Abstract
The quantum dimer and loop models exemplify correlated systems governed by local constraints, relevant to concepts like topological order and lattice gauge theories. However, finding generic solutions in the thermodynamic limit is challenging.
Using the sweeping cluster quantum Monte Carlo (QMC) algorithm, we uncover the complete phase diagram of the fully packed quantum loop model (QLM) on the triangular lattice. In addition to established phases, we identify a previously overlooked hidden vison plaquette (VP) phase, , which had been overlooked and misinterpreted as a quantum spin liquid for over a decade. The transition from the VP phase to the quantum spin liquid (QSL) phase belongs to the (2+1)D cubic* universality class. We investigate this quantum criticality through static and dynamic QMC probes, revealing that fractionalized visons in the QSL phase condense into the crystalline VP phase, marked by an anomalously large dimension exponent. We also find that the hidden VP quantum crystal undergoes a finite-temperature continuous transition, which exhibits unique “remnants of fractionalization" at finite temperature.
Research on constrained models in condensed matter physics remains an active and intriguing area of study. The QLM provide theoretical and numerical guidance for ongoing experiments on frustrated quantum magnets and synthetic quantum simulators, such as Rydberg atom arrays. Additionally, numerical methods for solving these constrained models, including QMC, density-matrix renormalization group, and neural networks, are advancing rapidly.
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