Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1806.08145 · Physical review. B./Physical review. B

Tunneling-induced restoration of classical degeneracy in quantum kagome ice

Kai-Hsin Wu, Yi-Ping Huang, Ying-Jer Kao

Published Apr 29, 2019• 8 citations
arXivHTMLPDF

Abstract

Quantum effect is expected to dictate the behavior of physical systems at low temperature. For quantum magnets with geometrical frustration, quantum fluctuation usually lifts the macroscopic classical degeneracy, and exotic quantum states emerge. However, how different types of quantum processes entangle wave functions in a constrained Hilbert space is not well understood. Here, we study the topological entanglement entropy and the thermal entropy of a quantum ice model on a geometrically frustrated kagome lattice. We find that the system does not show a ${Z}_{2}$ topological order down to extremely low temperature, yet continues to behave like a classical kagome ice with finite residual entropy. Our theoretical analysis indicates an intricate competition of off-diagonal and diagonal quantum processes leading to the quasidegeneracy of states and effectively, the classical degeneracy is restored.

DOI
10.1103/physrevb.99.134440

Related papers

A Semi-Classical Analysis of Order from Disorder

Benoît Douçot, Pascal Simon

We study in this paper the Heisenberg antiferromagnet with nearest neighbours interactions on the Husimi cactus, a system which has locally the same topology as the Kagomé lattice. This system has a huge classical degeneracy corresponding to an extensive number of degrees of freedom. We show that unlike thermal fluctuations, quantum fluctuations lift partially this degeneracy and favour a discrete subset of classical ground states. In order to clarify the origin of these effects, we have set up a general semi-classical analysis of the order from disorder phenomenon and clearly identified the differences between classical and quantum fluctuations. This semi-classical approach also enables us to classify various situations where a selection mechanism still occurs. Moreover, once a discrete set of ground states has been preselected, our analysis suggests that tunelling processes within this set should be the dominant effect underlying the strange low energy spectrum of Kagomé-like lattices.

•Jan 1, 1998•5 citations

Frustration-induced emergent Hilbert space fragmentation

Kyungmin Lee, Arijeet Pal, Hitesh J. Changlani

Although most quantum systems thermalize locally on short timescales independent of initial conditions, recent developments have shown this is not always the case. Lattice geometry and quantum mechanics can conspire to produce constrained quantum dynamics and associated glassy behavior, a phenomenon that falls outside the rubric of the eigenstate thermalization hypothesis. Constraints ``fragment'' the many-body Hilbert space due to which some states remain insulated from others and the system fails to attain thermal equilibrium. Such fragmentation is a hallmark of geometrically frustrated magnets with low-energy ``icelike manifolds'' exhibiting a broad range of relaxation times for different initial states. Focusing on the highly frustrated kagome lattice, we demonstrate these phenomena in the Balents-Fisher-Girvin Hamiltonian (easy-axis regime), and a three-coloring model (easy-plane regime), both with constrained Hilbert spaces. We study their level statistics and relaxation dynamics to develop a coherent picture of fragmentation in various limits of the XXZ model on the kagome lattice.

arXiv:2011.01936•Physical review. B./Physical review. B•Jun 15, 2021•48 citations

A semiclassical analysis of order from disorder

Benoît Douçot, Pascal Simon

In this paper we present several examples of order due to disorder phenomena and mainly focus on the Heisenberg antiferromagnet with nearest neighbour interactions on the Husimi cactus, a system which locally has the same topology as the Kagomé lattice. This system has a huge classical degeneracy corresponding to an extensive number of degrees of freedom. We show that unlike thermal fluctuations, quantum fluctuations partially lift this degeneracy and favour a discrete subset of classical ground states. In order to clarify the origin of these effects, we have set up a general semiclassical analysis of the order from disorder phenomenon and clearly identified the differences between classical and quantum fluctuations. This semiclassical approach also enables us to classify various situations where a selection mechanism still occurs. Moreover, once a discrete set of ground states has been preselected, our analysis suggests that tunelling processes within this set should be the dominant effect underlying the strange low-energy spectrum of Kagomé-like lattices.

arXiv:cond-mat/9802212•Journal of Physics A Mathematical and General•Jul 17, 1998•11 citations

