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

Dirac and Weyl nodes in the plaquette excitations of the frustrated Heisenberg antiferromagnet on the honeycomb lattice

Moumita Deb, Asim Kumar Ghosh

Published Aug 8, 2018• 0 citations
OpenAlex

Abstract

The plaquette valence bond solid (VBS) phase of the $J_1-J_2$ antiferromagnetic (AFM) Heisenberg honeycomb model has been studied using plaquette operator theory. Considering six $S =\frac{1}{2}$ spins on a single plaquette the plaquette operator representation for the spin operators in terms of plaquette-singlet and plaquette-triplet boson operators has been developed. The formalism has been applied to the $J_1-J_2$ honeycomb antiferromagnet to derive an effective interacting boson model in terms of those singlets and triplets. The effective model has been analyzed within the harmonic approximation and results have been compared with the exact diagonalization data. The evolution of Dirac and Weyl nodes with respect to $J_2/J_1$ for this model has been studied.

Related papers

Plaquette valence-bond solid in the square-lattice J1 - J2 antiferromagnet Heisenberg model: A bond operator approach

R. L. Doretto

We study the plaquette valence-bond solid phase of the spin-$1/2$${J}_{1}$-${J}_{2}$ antiferromagnet Heisenberg model on the square lattice within the bond-operator theory. We start by considering four $S=1/2$ spins on a single plaquette and determine the bond operator representation for the spin operators in terms of singlet, triplet, and quintet boson operators. The formalism is then applied to the ${J}_{1}$-${J}_{2}$ model and an effective interacting boson model in terms of singlets and triplets is derived. The effective model is analyzed within the harmonic approximation and the previous results of Zhitomirsky and Ueda [Phys. Rev. B 54, 9007 (1996)] are recovered. By perturbatively including cubic (triplet-triplet-triplet and singlet-triplet-triplet) and quartic interactions, we find that the plaquette valence-bond solid phase is stable within the parameter region $0.34<{J}_{2}/{J}_{1}<0.59$, which is narrower than the harmonic one. Differently from the harmonic approximation, the excitation gap vanishes at both critical couplings ${J}_{2}=0.34{J}_{1}$ and ${J}_{2}=0.59{J}_{1}$. Interestingly, for ${J}_{2}<0.48{J}_{1}$, the excitation gap corresponds to a singlet-triplet excitation at the $\ensuremath{\Gamma}$ point while, for ${J}_{2}>0.48{J}_{1}$, it is related to a singlet-singlet excitation at the $\mathbf{X}=(\ensuremath{\pi}/2,0)$ point of the tetramerized Brillouin zone.

arXiv:1309.6490•Physical Review B•Mar 19, 2014•55 citations

Exotic topological point and line nodes in the plaquette excitations of a frustrated Heisenberg antiferromagnet on the honeycomb lattice

Moumita Deb, Asim Kumar Ghosh

antiferromagnetic Heisenberg honeycomb model when the ground state of the system lies in a spin-disordered plaquette-valence-bond-solid phase. A six-spin plaquette operator theory of this honeycomb model has been developed for this purpose by using the eigenstates of an isolated Heisenberg hexagonal plaquette. Spin-1/2 operators are thus expressed in the Fock space spanned by the plaquette operators those are obtained in terms of exact analytic form of eigenstates for a single frustrated Heisenberg hexagon. Ultimately, an effective interacting boson model of this system is obtained on the basis of low energy singlets and triplets plaquette operators by employing a mean-field approximation. The values of ground state energy and spin gap of this system have been estimated and the validity of this formalism has been tested upon comparison with the known results. Emergence of topological point and line nodes on the basis of spin-disordered ground state noted in this investigation is very rare on any frustrated system as well as the presence of triplet flat band. Evolution of those topological nodes is studied throughout the full frustrated regime. Finally, emergence of topological phases has been reported upon adding a time-reversal-symmetry breaking term to the Hamiltonian. Coexistence of spin gap with either topological nodes or phases turns this honeycomb model an interesting one.

