The roles of magnetic and electric perturbations in the quantum Lifshitz model in $2+1$ dimensions are examined in this paper. The quantum Lifshitz model is an effective field theory for quantum multicritical systems, which include generalized two-dimensional (2D) quantum dimer models in bipartite lattices and their generalizations. It describes a class of quantum phase transitions between ordered and topological phases in $2+1$ dimensions. Magnetic perturbations break the dimer conservation law. Electric excitations, the condensation of which leads to ordered phases, have been studied extensively both in the classical three-dimensional model and in the quantum 2D model. The role of magnetic vortex excitations, the condensation of which drives these systems into a ${\mathbb{Z}}_{2}$ topological phase, has been largely ignored. Recent numerical studies claim that the quantum theory has a peculiar feature: the dynamical exponent $z$ flows continuously and the quantum theory is hence unstable to magnetic vortices. To study the interplay of both excitations, we perform a perturbative renormalization group study to one-loop order and study the stability of the theory away from quantum multicriticality. This is done by generalizing the operator-product expansion to anisotropic models. It is found that the dynamical exponent does not appear to flow, in contrast to the classical Monte Carlo study. Possible reasons for this difference are discussed at length.The roles of magnetic and electric perturbations in the quantum Lifshitz model in $2+1$ dimensions are examined in this paper. The quantum Lifshitz model is an effective field theory for quantum multicritical systems, which include generalized two-dimensional (2D) quantum dimer models in bipartite lattices and their generalizations. It describes a class of quantum phase transitions between ordered and topological phases in $2+1$ dimensions. Magnetic perturbations break the dimer conservation law. Electric excitations, the condensation of which leads to ordered phases, have been studied extensively both in the classical three-dimensional model and in the quantum 2D model. The role of magnetic vortex excitations, the condensation of which drives these systems into a ${\mathbb{Z}}_{2}$ topological phase, has been largely ignored. Recent numerical studies claim that the quantum theory has a peculiar feature: the dynamical exponent $z$ flows continuously and the quantum theory is hence unstable to magnetic vortices. To study the interplay of both excitations, we perform a perturbative renormalization group study to one-loop order and study the stability of the theory away from quantum multicriticality. This is done by generalizing the operator-product expansion to anisotropic models. It is found that the dynamical exponent does not appear to flow, in contrast to the classical Monte Carlo study. Possible reasons for this difference are discussed at length.

arXiv:1205.4911Physical Review BFeb 4, 201316 citations

Finite Temperature Phase Transition in Quantum Dimer Model

Ruixiao Cao, Hidemaro Suwa, Synge Todo

日本物理学会講演概要集Jan 1, 20200 citations

Approaching Kasteleyn Transition in Frustrated Quantum Heisenberg Antiferromagnets

Anonymous, Afonso Rufino, Taras Verkholyak +5 more

We show that the Kasteleyn transition, the abrupt proliferation of infinite strings of defects in classical dimer and related models, can also be relevant for frustrated 2D quantum magnets. This is explicitly demonstrated in a phase of the spin-1/2 Heisenberg diamond-decorated honeycomb lattice where a family of exact eigenstates built as products of dimer and plaquette singlets can be mapped onto the dimer coverings of the honeycomb lattice. The low-temperature properties of this phase are accurately described by an effective dimer model with anisotropic activities and a small, tunable density of monomers, leading to an arbitrarily sharp crossover version of the Kasteleyn transition. The generalization to other geometries and the possibility of realizing this model in organometallic compounds are briefly discussed.We show that the Kasteleyn transition, the abrupt proliferation of infinite strings of defects in classical dimer and related models, can also be relevant for frustrated 2D quantum magnets. This is explicitly demonstrated in a phase of the spin-1/2 Heisenberg diamond-decorated honeycomb lattice where a family of exact eigenstates built as products of dimer and plaquette singlets can be mapped onto the dimer coverings of the honeycomb lattice. The low-temperature properties of this phase are accurately described by an effective dimer model with anisotropic activities and a small, tunable density of monomers, leading to an arbitrarily sharp crossover version of the Kasteleyn transition. The generalization to other geometries and the possibility of realizing this model in organometallic compounds are briefly discussed.

arXiv:2601.14382Physical Review LettersAug 3, 20260 citations

Quantum Dimer Model: Phase Diagrams

Garry Goldstein, Claudio Chamon, Claudio Castelnovo

Bulletin of the American Physical SocietyMar 14, 20160 citations

Exactly Solvable Topological Phase Transition in a Quantum Dimer Model

Laura Shou, Jeet Shah, Matthew Lerner-Brecher +3 more

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 $α$ . We analytically show that the model exhibits a continuous quantum phase transition at $α=3$ , changing from a topological $\mathbb{Z}_2$ quantum spin liquid ( $α<3$ ) to a columnar ordered state ( $α>3$ ). The dimer-dimer correlator decays exponentially on both sides of the transition with the correlation length $ξ\propto1/|α-3|$ 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 $α<3$ , to $0$ for the ordered phase $α>3$ , thereby analytically confirming the topological nature of the phase transition.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 $α$. We analytically show that the model exhibits a continuous quantum phase transition at $α=3$, changing from a topological $\mathbb{Z}_2$ quantum spin liquid ($α<3$) to a columnar ordered state ($α>3$). The dimer-dimer correlator decays exponentially on both sides of the transition with the correlation length $ξ\propto1/|α-3|$ 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 $α<3$, to $0$ for the ordered phase $α>3$, thereby analytically confirming the topological nature of the phase transition.

cond-mat.str-elCross-listedarXiv:2601.15377Physical Review LettersJan 23, 20260 citations

The roles of magnetic and electric perturbations in the quantum Lifshitz model in

2+1

dimensions are examined in this paper. The quantum Lifshitz model is an effective field theory for quantum multicritical systems, which include generalized two-dimensional (2D) quantum dimer models in bipartite lattices and their generalizations. It describes a class of quantum phase transitions between ordered and topological phases in

2+1

dimensions. Magnetic perturbations break the dimer conservation law. Electric excitations, the condensation of which leads to ordered phases, have been studied extensively both in the classical three-dimensional model and in the quantum 2D model. The role of magnetic vortex excitations, the condensation of which drives these systems into a

{\mathbb{Z}}_{2}

topological phase, has been largely ignored. Recent numerical studies claim that the quantum theory has a peculiar feature: the dynamical exponent

z

flows continuously and the quantum theory is hence unstable to magnetic vortices. To study the interplay of both excitations, we perform a perturbative renormalization group study to one-loop order and study the stability of the theory away from quantum multicriticality. This is done by generalizing the operator-product expansion to anisotropic models. It is found that the dynamical exponent does not appear to flow, in contrast to the classical Monte Carlo study. Possible reasons for this difference are discussed at length.

2\times1

periodic model in which all weights are set to one except for a tunable horizontal edge weight labeled

α

. We analytically show that the model exhibits a continuous quantum phase transition at

α=3

, changing from a topological

\mathbb{Z}_2

quantum spin liquid (

α<3

) to a columnar ordered state (

α>3

). The dimer-dimer correlator decays exponentially on both sides of the transition with the correlation length

ξ\propto1/|α-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

α<3

, to

0

for the ordered phase

α>3

, thereby analytically confirming the topological nature of the phase transition.