Exactly Solvable Topological Phase Transition in a Quantum Dimer Model

arXiv:2601.15377v4 Announce Type: replace-cross Abstract: We consider a family of generalized Rokhsar-Kivelson (RK) Hamiltonians, which are reverse-engineered to have an arbitrary edge-weighted superposition of dimer coverings as their exact ground state at the RK point. We focus on a quantum dimer model on the triangular lattice, with doubly periodic edge weights. For simplicity we consider a $2\times1$ periodic model in which all weights are set to one except for a tunable horizontal edge weight labeled $\alpha$. We analytically show that the model exhibits a continuous quantum phase transition at $\alpha=3$, changing from a topological $\mathbb{Z}_2$ quantum spin liquid ($\alpha3$). The dimer-dimer correlator decays exponentially on both sides of the transition with the correlation length $\xi\propto1/|\alpha-3|$ and as a power-law at criticality. The vison correlator exhibits an exponential decay in the spin liquid phase, but becomes a constant in the ordered phase, which we explain in terms of loop statistics of the double-dimer model. Using finite-size scaling of the vison correlator, we extract critical exponents consistent with the 2D Ising universality class. Additionally, we analytically show that the topological R\'enyi entropy of order $\infty$ (topological min-entropy) changes from $\log2$ for the quantum spin liquid phase $\alpha3$, thereby analytically confirming the topological nature of the phase transition.

Abstract:We consider a family of generalized Rokhsar-Kivelson (RK) Hamiltonians, which are reverse-engineered to have an arbitrary edge-weighted superposition of dimer coverings as their exact ground state at the RK point. We focus on a quantum dimer model on the triangular lattice, with doubly periodic edge weights. For simplicity we consider a $2\times1$ periodic model in which all weights are set to one except for a tunable horizontal edge weight labeled $\alpha$. We analytically show that the model exhibits a continuous quantum phase transition at $\alpha=3$, changing from a topological $\mathbb{Z}_2$ quantum spin liquid ($\alpha<3$) to a columnar ordered state ($\alpha>3$). The dimer-dimer correlator decays exponentially on both sides of the transition with the correlation length $\xi\propto1/|\alpha-3|$ and as a power-law at criticality. The vison correlator exhibits an exponential decay in the spin liquid phase, but becomes a constant in the ordered phase, which we explain in terms of loop statistics of the double-dimer model. Using finite-size scaling of the vison correlator, we extract critical exponents consistent with the 2D Ising universality class. Additionally, we analytically show that the topological Rényi entropy of order $\infty$ (topological min-entropy) changes from $\log2$ for the quantum spin liquid phase $\alpha<3$, to $0$ for the ordered phase $\alpha>3$, thereby analytically confirming the topological nature of the phase transition.

Strongly Correlated Electrons (cond-mat.str-el); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Quantum Physics (quant-ph)

arXiv:2601.15377 [cond-mat.str-el]

(or arXiv:2601.15377v4 [cond-mat.str-el] for this version)

Phys. Rev. Lett. 137, 056503 (2026)

https://doi.org/10.1103/gdd1-mxy3 DOI(s) linking to related resources

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Exactly Solvable Topological Phase Transition in a Quantum Dimer Model

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