arXiv:1808.02739•Journal of Physics Condensed Matter•Apr 2, 2020•5 citations

Frustrated Heisenberg antiferromagnet on the honeycomb lattice: A candidate for deconfined quantum criticality

DAMIAN J. J. FARNELL, R. F. Bishop, P. H. Y. Li +2 more

We study the ground-state (gs) phase diagram of the frustrated spin-$\frac{1}{2}$ ${J}_{1}$--${J}_{2}$--${J}_{3}$ antiferromagnet with ${J}_{2}={J}_{3}=\ensuremath{\kappa}{J}_{1}$ on the honeycomb lattice using coupled-cluster theory and exact diagonalization methods. We present results for the gs energy, magnetic order parameter, spin-spin correlation function, and plaquette valence-bond crystal (PVBC) susceptibility. We find a N\'eel antiferromagnetic (AFM) phase for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{1}}\ensuremath{\approx}0.47$, a collinear striped AFM phase for $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{2}}\ensuremath{\approx}0.60$, and a paramagnetic PVBC phase for ${\ensuremath{\kappa}}_{{c}_{1}}\ensuremath{\lesssim}\ensuremath{\kappa}\ensuremath{\lesssim}{\ensuremath{\kappa}}_{{c}_{2}}$. The transition at ${\ensuremath{\kappa}}_{{c}_{2}}$ appears to be of first-order type, while that at ${\ensuremath{\kappa}}_{{c}_{1}}$ is continuous. Since the N\'eel and PVBC phases break different symmetries our results favor the deconfinement scenario for the transition at ${\ensuremath{\kappa}}_{{c}_{1}}$.

arXiv:1103.3856•Physical Review B•Jul 8, 2011•65 citations

Plaquette resonating valence bond state in a frustrated honeycomb antiferromagnet

R. Ganesh, Satoshi Nishimoto, Jeroen van den Brink

We study the proposed plaquette resonating valence bond (pRVB) state in the honeycomb lattice ${J}_{1}\ensuremath{-}{J}_{2}$ model with frustration arising from next-nearest-neighbor interactions. Starting with the limit of decoupled hexagons, we develop a plaquette operator approach to describe the pRVB state and its low-energy excitations. Our calculation clarifies that the putative pRVB state necessarily has $f$-wave symmetry: the plaquette wave function is an antisymmetric combination of the Kekul\'e structures. We estimate the plaquette ordering amplitude, ground-state energy, and spin gap as a function of ${J}_{2}/{J}_{1}$. The pRVB state is most stable around ${J}_{2}/{J}_{1}\ensuremath{\sim}0.25$. We identify the wave vectors of the lowest triplet excitations, which can be verified using exact diagonalization or density-matrix renormalization group (DMRG) studies. When ${J}_{2}$ is reduced, we can have either a deconfined quantum phase transition (QPT) or a first-order transition into a N\'eel state. When ${J}_{2}$ is increased, we surmise that the system will undergo a first-order phase transition into a state which breaks lattice rotational symmetry.

arXiv:1209.6091•Physical Review B•Feb 13, 2013•26 citations

Quantum phase diagram of the spin-1 J1−J2 Heisenberg model on the honeycomb lattice

