arXiv:2111.01611 · Physical review. B./Physical review. B

Intertwining SU( N ) symmetry and frustration on a honeycomb lattice

Xu-Ping Yao, Rui Leonard Luo, Gang Chen

Published Jan 3, 2022• 10 citations

Abstract

Large symmetry groups in quantum many-body systems could strongly enhance quantum fluctuations and thereby stabilize exotic quantum phases. Frustrated interactions were long known to have similar effects. Here we intertwine the large $\mathrm{SU}(N$) symmetry and the frustration in a ${J}_{1}\text{\ensuremath{-}}{J}_{2}\phantom{\rule{0.16em}{0ex}}\mathrm{SU}(N$) Heisenberg model on a honeycomb lattice, where ${J}_{1}$ is the nearest-neighbor coupling and ${J}_{2}$ is the next-nearest-neighbor coupling. With a large-$N$ analysis, we obtain a rich phase diagram by varying both $N$ and the ratio ${J}_{2}/{J}_{1}$. The ground states include Dirac spin liquid, chiral spin liquid, valence cluster solids, flux ordered state, and stripe states. The physical properties of each phase are discussed.

DOI: 10.1103/physrevb.105.024401

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

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

arXiv:1508.00515Physical Review BNov 6, 201544 citations

Quantum phase diagram of a frustrated spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ Heisenberg model on an $AA$-stacked bilayer honeycomb lattice

P. H. Y. Li, R. F. Bishop

May 3, 20180 citations

Quantum phase diagram and chiral spin liquid in the extended spin- 12 honeycomb XY model

Yixuan Huang, Xiaoyu Dong, D. N. Sheng +1 more

arXiv:1912.11156Physical review. B./Physical review. BJan 19, 202113 citations

Frustrated honeycomb-bilayer Heisenberg antiferromagnet: The spin- 12 J1−J2−J1⊥ model

R. F. Bishop, P. H. Y. Li

arXiv:1611.03287Physical review. B./Physical review. BApr 11, 201722 citations

Meandering stripes in the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice

Denis Gessert, Martin Weigel, Wolfhard Janke E

arXiv:2608.21261Aug 21, 20260 citations

Randomness-Induced Quantum Spin Liquid Behavior in the s = 1/2 Random J1–J2 Heisenberg Antiferromagnet on the Honeycomb Lattice

Kazuki Uematsu, Hikaru Kawamura

arXiv:1701.02255Journal of the Physical Society of JapanMar 7, 201749 citations

arXiv:2111.01611 · Physical review. B./Physical review. B

Intertwining SU( N ) symmetry and frustration on a honeycomb lattice

Xu-Ping Yao, Rui Leonard Luo, Gang Chen

Published Jan 3, 2022• 10 citations

arXiv HTML PDF

Abstract

\mathrm{SU}(N

) symmetry and the frustration in a

{J}_{1}\text{\ensuremath{-}}{J}_{2}\phantom{\rule{0.16em}{0ex}}\mathrm{SU}(N

) Heisenberg model on a honeycomb lattice, where

{J}_{1}

is the nearest-neighbor coupling and

{J}_{2}

is the next-nearest-neighbor coupling. With a large-

N

analysis, we obtain a rich phase diagram by varying both

N

and the ratio

{J}_{2}/{J}_{1}

. The ground states include Dirac spin liquid, chiral spin liquid, valence cluster solids, flux ordered state, and stripe states. The physical properties of each phase are discussed.

DOI: 10.1103/physrevb.105.024401

Related papers

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.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:1508.00515Physical Review BNov 6, 201544 citations

Quantum phase diagram of a frustrated spin- $\frac{1}{2}$ $J_{1}$ -- $J_{2}$ -- $J_{1}^{\perp}$ Heisenberg model on an $AA$ -stacked bilayer honeycomb latticeQuantum phase diagram of a frustrated spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ Heisenberg model on an $AA$-stacked bilayer honeycomb lattice

