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:2110.06491 · Physical review. B./Physical review. B

Dimensional reduction in quantum spin- 12 system on a 17 -depleted triangular lattice

Ryo Makuta, Chisa Hotta

Published Dec 10, 2021• 13 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.104.224415

Related papers

Theory of partial quantum disorder in the stuffed honeycomb Heisenberg antiferromagnet

Urban F. P. Seifert, Matthias Vojta C

Recent numerical results [Gonzalez et al., Phys. Rev. Lett. 122, 017201 (2019); Shimada et al., J. Phys. Conf. Ser. 969, 012126 (2018)] point to the existence of a partial-disorder ground state for a spin-1/2 antiferromagnet on the stuffed honeycomb lattice, with 2/3 of the local moments ordering in an antiferromagnetic N\'eel pattern, while the remaining 1/3 of the sites display short-range correlations only, akin to a quantum spin liquid. We derive an effective model for this disordered subsystem, by integrating out fluctuations of the ordered local moments, which yield couplings in a formal $1/S$ expansion, with $S$ being the spin amplitude. The result is an effective triangular-lattice XXZ model, with planar ferromagnetic order for large $S$ and a stripe-ordered Ising ground state for small $S$, the latter being the result of frustrated Ising interactions. Within the semiclassical analysis, the transition point between the two orders is located at ${S}_{c}=0.646$, being very close to the relevant case $S=1/2$. Near $S={S}_{c}$ quantum fluctuations tend to destabilize magnetic order. We conjecture that this applies to $S=1/2$, thus explaining the observed partial-disorder state.

arXiv:1812.08168•Physical review. B./Physical review. B•Apr 30, 2019•15 citations

Spin excitation of the Heisenberg antiferromagnet with frustration: from the bounce-lattice antiferromagnet through the maple-leaf-lattice antiferromagnet to the exact-dimer system

Hiroki Nakano, Tôru Sakai

Abstract The spin- S Heisenberg antiferromagnet on the two-dimensional lattice is investigated for S = 1/2 and S = 1. We consider interaction at isolated dimers ( J d ) and interaction bonds that form the bounce lattice ( J b ). For J d = J b , the system is reduced to the maple-leaf-lattice antiferromagnet. We primarily conduct highly parallelized numerical diagonalization to examine the spin excitation gap above the ground state for various J b / J d cases. For S = 1/2, we report calculations for a 42-site cluster that has not been previously treated. The S = 1 case is examined for the first time for clusters up to 24 sites. Regardless of whether S = 1/2 or 1, we find that the system has a gapped nature for small J d / J b and becomes gapless at J d / J b ∼ 1.4. For S = 1, we also find that another gapped region appears between the gapless case at J d / J b ∼ 1.4 and the boundary of the exact-dimer phase.

arXiv:2604.24055•Zeitschrift für Naturforschung A•May 20, 2026•1 citation

An extended non-magnetic phase in the spin-1/2 Heisenberg antiferromagnet from the ruby to the maple-leaf lattice

Philipp Schmoll, Jan Naumann, Weerda, Erik Lennart +2 more

The spin-1/2 Heisenberg antiferromagnet on the two-dimensional ruby and maple-leaf lattices provides a stringent test case for frustrated quantum magnetism, where semiclassical magnetic order competes closely with quantum-paramagnetic states. We study the generalized maple-leaf model along the axis interpolating between the isotropic ruby lattice and the isotropic maple-leaf lattice, using two independent variational infinite projected entangled-pair state ansätze: one defined on the mapped square lattice and one directly on the native triangular lattice. Our lowest-energy variational states show no magnetic order throughout the region connecting the two isotropic limits, and the local bond correlations recover the $120^\circ$ lattice rotation symmetry without imposing it explicitly. Magnetic-field simulations at the two endpoints further indicate a finite zero-magnetization plateau in both cases, with a gradual onset of magnetization on the ruby lattice and a sharper onset on the maple-leaf lattice. These results establish a broad gapped non-magnetic regime in a minimal nearest-neighbor Heisenberg model on lattices of direct relevance to both frustrated quantum magnets and programmable ruby-lattice simulators.

arXiv:2407.07145•Jul 9, 2024•1 citation

Frustrated honeycomb-lattice bilayer quantum antiferromagnet in a magnetic field: Unconventional phase transitions in a two-dimensional isotropic Heisenberg model

