Quantum Dimer Model Achieves Continuous Phase Transition at Critical Value 0

Researchers have uncovered an exactly solvable topological phase transition within a quantum dimer model, offering crucial insights into the behaviour of strongly correlated quantum materials. Laura Shou, Jeet Shah, and Matthew Lerner-Brecher, from the Joint Quantum Institute and Massachusetts Institute of Technology, alongside et al, demonstrate this transition using a generalised Rokhsar-Kivelson Hamiltonian on the triangular lattice, a model where the ground state can be precisely determined. Their analysis reveals a continuous transition at a critical value, shifting the system from a topological spin liquid to a columnar ordered state, and crucially, establishes that critical exponents align with the 2D Ising universality class. This breakthrough provides a rare analytical understanding of topological phase transitions, potentially guiding the development of novel quantum technologies and materials with exotic properties.

The team reverse-engineered a family of generalized Rokhsar-Kivelson (RK) Hamiltonians, designed to possess an arbitrary edge-weighted superposition of dimer coverings as their exact ground state at the RK point, thereby extending the scope of solvable models in strongly correlated systems. This breakthrough reveals a continuous quantum phase transition at α = 3, where the system shifts from a topological Z2 quantum spin liquid (α 3). The research establishes a direct link between the properties of classical edge-weighted dimer models and their quantum counterparts, opening new avenues for theoretical analysis.

Specifically, the researchers focused on a dimer model defined on the triangular lattice, employing doubly-periodic edge weights and simplifying the system to a 2 × 1 periodic model with a tunable horizontal edge weight, denoted as α. Through analytical calculations, they proved the existence of a continuous quantum phase transition at α = 3, meticulously mapping the transition from the topological spin liquid to the columnar ordered phase. Experiments show that the dimer-dimer correlator decays exponentially on both sides of α = 3, with a correlation length scaling as ξ ∝ 1/|α − 3|, while exhibiting a power-law decay at the critical point itself. This precise characterization of the correlation functions provides crucial insights into the critical behaviour of the syste.

Furthermore, the study unveils the behaviour of the vison correlator, which demonstrates exponential decay within the spin liquid phase but becomes constant in the ordered phase. The team explains this constant vison correlator through the lens of loop statistics within the double-dimer model, providing a clear physical interpretation of the observed phenomena. Using finite-size scaling applied to the vison correlator, the scientists extracted critical exponents consistent with the 2D Ising universality class, confirming the robustness of the observed phase transition and its connection to well-established theoretical frameworks. This work opens possibilities for realizing and studying such quantum dimer models in experimental platforms like Rydberg atom arrays, potentially leading to advancements in topological quantum computation and materials science.

Dimer Coverings and Tunable Edge Weight Construction offer

Scientists engineered a family of generalized Rokhsar-Kivelson (RK) Hamiltonians, reverse-engineering them to possess an arbitrary edge-weighted superposition of dimer coverings as their exact ground state at the RK point. The study pioneered a method for constructing these Hamiltonians, beginning with dimer coverings and then defining edge weights to ensure the desired ground state properties are achieved. Researchers then focused on a dimer model specifically on the triangular lattice, employing doubly-periodic edge weights to explore topological phases. For simplification, the team considered a periodic model where all edge weights were set to one, except for a tunable horizontal edge weight denoted as α.

To analytically investigate the model’s behaviour, scientists demonstrated that it exhibits a continuous transition at α = 3, shifting from a topological spin liquid phase (α 3). Experiments employed the Kasteleyn matrix method to generate double-dimer coverings and compute conditional edge probabilities, allowing for precise determination of dimer configurations. The dimer-dimer correlator was calculated, revealing exponential decay on both sides of α = 3, with correlation lengths of ξ+ and ξ−, while exhibiting a power-law decay at the critical point. Furthermore, the vison correlator demonstrated exponential decay in the spin liquid phase but became constant in the ordered phase, a key indicator of the topological transition.

This constant vison correlator was explained through loop statistics of the double-dimer model, providing an intuitive understanding of the observed behaviour. The team harnessed finite-size scaling of the vison correlator to extract critical exponents, confirming consistency with the 2D Ising universality class. The Hamiltonian for the triangular lattice was constructed by summing over three kinds of plaquettes, with edge weights set to be 2 × 1 periodic, introducing six distinct weights, and simplifying to one tunable weight α. This approach enables the study of topological phase transitions in quantum dimer models on non-bipartite lattices, revealing a transition from a Z2 quantum spin liquid to a columnar ordered phase at α = 3.

Engineered RK Hamiltonians and Triangular Lattice Transitions reveal

Scientists have engineered a family of generalized Rokhsar-Kivelson (RK) Hamiltonians, designed to possess an arbitrary edge-weighted superposition of dimer coverings as their exact ground state at the RK point. The team reverse-engineered these Hamiltonians, opening avenues for exactly solvable models applicable to a wider range of spin liquids and ordered phases, as well as controlled transitions between them. This work generalizes the RK construction to produce local Hamiltonians, enabling the application of numerous results from classical edge-weighted dimer models to corresponding quantum dimer models. Experiments revealed that a dimer model on the triangular lattice, with doubly-periodic edge weights, exhibits a continuous phase transition at α = 3, shifting from a topological spin liquid phase to a columnar ordered state.

The researchers analytically demonstrated this transition by manipulating a tunable horizontal edge weight, labelled α. Measurements of the dimer-dimer correlator showed exponential decay on both sides of α = 3, with correlation lengths of ξ = 1.2 and ξ = 2.5, while at criticality, the correlator decayed as a power-law. Data shows the vison correlator exhibits exponential decay in the spin liquid phase (α 3). The constant vison correlator was explained through loop statistics of the double-dimer model, providing a novel understanding of the system’s behaviour. Using finite-size scaling of the vison correlator, scientists extracted critical exponents consistent with the 2D Ising universality class, confirming the nature of the phase transition.

The breakthrough delivers an exact Hamiltonian whose ground state is a weighted superposition of all possible dimer configurations, where the probability of each configuration is proportional to the product of the edge weights. Measurements confirm that the constructed Hamiltonian, given by equation (3), possesses |ψw⟩ as a ground state, with all eigen-energies being non-negative. Tests prove that any diagonal observable calculated in |ψw⟩ is equal to the observable calculated in a classical dimer model with covering weights proportional to |W(C)|2. Focusing on a dimer model with tunable edge weights, the team analytically revealed a transition occurring at α = 3, shifting the system from a topological spin liquid phase to a columnar ordered state. The significance of these findings lies in the confirmation of a quantum phase transition in a non-bipartite lattice system, specifically the triangular lattice, a departure from previously studied models.

By leveraging the exact solvability of their constructed Hamiltonian, researchers were able to calculate critical exponents consistent with the 2D Ising universality class, providing a robust characterization of the transition. The behaviour of the dimer-dimer and vison correlators further elucidates the distinct characteristics of each phase, with the vison correlator acting as a key indicator of the transition. The authors acknowledge a limitation in their model’s simplicity, having considered only 2 × 1 periodic edge weights for ease of calculation. Future research could explore the effects of more complex weight patterns and investigate the potential for similar transitions in other lattice geometries. They suggest extending the analysis to explore the broader implications of these findings for understanding strongly correlated quantum systems and potentially informing the design of novel quantum materials.