P. H. Y. Li, R. F. Bishop

The zero-temperature quantum phase diagram of the spin- $\frac{1}{2}$ $J_{1}$ -- $J_{2}$ -- $J_{1}^{\perp}$ model on an $AA$ -stacked bilayer honeycomb lattice is investigated using the coupled cluster method (CCM). The model comprises two monolayers in each of which the spins, residing on honeycomb-lattice sites, interact via both nearest-neighbor (NN) and frustrating next-nearest-neighbor isotropic antiferromagnetic (AFM) Heisenberg exchange iteractions, with respective strengths $J_{1} > 0$ and $J_{2} \equiv \kappa J_{1}>0$ . The two layers are coupled via a comparable Heisenberg exchange interaction between NN interlayer pairs, with a strength $J_{1}^{\perp} \equiv \delta J_{1}$ . The complete phase boundaries of two quasiclassical collinear AFM phases, namely the Neel and Neel-II phases, are calculated in the $\kappa \delta$ half-plane with $\kappa > 0$ . Whereas on each monolayer in the Neel state all NN pairs of spins are antiparallel, in the Neel-II state NN pairs of spins on zigzag chains along one of the three equivalent honeycomb-lattice directions are antiparallel, while NN interchain spins are parallel. We calculate directly in the thermodynamic (infinite-lattice) limit both the magnetic order parameter $M$ and the excitation energy $\Delta$ from the $s^{z}_{T}=0$ ground state to the lowest-lying $|s^{z}_{T}|=1$ excited state (where $s^{z}_{T}$ is the total $z$ component of spin for the system as a whole, and where the collinear ordering lies along the $z$ direction) for both quasiclassical states used (separately) as the CCM model state, on top of which the multispin quantum correlations are then calculated to high orders ( $n \leq 10$ ) in a systematic series of approximations involving $n$ -spin clusters. The sole approximation made is then to extrapolate the sequences of $n$ th-order results for $M$ and $\Delta$ to the exact limit, $n \to \infty$ .The zero-temperature quantum phase diagram of the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ model on an $AA$-stacked bilayer honeycomb lattice is investigated using the coupled cluster method (CCM). The model comprises two monolayers in each of which the spins, residing on honeycomb-lattice sites, interact via both nearest-neighbor (NN) and frustrating next-nearest-neighbor isotropic antiferromagnetic (AFM) Heisenberg exchange iteractions, with respective strengths $J_{1} > 0$ and $J_{2} \equiv \kappa J_{1}>0$. The two layers are coupled via a comparable Heisenberg exchange interaction between NN interlayer pairs, with a strength $J_{1}^{\perp} \equiv \delta J_{1}$. The complete phase boundaries of two quasiclassical collinear AFM phases, namely the Neel and Neel-II phases, are calculated in the $\kappa \delta$ half-plane with $\kappa > 0$. Whereas on each monolayer in the Neel state all NN pairs of spins are antiparallel, in the Neel-II state NN pairs of spins on zigzag chains along one of the three equivalent honeycomb-lattice directions are antiparallel, while NN interchain spins are parallel. We calculate directly in the thermodynamic (infinite-lattice) limit both the magnetic order parameter $M$ and the excitation energy $\Delta$ from the $s^{z}_{T}=0$ ground state to the lowest-lying $|s^{z}_{T}|=1$ excited state (where $s^{z}_{T}$ is the total $z$ component of spin for the system as a whole, and where the collinear ordering lies along the $z$ direction) for both quasiclassical states used (separately) as the CCM model state, on top of which the multispin quantum correlations are then calculated to high orders ($n \leq 10$) in a systematic series of approximations involving $n$-spin clusters. The sole approximation made is then to extrapolate the sequences of $n$th-order results for $M$ and $\Delta$ to the exact limit, $n \to \infty$.

