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The physics of the triangular lattice Hubbard model exhibits a richphenomenology, ranging from a metal-insulator transition, intriguingthermodynamic behavior, and a putative spin liquid phase at intermediatecoupling, ultimately becoming a magnetic insulator at strong coupling. In thismultimethod study, we combine a finite-temperature tensor network method,minimally entangled thermal typical states (METTS), with twoGreen-function-based methods, connected-determinant diagrammatic Monte Carloand cellular dynamical mean-field theory, to establish several aspects of thismodel. We elucidate the evolution from the metallic to the insulating regimefrom the complementary perspectives brought by these different methods. Wecompute the full thermodynamics of the model on a width-four cylinder usingMETTS in the intermediate to strong coupling regime. We find that theinsulating state hosts a large entropy at intermediate temperatures, whichincreases with the strength of the coupling. Correspondingly, and consistentlywith a thermodynamic Maxwell relation, the double occupancy has a minimum as afunction of temperature which is the manifestation of the Pomeranchuk effect ofincreased localization upon heating. The intermediate coupling regime is foundto exhibit both pronounced chiral as well as stripy antiferromagnetic spincorrelations. We propose a scenario in which time-reversal symmetry-brokenstates compete with stripy-spin states at lowest temperatures.

Mott insulating states with competing orders in the triangular lattice Hubbard model