We study the magnetism of a quantum spin- $\frac{1}{2}$ antiferromagnet on a maple-leaf lattice which is obtained by regularly depleting $\frac{1}{7}$ of the sites of a triangular lattice. Although the interactions are set to be spatially isotropic, the ground state shows a stripe N\'eel order and the temperature dependence of magnetic susceptibility follows that of the one-dimensional XXZ model with a finite spin gap. We examine the nature of frustration by mapping the low-energy degenerate manifold of states to the fully packed loop-string model on a dual cluster-depleted honeycomb lattice, finding that the order-by-disorder due to quantum fluctuation characteristic of highly frustrated magnets is responsible for the emergent stripes. The excited magnons split into two spinons and propagate in the one-dimensional direction along the stripe, which is reminiscent of the XXZ or Ising model in one dimension. Unlike most of the previously studied dimensional-reduction effects, our case is purely spontaneous as the interactions of the Hamiltonian retain a two-dimensional structure.We study the magnetism of a quantum spin-$\frac{1}{2}$ antiferromagnet on a maple-leaf lattice which is obtained by regularly depleting $\frac{1}{7}$ of the sites of a triangular lattice. Although the interactions are set to be spatially isotropic, the ground state shows a stripe N\'eel order and the temperature dependence of magnetic susceptibility follows that of the one-dimensional XXZ model with a finite spin gap. We examine the nature of frustration by mapping the low-energy degenerate manifold of states to the fully packed loop-string model on a dual cluster-depleted honeycomb lattice, finding that the order-by-disorder due to quantum fluctuation characteristic of highly frustrated magnets is responsible for the emergent stripes. The excited magnons split into two spinons and propagate in the one-dimensional direction along the stripe, which is reminiscent of the XXZ or Ising model in one dimension. Unlike most of the previously studied dimensional-reduction effects, our case is purely spontaneous as the interactions of the Hamiltonian retain a two-dimensional structure.

arXiv:2110.06491Physical review. B./Physical review. BDec 10, 202113 citations

Classical vertex model dualities in a family of two-dimensional frustrated quantum antiferromagnets

Shankar Balasubramanian, Victor M. Galitski, Ashvin Vishwanath

We study a general class of easy-axis spin models on a lattice of corner sharing even-sided polygons with all-to-all interactions within a plaquette. The low-energy description corresponds to a quantum dimer model on a dual lattice of even coordination number with a multidimer constraint. At an appropriately constructed frustration-free Rokhsar-Kivelson (RK) point, the ground-state wavefunction can be exactly mapped onto a classical vertex model on the dual lattice. When the dual lattice is bipartite, the vertex models are bonded and are self-dual under Wegner's duality, with the self-dual point corresponding to the RK point of the original multidimer model. We argue that the self-dual point is a critical point based on known exact solutions to some of the vertex models. When the dual lattice is nonbipartite, the vertex model is arrowed, and we use numerical methods to argue that there is no phase transition as a function of the vertex weights. Motivated by these wavefunction dualities, we construct two other distinct families of frustration-free Hamiltonians whose ground states can be mapped onto these vertex models. Many of these RK Hamiltonians provably host ${\mathbb{Z}}_{2}$ topologically ordered phases.We study a general class of easy-axis spin models on a lattice of corner sharing even-sided polygons with all-to-all interactions within a plaquette. The low-energy description corresponds to a quantum dimer model on a dual lattice of even coordination number with a multidimer constraint. At an appropriately constructed frustration-free Rokhsar-Kivelson (RK) point, the ground-state wavefunction can be exactly mapped onto a classical vertex model on the dual lattice. When the dual lattice is bipartite, the vertex models are bonded and are self-dual under Wegner's duality, with the self-dual point corresponding to the RK point of the original multidimer model. We argue that the self-dual point is a critical point based on known exact solutions to some of the vertex models. When the dual lattice is nonbipartite, the vertex model is arrowed, and we use numerical methods to argue that there is no phase transition as a function of the vertex weights. Motivated by these wavefunction dualities, we construct two other distinct families of frustration-free Hamiltonians whose ground states can be mapped onto these vertex models. Many of these RK Hamiltonians provably host ${\mathbb{Z}}_{2}$ topologically ordered phases.

arXiv:2112.12161Physical review. B./Physical review. BNov 16, 202210 citations

Frustrated quantum spin models

Ankit Kumar

Jan 1, 20160 citations

Enhanced Quantum behavior on frustrated Ising model: Quantum Approximate Optimization Algorithm study

Seunghan Lee, Hunpyo Lee

We investigated the quantum effects of a frustrated Ising model on a two-dimensional square lattice using the Quantum Approximate Optimization Algorithm (QAOA). While strong spin frustration is known to induce quantum fluctuations at low temperatures, previous classical approaches restricted to binary (up or down) spin configurations have been insufficient to fully capture the quantum contributions of frustration. In this study, we introduced a quantitative metric to evaluate the quantum effects arising from frustration and employed QAOA to differentiate between classical and quantum regimes. Notably, we found that in the weakly frustrated region, QAOA measurements rarely capture first excited states, as they are energetically well separated from the ground state. In contrast, near the quantum phase transition point, excited states appear more frequently in QAOA measurements, highlighting the increased role of quantum fluctuations.We investigated the quantum effects of a frustrated Ising model on a two-dimensional square lattice using the Quantum Approximate Optimization Algorithm (QAOA). While strong spin frustration is known to induce quantum fluctuations at low temperatures, previous classical approaches restricted to binary (up or down) spin configurations have been insufficient to fully capture the quantum contributions of frustration. In this study, we introduced a quantitative metric to evaluate the quantum effects arising from frustration and employed QAOA to differentiate between classical and quantum regimes. Notably, we found that in the weakly frustrated region, QAOA measurements rarely capture first excited states, as they are energetically well separated from the ground state. In contrast, near the quantum phase transition point, excited states appear more frequently in QAOA measurements, highlighting the increased role of quantum fluctuations.

arXiv:2507.07457Jul 10, 20250 citations

Towards quantum simulation of spin dynamics in frustrated systems

Ippei Nakamura, Ryuta Yamamoto, Takeshi Fukuhara

Bulletin of the American Physical SocietyMay 29, 20180 citations

We study the magnetism of a quantum spin-

\frac{1}{2}

antiferromagnet on a maple-leaf lattice which is obtained by regularly depleting

\frac{1}{7}

of the sites of a triangular lattice. Although the interactions are set to be spatially isotropic, the ground state shows a stripe N\'eel order and the temperature dependence of magnetic susceptibility follows that of the one-dimensional XXZ model with a finite spin gap. We examine the nature of frustration by mapping the low-energy degenerate manifold of states to the fully packed loop-string model on a dual cluster-depleted honeycomb lattice, finding that the order-by-disorder due to quantum fluctuation characteristic of highly frustrated magnets is responsible for the emergent stripes. The excited magnons split into two spinons and propagate in the one-dimensional direction along the stripe, which is reminiscent of the XXZ or Ising model in one dimension. Unlike most of the previously studied dimensional-reduction effects, our case is purely spontaneous as the interactions of the Hamiltonian retain a two-dimensional structure.

{\mathbb{Z}}_{2}

topologically ordered phases.