for high-$T_\text{c}$ cuprates, we find that an axial-sLC
texture emerges at hole-carrier density $\delta=0.125$, where the charge stripe
simultaneously appears.