Taras Krokhmalskii, Vasyl Baliha, Oleg Derzhko +2 more

We consider the spin-1/2 antiferromagnetic Heisenberg model on a bilayer honeycomb lattice including interlayer frustration in the presence of an external magnetic field. In the vicinity of the saturation field, we map the low-energy states of this quantum system onto the spatial configurations of hard hexagons on a honeycomb lattice. As a result, we can construct effective classical models (lattice-gas as well as Ising models) on the honeycomb lattice to calculate the properties of the frustrated quantum Heisenberg spin system in the low-temperature regime. We perform classical Monte Carlo simulations for a hard-hexagon model and adopt known results for an Ising model to discuss the finite-temperature order-disorder phase transition that is driven by a magnetic field at low temperatures. We also discuss an effective-model description around the ideal frustration case and find indications for a spin-flop-like transition in the considered isotropic spin model.

arXiv:1701.07876•Physical review. B./Physical review. B•Mar 13, 2017•17 citations

Study of the excited states of the quantum antiferromagnets

Mohammad G. Merdan

We investigate the quantum dynamics of the spins on different Heisenberg antiferromagnetic spin lattice systems. Firstly, we applied the coupled-cluster method to the spin-1/2 antiferromagnetic \emph{XXZ} model on a square lattice by employing an approximation which contains two-body long-range correlations and high-order four-body local correlations. Improvement is found for the ground-state energy, sublattice magnetization, and the critical anisotropy when comparing with the approximation including the two-body correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the high-order spin-wave theory.Secondly, we study the longitudinal excitations of quantum antiferromagnets on a triangular lattice by a recently proposed microscopic many-body approach based on magnon-density waves. We calculate the full longitudinal excitation spectra of the antiferromagnetic Heisenberg model for a general spin quantum number in the isotropic limit. Similar to the square lattice model, we find that, at the center of the first hexagonal Brillouin zone $\Gamma(\mathbf q=0)$ and at the magnetic ordering wavevectors $\pm[\mathbf Q= (4\pi/3,0)]$, the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We have also investigated the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin-wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compares our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and we find good agreements after the higher-order contributions are included in our calculations.

•Nov 10, 2013•0 citations

Magnetization plateaus in frustrated antiferromagnetic quantum spin models

A. Honecker, J. Schulenburg, Johannes Richter

Plateaus can be observed in the zero-temperature magnetization curve of quantum spin systems at rational values of the magnetization. In one dimension, the appearance of a plateau is controlled by a quantization condition for the magnetization which involves the length of the local spin and the volume of a translational unit cell of the ground state. We discuss examples of geometrically frustrated quantum spin systems with large (in general unbounded) periodicities of spontaneous breaking of translational symmetry in the ground state. In two dimensions, we discuss the square, triangular and Kagomé lattices using exact diagonalization (ED) for up to N = 40 sites. For the spin-1/2 XXZ model on the triangular lattice we study the nature and stability region of a plateau at one third of the saturation magnetization. The Kagomé lattice gives rise to particularly rich behaviour with several plateaus in the magnetization curve and a jump due to local magnon excitations just below saturation.

