  A quantum spin liquid (QSL) is a state of matter characterized by
fractionalized quasiparticle excitations, quantum entanglement, and a lack of
long-range magnetic order. However, QSLs have evaded definitive experimental
observation. Several Yb$^{3+}$-based triangular lattice antiferromagnets with
effective $S$ = $\frac{1}{2}$ have been suggested to stabilize the QSL state as
the ground state. Here, we build a comprehensive magnetic temperature phase
diagram of a high-quality single crystalline KYbSe$_2$ via heat capacity and
magnetocaloric effect down to 30 mK with magnetic field applied along the
$a$-axis. At zero magnetic field, we observe the magnetic long-range order at
$T_N$ = 0.29 K entering 120 degrees ordered state in heat capacity, consistent
with neutron scattering studies. Analysis of the low-temperature ($T$) specific
heat ($C$) at zero magnetic field indicates linear $T$-dependence of $C/T$ and
a broad hump of $C/T$ in the proximate QSL region above $T_N$. By applying
magnetic field, we observe the up-up-down phase with 1/3 magnetization plateau
and oblique phases, in addition to two new phases. These observations strongly
indicate that while KYbSe$_2$ closely exhibits characteristics resembling an
ideal triangular lattice, deviations may exist, such as the effect of the
next-nearest-neighbor exchange interaction, calling for careful consideration
for spin Hamiltonian modeling. Further investigations into tuning parameters,
such as chemical pressure, could potentially induce an intriguing QSL phase in
the material.