Quantum simulation of interlayer charge ordering in Kagome frustrated-magnet

Kumar Ghosh, Sabre Kais

The interplay between interlayer coupling and quantum fluctuations governs charge ordering and defect dynamics in Kagome systems, yet these parameters are intrinsically entangled in existing Kagome metals and artificial spin-ice platforms, preventing their independent control. Here we realize a bilayer Kagome frustrated-magnet simulator comprising 1,536 connected spins on D-Wave quantum annealer, in which the effective quantum drive, $Γ_{\rm eff}$, and interlayer exchange, $J_{\perp}$, are independently programmable. We observe an interlayer-driven transition from ferroelectric to antiferroelectric Ice-II charge order at a critical coupling $(J_\perp/J_1)^*\approx0.04$, a phenomenon absent in single-layer geometries. Monte Carlo calculations show the transition persists in the classical limit, allowing the experimentally observed critical coupling to quantify the quantum renormalization induced by fluctuations. Applying resulting phase diagram to Kagome charge-density-wave materials places KV$_3$Sb$_5$ and RbV$_3$Sb$_5$ deep within the ordered antiferroelectric regime, while locating CsV$_3$Sb$_5$ near the phase boundary, providing a natural explanation for its metastable $2\times2\times4$ stacking order. We further show that restricting charge-correlation measurements to ice-rule configurations resolves a systematic underestimation of ordering in conventional analyses, enabling direct reinterpretation of resonant X-ray, XMCD, STM and anomalous Hall experiments. Finally, we demonstrate that the same charge-sector reorganization framework explains near-degenerate plateau states in the metallic Kagome spin-ice HoAgGe and yields experimentally testable predictions for nanomagnetic, Kagome-metal and van der Waals frustrated systems. These results establish programmable quantum annealers as scalable simulators of emergent charge order and monopole physics in frustrated quantum matter.

cond-mat.str-elCross-listedarXiv:2603.27826•Mar 31, 2026

Ground-state properties of quantum triangular ice

S. A. Owerre

Motivated by recent quantum Monte Carlo (QMC) simulations of the quantum Kagome ice model by Juan Carrasquilla et al., [Nat. Commun., 6, 7421 (2015)], we study the ground-state properties of this model on the triangular lattice. In the presence of a magnetic field $h$, the Hamiltonian possesses competing interactions between a ${Z}_{2}$-invariant easy-axis ferromagnetic interaction ${J}_{\ifmmode\pm\else\textpm\fi{}\ifmmode\pm\else\textpm\fi{}}$ and a frustrated Ising term ${J}_{z}$. As in the U(1)-invariant model, we obtain four classical distinctive phases, however, the classical phases in the ${Z}_{2}$-invariant model are different. They are as follows: a fully polarized (FP) ferromagnet for large $h$, an easy-axis canted ferromagnet (CFM) with broken ${Z}_{2}$ symmetry for small $h$ and dominant ${J}_{\ifmmode\pm\else\textpm\fi{}\ifmmode\pm\else\textpm\fi{}}$, a ferrosolid phase with broken translational and ${Z}_{2}$ symmetries for small $h$ and dominant ${J}_{z}$, and two lobes with $m=\ensuremath{\langle}{S}_{z}\ensuremath{\rangle}=\ifmmode\pm\else\textpm\fi{}1/6$ for small $h$ and dominant ${J}_{z}$. We show that quantum fluctuations are suppressed in this model, hence the large-$S$ expansion gives an accurate picture of the ground-state properties. When quantum fluctuations are introduced, we show that the ferrosolid state is the ground state in the dominant Ising limit at zero magnetic field. It remains robust for ${J}_{z}\ensuremath{\rightarrow}\ensuremath{\infty}$. With nonzero magnetic field the classical lobes acquire a finite magnetic susceptibility with no ${S}_{z}$ order. We present the trends of the ground-state energy and the magnetizations. We also present a detail analysis of the CFM.

arXiv:1511.01843•Physical review. B./Physical review. B•Mar 29, 2016•2 citations

Quantum Triangular Ice: Complete quantum phase diagram

S. A. Owerre

Motivated by recent quantum Monte Carlo (QMC) simulations of the quantum Kagome ice model by Juan Carrasquilla, et al., [Nature Communications 6, 7421 (2015)], we study the ground state properties of this model on the triangular lattice. In the presence of a magnetic field $h$, the Hamiltonian possesses competing interactions between a $Z_2$-invariant easy-axis ferromagnetic interaction $J_{\pm\pm}$ and a frustrated Ising term $J_z$. As in the U(1)-invariant model, we obtain four classical distinctive phases, however, the classical phases in the $Z_2$-invariant model are different. They are as follows: a fully polarized (FP) ferromagnet for large $h$, an easy-axis canted ferromagnet (CFM) with broken $Z_2$ symmetry for small $h$ and dominant $J_{\pm\pm}$, a {\it ferrosolid} phase with broken translational and $Z_2$ symmetries for small $h$ and dominant $J_{z}$, and two lobes with $m=\langle S_z\rangle=\pm 1/6$ for small $h$ and dominant $J_{z}$. We show that quantum fluctuations are suppressed in this model, hence the large-$S$ expansion gives an accurate picture of the ground state properties. When quantum fluctuations are introduced, we show that the {\it ferrosolid} state is the ground state in the dominant Ising limit at zero magnetic field. It remains robust for $J_z\to\infty$. With nonzero magnetic field the classical lobes acquire a finite magnetic susceptibility with no $S_z$-order. We present the trends of the ground state energy and the magnetizations. We also present a detail analysis of the CFM.