Shou-Shu Gong, Wei Kang Zhu, D. N. Sheng

Strongly correlated systems with geometric frustrations can host the emergent phases of matter with unconventional properties. Here, we study the spin $S=1$ Heisenberg model on the honeycomb lattice with the antiferromagnetic first- (${J}_{1}$) and second-neighbor (${J}_{2}$) interactions ($0.0\ensuremath{\le}{J}_{2}/{J}_{1}\ensuremath{\le}0.5$) by means of density-matrix renormalization group. In the parameter regime ${J}_{2}/{J}_{1}\ensuremath{\lesssim}0.27$, the system sustains a N\'eel antiferromagnetic phase. At the large ${J}_{2}$ side ${J}_{2}/{J}_{1}\ensuremath{\gtrsim}0.32$, a stripe antiferromagnetic phase is found. Between the two magnetic ordered phases $0.27\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.32$, we find a nonmagnetic intermediate region with a plaquette valence-bond order. Although our calculations are limited within a six unit-cell width on cylinder, we present evidence that this plaquette state could be a strong candidate for this nonmagnetic region in the thermodynamic limit. We also briefly discuss the nature of the quantum phase transitions in the system. We gain further insight into the nonmagnetic phases in the spin-1 system by comparing its phase diagram with the spin-$1/2$ system.

arXiv:1508.00515•Physical Review B•Nov 6, 2015•44 citations

Competition between spin liquids and valence-bond order in the frustrated spin- 12 Heisenberg model on the honeycomb lattice

Francesco Ferrari, Samuel Bieri, Federico Becca

Using variational wave functions and Monte Carlo techniques, we study the antiferromagnetic Heisenberg model with first-neighbor ${J}_{1}$ and second-neighbor ${J}_{2}$ antiferromagnetic couplings on the honeycomb lattice. We perform a systematic comparison of magnetically ordered and nonmagnetic states (spin liquids and valence-bond solids) to obtain the ground-state phase diagram. N\'eel order is stabilized for small values of the frustrating second-neighbor coupling. Increasing the ratio ${J}_{2}/{J}_{1}$, we find strong evidence for a continuous transition to a nonmagnetic phase at ${J}_{2}/{J}_{1}\ensuremath{\approx}0.23$. Close to the transition point, the Gutzwiller-projected uniform resonating valence-bond state gives an excellent approximation to the exact ground-state energy. For $0.23\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.36$, a gapless ${Z}_{2}$ spin liquid with Dirac nodes competes with a plaquette valence-bond solid. In contrast, the gapped spin liquid considered in previous works has significantly higher variational energy. Although the plaquette valence-bond order is expected to be present as soon as the N\'eel order melts, this ordered state becomes clearly favored only for ${J}_{2}/{J}_{1}\ensuremath{\gtrsim}0.3$. Finally, for $0.36\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\le}0.5$, a valence-bond solid with columnar order takes over as the ground state, being also lower in energy than the magnetic state with collinear order. We perform a detailed finite-size scaling and standard data collapse analysis, and we discuss the possibility of a deconfined quantum critical point separating the N\'eel antiferromagnet from the plaquette valence-bond solid.

