Phase transitions and remnants of fractionalization at finite temperature in the triangular lattice quantum loop model

Abstract

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 arrays quantum simulators. However, how the thermal fluctuations interact with constraints has not been explored in the important class of non-bipartite 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 [1] experiences a finite-temperature continuous transition, which smoothly connects to the (2+1)d Cubic* quantum critical point separating the VP and ${\mathbb{Z}}_2$ 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 3-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.

8+10 pages, 4+7 figures

References in corpus (36)

• Probing many-body dynamics on a 51-atom quantum simulator
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
• Prediction of Toric Code Topological Order from Rydberg Blockade
• Quantum phases of Rydberg atoms on a kagome lattice
• Continuous Symmetry Breaking in a Two-dimensional Rydberg Array
• Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems
• Entanglement and topological entropy of the toric code at finite temperature
• Bootstrapping Heisenberg Magnets and their Cubic Instability
• Duality between the deconfined quantum-critical point and the bosonic topological transition
• Algorithms for quantum simulation at finite energies
• Finite-temperature critical point of a glass transition
• A dual-species Rydberg array
• Thermal Order in Conformal Theories
• Six-loop $\epsilon$ expansion study of three-dimensional $n$-vector model with cubic anisotropy
• Triangular lattice quantum dimer model with variable dimer density
• Emergent glassy behavior in a kagome Rydberg atom array
• Quantum Dimer Model on the triangular lattice: Semiclassical and variational approaches to vison dispersion and condensation
• Topological phase transition and single/multi anyon dynamics of $Z_2$ spin liquid
• Dynamics of the quantum dimer model on the triangular lattice: Soft modes and local resonating valence-bond correlations
• Global scheme of sweeping cluster algorithm to sample among topological sectors
• Kernel method for corrections to scaling
• Phase Diagram of Triangular Lattice Quantum Ising Model under External Field
• Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: multicritical point and disorder phase
• Measuring the Loschmidt amplitude for finite-energy properties of the Fermi-Hubbard model on an ion-trap quantum computer
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics
• Cubic fixed point in three dimensions: Monte Carlo simulations of the ${\varphi }^4$ model on the lattice
• Different critical behaviors in cubic to trigonal and tetragonal perovskites
• String Picture of a Frustrated Quantum Magnet and Dimer Model
• Criticality and scaling corrections for two-dimensional Heisenberg models in plaquette patterns with strong and weak couplings
• Interaction-induced topological phase transition at finite temperature
• Quantum Simulation of Two-Dimensional $\mathrm{U}(1)$ Gauge Theory in Rydberg and Rydberg-Dressed Atom Arrays
• Re-entrance effect in the high-temperature critical phase of the quantum dimer model on the square lattice
• Hidden orders and phase transitions for the fully packed quantum loop model on the triangular lattice
• Cubic* criticality emerging from a quantum loop model on triangular lattice