•Nov 5, 2015•0 citations
Quantum effect is expected to dictate the behavior of physical systems at low temperature. For quantum magnets with geometrical frustration, quantum fluctuation usually lifts the macroscopic classical degeneracy, and exotic quantum states emerge. However, how different types of quantum processes entangle wave functions in a constrained Hilbert space is not well understood. Here, we study the topological entanglement entropy and the thermal entropy of a quantum ice model on a geometrically frustrated kagome lattice. We find that the system does not show a Z2{Z}_{2}Z2​ topological order down to extremely low temperature, yet continues to behave like a classical kagome ice with finite residual entropy. Our theoretical analysis indicates an intricate competition of off-diagonal and diagonal quantum processes leading to the quasidegeneracy of states and effectively, the classical degeneracy is restored.
We study in this paper the Heisenberg antiferromagnet with nearest neighbours interactions on the Husimi cactus, a system which has locally the same topology as the Kagomé lattice. This system has a huge classical degeneracy corresponding to an extensive number of degrees of freedom. We show that unlike thermal fluctuations, quantum fluctuations lift partially this degeneracy and favour a discrete subset of classical ground states. In order to clarify the origin of these effects, we have set up a general semi-classical analysis of the order from disorder phenomenon and clearly identified the differences between classical and quantum fluctuations. This semi-classical approach also enables us to classify various situations where a selection mechanism still occurs. Moreover, once a discrete set of ground states has been preselected, our analysis suggests that tunelling processes within this set should be the dominant effect underlying the strange low energy spectrum of Kagomé-like lattices.
Although most quantum systems thermalize locally on short timescales independent of initial conditions, recent developments have shown this is not always the case. Lattice geometry and quantum mechanics can conspire to produce constrained quantum dynamics and associated glassy behavior, a phenomenon that falls outside the rubric of the eigenstate thermalization hypothesis. Constraints ``fragment'' the many-body Hilbert space due to which some states remain insulated from others and the system fails to attain thermal equilibrium. Such fragmentation is a hallmark of geometrically frustrated magnets with low-energy ``icelike manifolds'' exhibiting a broad range of relaxation times for different initial states. Focusing on the highly frustrated kagome lattice, we demonstrate these phenomena in the Balents-Fisher-Girvin Hamiltonian (easy-axis regime), and a three-coloring model (easy-plane regime), both with constrained Hilbert spaces. We study their level statistics and relaxation dynamics to develop a coherent picture of fragmentation in various limits of the XXZ model on the kagome lattice.
In this paper we present several examples of order due to disorder phenomena and mainly focus on the Heisenberg antiferromagnet with nearest neighbour interactions on the Husimi cactus, a system which locally has the same topology as the Kagomé lattice. This system has a huge classical degeneracy corresponding to an extensive number of degrees of freedom. We show that unlike thermal fluctuations, quantum fluctuations partially lift this degeneracy and favour a discrete subset of classical ground states. In order to clarify the origin of these effects, we have set up a general semiclassical analysis of the order from disorder phenomenon and clearly identified the differences between classical and quantum fluctuations. This semiclassical approach also enables us to classify various situations where a selection mechanism still occurs. Moreover, once a discrete set of ground states has been preselected, our analysis suggests that tunelling processes within this set should be the dominant effect underlying the strange low-energy spectrum of Kagomé-like lattices.
