  By utilizing tensor-network-based methods, we investigate the zero- and
finite-temperature properties of the spin-1/2 Heisenberg antiferromagnetic
(HAF) model on an infinite Husimi lattice that contains 3/2 sites per triangle.
The ground state of this model is found to possess vanishing local
magnetization and is featureless; the spin-spin and dimer-dimer correlation
functions are verified to decay exponentially; and its ground-state energy per
site is determined to be $e_0=-0.4343(1)$, which is very close to that
[$e_0=-0.4386(5)$] of the intriguing kagome HAF model. The magnetization curve
shows the absence of a zero-magnetization plateau, implying a gapless
excitation. A $1/3$-magnetization plateau with spin up-up-down state is
observed, which is selected and stabilized by quantum fluctuations. A ground
state phase diagram under magnetic fields is presented. Moreover, both magnetic
susceptibility and the specific heat are studied, whose low-temperature
behaviors reinforce the conclusion that the HAF model on the infinite Husimi
lattice owns a gapless and featureless spin liquid ground state.