arXiv:cond-mat/0309425•Journal of Physics Condensed Matter•Mar 4, 2004•185 citations
We study the magnetism of a quantum spin-12\frac{1}{2}21​ antiferromagnet on a maple-leaf lattice which is obtained by regularly depleting 17\frac{1}{7}71​ 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.
Recent numerical results [Gonzalez et al., Phys. Rev. Lett. 122, 017201 (2019); Shimada et al., J. Phys. Conf. Ser. 969, 012126 (2018)] point to the existence of a partial-disorder ground state for a spin-1/2 antiferromagnet on the stuffed honeycomb lattice, with 2/3 of the local moments ordering in an antiferromagnetic N\'eel pattern, while the remaining 1/3 of the sites display short-range correlations only, akin to a quantum spin liquid. We derive an effective model for this disordered subsystem, by integrating out fluctuations of the ordered local moments, which yield couplings in a formal 1/S1/S1/S expansion, with SSS being the spin amplitude. The result is an effective triangular-lattice XXZ model, with planar ferromagnetic order for large SSS and a stripe-ordered Ising ground state for small SSS, the latter being the result of frustrated Ising interactions. Within the semiclassical analysis, the transition point between the two orders is located at Sc=0.646{S}_{c}=0.646Sc​=0.646, being very close to the relevant case S=1/2S=1/2S=1/2. Near S=ScS={S}_{c}S=Sc​ quantum fluctuations tend to destabilize magnetic order. We conjecture that this applies to S=1/2S=1/2S=1/2, thus explaining the observed partial-disorder state.
Abstract The spin- S Heisenberg antiferromagnet on the two-dimensional lattice is investigated for S = 1/2 and S = 1. We consider interaction at isolated dimers ( J d ) and interaction bonds that form the bounce lattice ( J b ). For J d = J b , the system is reduced to the maple-leaf-lattice antiferromagnet. We primarily conduct highly parallelized numerical diagonalization to examine the spin excitation gap above the ground state for various J b / J d cases. For S = 1/2, we report calculations for a 42-site cluster that has not been previously treated. The S = 1 case is examined for the first time for clusters up to 24 sites. Regardless of whether S = 1/2 or 1, we find that the system has a gapped nature for small J d / J b and becomes gapless at J d / J b ∼ 1.4. For S = 1, we also find that another gapped region appears between the gapless case at J d / J b ∼ 1.4 and the boundary of the exact-dimer phase.
The spin-1/2 Heisenberg antiferromagnet on the two-dimensional ruby and maple-leaf lattices provides a stringent test case for frustrated quantum magnetism, where semiclassical magnetic order competes closely with quantum-paramagnetic states. We study the generalized maple-leaf model along the axis interpolating between the isotropic ruby lattice and the isotropic maple-leaf lattice, using two independent variational infinite projected entangled-pair state ansätze: one defined on the mapped square lattice and one directly on the native triangular lattice. Our lowest-energy variational states show no magnetic order throughout the region connecting the two isotropic limits, and the local bond correlations recover the 120∘120^\circ120∘ lattice rotation symmetry without imposing it explicitly. Magnetic-field simulations at the two endpoints further indicate a finite zero-magnetization plateau in both cases, with a gradual onset of magnetization on the ruby lattice and a sharper onset on the maple-leaf lattice. These results establish a broad gapped non-magnetic regime in a minimal nearest-neighbor Heisenberg model on lattices of direct relevance to both frustrated quantum magnets and programmable ruby-lattice simulators.
We consider the spin-1/2 antiferromagnetic Heisenberg model on a bilayer honeycomb lattice including interlayer frustration in the presence of an external magnetic field. In the vicinity of the saturation field, we map the low-energy states of this quantum system onto the spatial configurations of hard hexagons on a honeycomb lattice. As a result, we can construct effective classical models (lattice-gas as well as Ising models) on the honeycomb lattice to calculate the properties of the frustrated quantum Heisenberg spin system in the low-temperature regime. We perform classical Monte Carlo simulations for a hard-hexagon model and adopt known results for an Ising model to discuss the finite-temperature order-disorder phase transition that is driven by a magnetic field at low temperatures. We also discuss an effective-model description around the ideal frustration case and find indications for a spin-flop-like transition in the considered isotropic spin model.
We investigate the quantum dynamics of the spins on different Heisenberg antiferromagnetic spin lattice systems. Firstly, we applied the coupled-cluster method to the spin-1/2 antiferromagnetic \emph{XXZ} model on a square lattice by employing an approximation which contains two-body long-range correlations and high-order four-body local correlations. Improvement is found for the ground-state energy, sublattice magnetization, and the critical anisotropy when comparing with the approximation including the two-body correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the high-order spin-wave theory.Secondly, we study the longitudinal excitations of quantum antiferromagnets on a triangular lattice by a recently proposed microscopic many-body approach based on magnon-density waves. We calculate the full longitudinal excitation spectra of the antiferromagnetic Heisenberg model for a general spin quantum number in the isotropic limit. Similar to the square lattice model, we find that, at the center of the first hexagonal Brillouin zone Γ(q=0)\Gamma(\mathbf q=0)Γ(q=0) and at the magnetic ordering wavevectors ±[Q=(4π/3,0)]\pm[\mathbf Q= (4\pi/3,0)]±[Q=(4π/3,0)], the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We have also investigated the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin-wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compares our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and we find good agreements after the higher-order contributions are included in our calculations.
Plateaus can be observed in the zero-temperature magnetization curve of quantum spin systems at rational values of the magnetization. In one dimension, the appearance of a plateau is controlled by a quantization condition for the magnetization which involves the length of the local spin and the volume of a translational unit cell of the ground state. We discuss examples of geometrically frustrated quantum spin systems with large (in general unbounded) periodicities of spontaneous breaking of translational symmetry in the ground state. In two dimensions, we discuss the square, triangular and Kagomé lattices using exact diagonalization (ED) for up to N = 40 sites. For the spin-1/2 XXZ model on the triangular lattice we study the nature and stability region of a plateau at one third of the saturation magnetization. The Kagomé lattice gives rise to particularly rich behaviour with several plateaus in the magnetization curve and a jump due to local magnon excitations just below saturation.