The interplay between interlayer coupling and quantum fluctuations governs charge ordering and defect dynamics in Kagome systems, yet these parameters are intrinsically entangled in existing Kagome metals and artificial spin-ice platforms, preventing their independent control. Here we realize a bilayer Kagome frustrated-magnet simulator comprising 1,536 connected spins on D-Wave quantum annealer, in which the effective quantum drive, ΓeffΓ_{\rm eff}Γeff​, and interlayer exchange, J⊥J_{\perp}J⊥​, are independently programmable. We observe an interlayer-driven transition from ferroelectric to antiferroelectric Ice-II charge order at a critical coupling (J⊥/J1)∗≈0.04(J_\perp/J_1)^*\approx0.04(J⊥​/J1​)∗≈0.04, a phenomenon absent in single-layer geometries. Monte Carlo calculations show the transition persists in the classical limit, allowing the experimentally observed critical coupling to quantify the quantum renormalization induced by fluctuations. Applying resulting phase diagram to Kagome charge-density-wave materials places KV3_33​Sb5_55​ and RbV3_33​Sb5_55​ deep within the ordered antiferroelectric regime, while locating CsV3_33​Sb5_55​ near the phase boundary, providing a natural explanation for its metastable 2×2×42\times2\times42×2×4 stacking order. We further show that restricting charge-correlation measurements to ice-rule configurations resolves a systematic underestimation of ordering in conventional analyses, enabling direct reinterpretation of resonant X-ray, XMCD, STM and anomalous Hall experiments. Finally, we demonstrate that the same charge-sector reorganization framework explains near-degenerate plateau states in the metallic Kagome spin-ice HoAgGe and yields experimentally testable predictions for nanomagnetic, Kagome-metal and van der Waals frustrated systems. These results establish programmable quantum annealers as scalable simulators of emergent charge order and monopole physics in frustrated quantum matter.
Motivated by recent quantum Monte Carlo (QMC) simulations of the quantum Kagome ice model by Juan Carrasquilla et al., [Nat. Commun., 6, 7421 (2015)], we study the ground-state properties of this model on the triangular lattice. In the presence of a magnetic field hhh, the Hamiltonian possesses competing interactions between a Z2{Z}_{2}Z2​-invariant easy-axis ferromagnetic interaction ${J}_{\ifmmode\pm\else\textpm\fi{}\ifmmode\pm\else\textpm\fi{}}$ and a frustrated Ising term Jz{J}_{z}Jz​. As in the U(1)-invariant model, we obtain four classical distinctive phases, however, the classical phases in the Z2{Z}_{2}Z2​-invariant model are different. They are as follows: a fully polarized (FP) ferromagnet for large hhh, an easy-axis canted ferromagnet (CFM) with broken Z2{Z}_{2}Z2​ symmetry for small hhh and dominant ${J}_{\ifmmode\pm\else\textpm\fi{}\ifmmode\pm\else\textpm\fi{}}$, a ferrosolid phase with broken translational and Z2{Z}_{2}Z2​ symmetries for small hhh and dominant Jz{J}_{z}Jz​, and two lobes with $m=\ensuremath{\langle}{S}_{z}\ensuremath{\rangle}=\ifmmode\pm\else\textpm\fi{}1/6$ for small hhh and dominant Jz{J}_{z}Jz​. We show that quantum fluctuations are suppressed in this model, hence the large-SSS expansion gives an accurate picture of the ground-state properties. When quantum fluctuations are introduced, we show that the ferrosolid state is the ground state in the dominant Ising limit at zero magnetic field. It remains robust for ${J}_{z}\ensuremath{\rightarrow}\ensuremath{\infty}$. With nonzero magnetic field the classical lobes acquire a finite magnetic susceptibility with no Sz{S}_{z}Sz​ order. We present the trends of the ground-state energy and the magnetizations. We also present a detail analysis of the CFM.
Motivated by recent quantum Monte Carlo (QMC) simulations of the quantum Kagome ice model by Juan Carrasquilla, et al., [Nature Communications 6, 7421 (2015)], we study the ground state properties of this model on the triangular lattice. In the presence of a magnetic field hhh, the Hamiltonian possesses competing interactions between a Z2Z_2Z2​-invariant easy-axis ferromagnetic interaction J±±J_{\pm\pm}J±±​ and a frustrated Ising term JzJ_zJz​. As in the U(1)-invariant model, we obtain four classical distinctive phases, however, the classical phases in the Z2Z_2Z2​-invariant model are different. They are as follows: a fully polarized (FP) ferromagnet for large hhh, an easy-axis canted ferromagnet (CFM) with broken Z2Z_2Z2​ symmetry for small hhh and dominant J±±J_{\pm\pm}J±±​, a {\it ferrosolid} phase with broken translational and Z2Z_2Z2​ symmetries for small hhh and dominant JzJ_{z}Jz​, and two lobes with m=⟨Sz⟩=±1/6m=\langle S_z\rangle=\pm 1/6m=⟨Sz​⟩=±1/6 for small hhh and dominant JzJ_{z}Jz​. We show that quantum fluctuations are suppressed in this model, hence the large-SSS expansion gives an accurate picture of the ground state properties. When quantum fluctuations are introduced, we show that the {\it ferrosolid} state is the ground state in the dominant Ising limit at zero magnetic field. It remains robust for Jz→∞J_z\to\inftyJz​→∞. With nonzero magnetic field the classical lobes acquire a finite magnetic susceptibility with no SzS_zSz​-order. We present the trends of the ground state energy and the magnetizations. We also present a detail analysis of the CFM.