Fig. 1: Fully packed quantum loop model on the triangular lattice.
a Schematic representation of the QLM; s1 and s2 are the primitive vectors. The t and V terms in the Hamiltonian (1) are depicted in the upper-right insets. The dimer configuration sketched is one of the three LN patterns, with fully packed loops along the s1 direction. b Phase diagram of the QLM obtained from our simulations. The first row of the left subfigure illustrates the three LN dimer configurations, corresponding to the three vison patterns shown on the second row. The triangles v1 and v2 represent two sublattices for the visons, and the red and grey colors in the triangles denote vison numbers ( ± 1) with opposite sign. The first-order phase transition between the LN and VP states occurs at V = 0.05(5). The first row of the middle subfigure is the kinetic energy correlation pattern and the second row is the vison plaquette (VP) pattern based on QMC simulation results, respectively (see Fig. S3a, b in Supplementary Note 3 for values in each triangle). VP is a hidden dimer solid phase without dimer order. The right subfigures illustrate the representative dimer coverings in the \({{\mathbb{Z}}}_{2}\) QSL phase. The continuous phase transition between the VP phase and the QSL occurs at Vc = 0.59(2).
