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The phase diagrams of highly frustrated quantum spin systems can exhibitfirst-order quantum phase transitions and thermal critical points even in theabsence of any long-ranged magnetic order. However, all unbiased numericaltechniques for investigating frustrated quantum magnets face significantchallenges, and for generic quantum Monte Carlo methods the challenge is thesign problem. Here we report on a general quantum Monte Carlo approach with aloop-update scheme that operates in any basis, and we show that, with anappropriate choice of basis, it allows us to study a frustrated model ofcoupled spin-1/2 trimers: simulations of the trilayer Heisenbergantiferromagnet in the spin-trimer basis are sign-problem-free when theintertrimer couplings are fully frustrated. This model features a first-orderquantum phase transition, from which a line of first-order transitions emergesat finite temperatures and terminates in a thermal critical point. The trimerunit cell hosts an internal degree of freedom that can be controlled to inducean extensive entropy jump at the quantum transition, which alters the shape ofthe first-order line. We explore the consequences for the thermal properties inthe vicinity of the critical point, which include profound changes in the linesof maxima defined by the specific heat. Our findings reveal trimer quantummagnets as fundamental systems capturing in full the complex thermal physics ofthe strongly frustrated regime.

Quantum Monte Carlo simulations in the trimer basis: first-order transitions and thermal critical points in frustrated trilayer magnets