  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
multi-method 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 (DiagMC)
and cellular dynamical mean-field theory (CDMFT), 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-4 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 localisation 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 nematic, lattice rotational symmetry breaking orders at
lowest temperatures.