arXiv:1706.07810•Physical review. B./Physical review. B•Sep 1, 2017•46 citations
The plaquette valence bond solid (VBS) phase of the J1−J2J_1-J_2J1​−J2​ antiferromagnetic (AFM) Heisenberg honeycomb model has been studied using plaquette operator theory. Considering six S=12S =\frac{1}{2}S=21​ spins on a single plaquette the plaquette operator representation for the spin operators in terms of plaquette-singlet and plaquette-triplet boson operators has been developed. The formalism has been applied to the J1−J2J_1-J_2J1​−J2​ honeycomb antiferromagnet to derive an effective interacting boson model in terms of those singlets and triplets. The effective model has been analyzed within the harmonic approximation and results have been compared with the exact diagonalization data. The evolution of Dirac and Weyl nodes with respect to J2/J1J_2/J_1J2​/J1​ for this model has been studied.
We study the plaquette valence-bond solid phase of the spin-1/21/21/2J1{J}_{1}J1​-J2{J}_{2}J2​ antiferromagnet Heisenberg model on the square lattice within the bond-operator theory. We start by considering four S=1/2S=1/2S=1/2 spins on a single plaquette and determine the bond operator representation for the spin operators in terms of singlet, triplet, and quintet boson operators. The formalism is then applied to the J1{J}_{1}J1​-J2{J}_{2}J2​ model and an effective interacting boson model in terms of singlets and triplets is derived. The effective model is analyzed within the harmonic approximation and the previous results of Zhitomirsky and Ueda [Phys. Rev. B 54, 9007 (1996)] are recovered. By perturbatively including cubic (triplet-triplet-triplet and singlet-triplet-triplet) and quartic interactions, we find that the plaquette valence-bond solid phase is stable within the parameter region 0.34<J2/J1<0.590.34<{J}_{2}/{J}_{1}<0.590.34<J2​/J1​<0.59, which is narrower than the harmonic one. Differently from the harmonic approximation, the excitation gap vanishes at both critical couplings J2=0.34J1{J}_{2}=0.34{J}_{1}J2​=0.34J1​ and J2=0.59J1{J}_{2}=0.59{J}_{1}J2​=0.59J1​. Interestingly, for J2<0.48J1{J}_{2}<0.48{J}_{1}J2​<0.48J1​, the excitation gap corresponds to a singlet-triplet excitation at the $\ensuremath{\Gamma}$ point while, for J2>0.48J1{J}_{2}>0.48{J}_{1}J2​>0.48J1​, it is related to a singlet-singlet excitation at the $\mathbf{X}=(\ensuremath{\pi}/2,0)$ point of the tetramerized Brillouin zone.
antiferromagnetic Heisenberg honeycomb model when the ground state of the system lies in a spin-disordered plaquette-valence-bond-solid phase. A six-spin plaquette operator theory of this honeycomb model has been developed for this purpose by using the eigenstates of an isolated Heisenberg hexagonal plaquette. Spin-1/2 operators are thus expressed in the Fock space spanned by the plaquette operators those are obtained in terms of exact analytic form of eigenstates for a single frustrated Heisenberg hexagon. Ultimately, an effective interacting boson model of this system is obtained on the basis of low energy singlets and triplets plaquette operators by employing a mean-field approximation. The values of ground state energy and spin gap of this system have been estimated and the validity of this formalism has been tested upon comparison with the known results. Emergence of topological point and line nodes on the basis of spin-disordered ground state noted in this investigation is very rare on any frustrated system as well as the presence of triplet flat band. Evolution of those topological nodes is studied throughout the full frustrated regime. Finally, emergence of topological phases has been reported upon adding a time-reversal-symmetry breaking term to the Hamiltonian. Coexistence of spin gap with either topological nodes or phases turns this honeycomb model an interesting one.
We study the ground-state (gs) phase diagram of the frustrated spin-12\frac{1}{2}21​ J1{J}_{1}J1​--J2{J}_{2}J2​--J3{J}_{3}J3​ antiferromagnet with ${J}_{2}={J}_{3}=\ensuremath{\kappa}{J}_{1}$ on the honeycomb lattice using coupled-cluster theory and exact diagonalization methods. We present results for the gs energy, magnetic order parameter, spin-spin correlation function, and plaquette valence-bond crystal (PVBC) susceptibility. We find a N\'eel antiferromagnetic (AFM) phase for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{1}}\ensuremath{\approx}0.47$, a collinear striped AFM phase for $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{2}}\ensuremath{\approx}0.60$, and a paramagnetic PVBC phase for ${\ensuremath{\kappa}}_{{c}_{1}}\ensuremath{\lesssim}\ensuremath{\kappa}\ensuremath{\lesssim}{\ensuremath{\kappa}}_{{c}_{2}}$. The transition at ${\ensuremath{\kappa}}_{{c}_{2}}$ appears to be of first-order type, while that at ${\ensuremath{\kappa}}_{{c}_{1}}$ is continuous. Since the N\'eel and PVBC phases break different symmetries our results favor the deconfinement scenario for the transition at ${\ensuremath{\kappa}}_{{c}_{1}}$.
