  Using a combination of quantum Monte Carlo simulations in adapted cluster
bases, the finite temperature Lanczos method, and an effective Hamiltonian
approach, we explore the thermodynamic properties of the spin-1/2 Heisenberg
antiferromagnet on the star lattice. We consider various parameter regimes on
this strongly frustrated Archimedean lattice, including the case of homogeneous
couplings as well as the distinct parameter regimes of dominant vs. weak dimer
coupling. For the latter case, we explore the quantum phase diagram in the
presence of inhomogeneous trimer couplings, preserving inversion symmetry. We
compare the efficiency of different cluster decoupling schemes for the quantum
Monte Carlo simulations in terms of the sign problem, contrast the
thermodynamic properties to those of other strongly frustrated quantum magnets,
such as the kagome lattice model, and comment on previous results from
tensor-network calculations regarding a valence bond crystal phase in the
regime of weak dimer coupling. Finally, we relate our results to recently
reported experimental findings on a Cu-based quantum magnetic spin-1/2 compound
with an underlying star lattice structure.
