Phase Transitions and Remnants of Fractionalization at Finite Temperature in the Triangular Lattice Quantum Loop Model

Abstract

<p>The quantum loop and dimer models are archetypal correlated systems with local constraints. With natural foundations in statistical mechanics, they are of direct relevance to various important physical concepts and systems, such as topological order, lattice gauge theories, geometric frustrations, or more recently Rydberg array quantum simulators. However, how the thermal fluctuations interact with constraints has not been explored in the important class of nonbipartite geometries. Here we study, via unbiased quantum Monte Carlo simulations and field theoretical analysis, the finite-temperature phase diagram of the quantum loop model on the triangular lattice. We discover that the recently identified, “hidden” vison plaquette (VP) quantum crystal [X. Ran <em>et al.</em>, Hidden orders and phase transitions for the fully packed quantum loop model on the triangular lattice, <a href="https://dx.doi.org/10.1038/s42005-024-01680-z">Commun. Phys. <strong>7</strong>, 207 (2024)</a>] experiences a finite-temperature continuous transition, which smoothly connects to the (2+1)⁢d Cubic* quantum critical point separating the VP and ℤ2 quantum spin liquid phases. This finite-temperature phase transition acquires a unique property of “remnants of fractionalization” at finite temperature, in that, both the cubic order parameter—the plaquette loop resonance—and its constituent—the vison field—exhibit independent criticality signatures. This phase transition is connected to a three-state Potts transition between the lattice nematic phase and the high-temperature disordered phase. We discuss the relevance of our results for current experiments on quantum simulation platforms.<br></p>