We study the proposed plaquette resonating valence bond (pRVB) state in the honeycomb lattice ${J}_{1}\ensuremath{-}{J}_{2}$ model with frustration arising from next-nearest-neighbor interactions. Starting with the limit of decoupled hexagons, we develop a plaquette operator approach to describe the pRVB state and its low-energy excitations. Our calculation clarifies that the putative pRVB state necessarily has fff-wave symmetry: the plaquette wave function is an antisymmetric combination of the Kekul\'e structures. We estimate the plaquette ordering amplitude, ground-state energy, and spin gap as a function of J2/J1{J}_{2}/{J}_{1}J2​/J1​. The pRVB state is most stable around ${J}_{2}/{J}_{1}\ensuremath{\sim}0.25$. We identify the wave vectors of the lowest triplet excitations, which can be verified using exact diagonalization or density-matrix renormalization group (DMRG) studies. When J2{J}_{2}J2​ is reduced, we can have either a deconfined quantum phase transition (QPT) or a first-order transition into a N\'eel state. When J2{J}_{2}J2​ is increased, we surmise that the system will undergo a first-order phase transition into a state which breaks lattice rotational symmetry.
Strongly correlated systems with geometric frustrations can host the emergent phases of matter with unconventional properties. Here, we study the spin S=1S=1S=1 Heisenberg model on the honeycomb lattice with the antiferromagnetic first- (J1{J}_{1}J1​) and second-neighbor (J2{J}_{2}J2​) interactions ($0.0\ensuremath{\le}{J}_{2}/{J}_{1}\ensuremath{\le}0.5$) by means of density-matrix renormalization group. In the parameter regime ${J}_{2}/{J}_{1}\ensuremath{\lesssim}0.27$, the system sustains a N\'eel antiferromagnetic phase. At the large J2{J}_{2}J2​ side ${J}_{2}/{J}_{1}\ensuremath{\gtrsim}0.32$, a stripe antiferromagnetic phase is found. Between the two magnetic ordered phases $0.27\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.32$, we find a nonmagnetic intermediate region with a plaquette valence-bond order. Although our calculations are limited within a six unit-cell width on cylinder, we present evidence that this plaquette state could be a strong candidate for this nonmagnetic region in the thermodynamic limit. We also briefly discuss the nature of the quantum phase transitions in the system. We gain further insight into the nonmagnetic phases in the spin-1 system by comparing its phase diagram with the spin-1/21/21/2 system.
Using variational wave functions and Monte Carlo techniques, we study the antiferromagnetic Heisenberg model with first-neighbor J1{J}_{1}J1​ and second-neighbor J2{J}_{2}J2​ antiferromagnetic couplings on the honeycomb lattice. We perform a systematic comparison of magnetically ordered and nonmagnetic states (spin liquids and valence-bond solids) to obtain the ground-state phase diagram. N\'eel order is stabilized for small values of the frustrating second-neighbor coupling. Increasing the ratio J2/J1{J}_{2}/{J}_{1}J2​/J1​, we find strong evidence for a continuous transition to a nonmagnetic phase at ${J}_{2}/{J}_{1}\ensuremath{\approx}0.23$. Close to the transition point, the Gutzwiller-projected uniform resonating valence-bond state gives an excellent approximation to the exact ground-state energy. For $0.23\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.36$, a gapless Z2{Z}_{2}Z2​ spin liquid with Dirac nodes competes with a plaquette valence-bond solid. In contrast, the gapped spin liquid considered in previous works has significantly higher variational energy. Although the plaquette valence-bond order is expected to be present as soon as the N\'eel order melts, this ordered state becomes clearly favored only for ${J}_{2}/{J}_{1}\ensuremath{\gtrsim}0.3$. Finally, for $0.36\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\le}0.5$, a valence-bond solid with columnar order takes over as the ground state, being also lower in energy than the magnetic state with collinear order. We perform a detailed finite-size scaling and standard data collapse analysis, and we discuss the possibility of a deconfined quantum critical point separating the N\'eel antiferromagnet from the plaquette valence-bond solid.