  The physics of the triangular lattice Hubbard model exhibits a rich
phenomenology, ranging from a metal-insulator transition, intriguing
thermodynamic behavior, and a putative spin liquid phase at intermediate
coupling, ultimately becoming a magnetic insulator at strong coupling. In this
multimethod study, we combine a finite-temperature tensor network method,
minimally entangled thermal typical states (METTS), with two
Green-function-based methods, connected-determinant diagrammatic Monte Carlo
and cellular dynamical mean-field theory, to establish several aspects of this
model. We elucidate the evolution from the metallic to the insulating regime
from the complementary perspectives brought by these different methods. We
compute the full thermodynamics of the model on a width-four cylinder using
METTS in the intermediate to strong coupling regime. We find that the
insulating state hosts a large entropy at intermediate temperatures, which
increases with the strength of the coupling. Correspondingly, and consistently
with a thermodynamic Maxwell relation, the double occupancy has a minimum as a
function of temperature which is the manifestation of the Pomeranchuk effect of
increased localization upon heating. The intermediate coupling regime is found
to exhibit both pronounced chiral as well as stripy antiferromagnetic spin
correlations. We propose a scenario in which time-reversal symmetry-broken
states compete with stripy-spin states at lowest temperatures.
