Frustration and quantum first-order transitions in trimer quantum magnets

Frustration in quantum magnets gives rise to many complex phase diagrams and phenomena. Yet, especially in higher dimensions, their unbiased treatment still poses a challenge. In the case of quantum Monte Carlo methods, such as the stochastic series expansion (SSE), large-scale simulations are hindered by the negative-sign problem. However, for certain models, a sign-free basis is known exactly. In this work, we extend this set to lattices comprised of fully-frustrated spin trimers. Using the SSE, we simulate two different spin-trimer models and investigate the role of the spin-chirality degree of freedom internal to each frustrated trimer. For the square lattice of triangles, we refute earlier claims of chirality order, whereas in the fully-frustrated trilayer limit, the chirality induces a macroscopic jump in the entropy at a quantum first-order phase transition. These results advance the understanding of frustrated models with multicomponent local Hilbert spaces and increase the applicability of Monte Carlo methods in these systems.