May 3, 20180 citations

Quantum phase diagram and chiral spin liquid in the extended spin- 12 honeycomb XY model

Yixuan Huang, Xiaoyu Dong, D. N. Sheng +1 more

The frustrated XY model on the honeycomb lattice has drawn lots of attention because of the potential emergence of chiral spin liquid (CSL) with the increasing of frustrations or competing interactions. In this paper, we study the extended spin- $\frac{1}{2}$ XY model with nearest-neighbor $({J}_{1})$ , and next-nearest-neighbor $({J}_{2})$ interactions in the presence of a three-spins chiral $({J}_{\ensuremath{\chi}})$ term using density matrix renormalization group methods. We obtain a quantum phase diagram with both conventionally ordered and topologically ordered phases. In particular, the long-sought Kalmeyer-Laughlin CSL is shown to emerge under a small ${J}_{\ensuremath{\chi}}$ perturbation due to the interplay of the magnetic frustration and chiral interactions. The CSL, which is a nonmagnetic phase, is identified by the scalar chiral order, the finite spin gap on a torus, and the chiral entanglement spectrum described by chiral $SU{(2)}_{1}$ conformal field theory.The frustrated XY model on the honeycomb lattice has drawn lots of attention because of the potential emergence of chiral spin liquid (CSL) with the increasing of frustrations or competing interactions. In this paper, we study the extended spin-$\frac{1}{2}$ XY model with nearest-neighbor $({J}_{1})$, and next-nearest-neighbor $({J}_{2})$ interactions in the presence of a three-spins chiral $({J}_{\ensuremath{\chi}})$ term using density matrix renormalization group methods. We obtain a quantum phase diagram with both conventionally ordered and topologically ordered phases. In particular, the long-sought Kalmeyer-Laughlin CSL is shown to emerge under a small ${J}_{\ensuremath{\chi}}$ perturbation due to the interplay of the magnetic frustration and chiral interactions. The CSL, which is a nonmagnetic phase, is identified by the scalar chiral order, the finite spin gap on a torus, and the chiral entanglement spectrum described by chiral $SU{(2)}_{1}$ conformal field theory.

arXiv:1912.11156Physical review. B./Physical review. BJan 19, 202113 citations

Frustrated honeycomb-bilayer Heisenberg antiferromagnet: The spin- 12 J1−J2−J1⊥ model

R. F. Bishop, P. H. Y. Li

We use the coupled cluster method to study the zero-temperature quantum phase diagram of the spin-$\frac{1}{2}{J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{1}^{\ensuremath{\perp}}$ model on the honeycomb bilayer lattice. In each layer, we include both nearest-neighbor and frustrating next-nearest-neighbor antiferromagnetic exchange couplings, of strength ${J}_{1}>0$ and ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, respectively. The two layers are coupled by an interlayer nearest-neighbor exchange, with coupling constant ${J}_{1}^{\ensuremath{\perp}}\ensuremath{\equiv}\ensuremath{\delta}{J}_{1}>0$. We calculate directly in the infinite-lattice limit both the ground-state energy per spin and the N\'eel magnetic order parameter, as well as the triplet spin gap. By implementing the method to very high orders of approximation we obtain an accurate estimate for the full boundary of the N\'eel phase in the $\ensuremath{\kappa}\ensuremath{\delta}$ plane. For each value $\ensuremath{\delta}<{\ensuremath{\delta}}_{c}^{>}(0)\ensuremath{\approx}1.70(5)$, we find an upper critical value ${\ensuremath{\kappa}}_{c}(\ensuremath{\delta})$, such that N\'eel order is present for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}(\ensuremath{\delta})$. Conversely, for each value $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}(0)\ensuremath{\approx}0.19(1)$, we find an upper critical value ${\ensuremath{\delta}}_{c}^{>}(\ensuremath{\kappa})$, such that N\'eel order persists for $0<\ensuremath{\delta}<{\ensuremath{\delta}}_{c}^{>}(\ensuremath{\kappa})$. Most interestingly, for values of $\ensuremath{\kappa}$ in the range ${\ensuremath{\kappa}}_{c}(0)<\ensuremath{\kappa}<{\ensuremath{\kappa}}^{>}\ensuremath{\approx}0.215(2)$, we find a reentrant behavior such that N\'eel order exists only in the range ${\ensuremath{\delta}}_{c}^{<}(\ensuremath{\kappa})<\ensuremath{\delta}<{\ensuremath{\delta}}_{c}^{>}(\ensuremath{\kappa})$, with ${\ensuremath{\delta}}_{c}^{<}(\ensuremath{\kappa})>0$. These latter upper and lower critical values coalesce when $\ensuremath{\kappa}={\ensuremath{\kappa}}^{>}$, such that ${\ensuremath{\delta}}_{c}^{<}({\ensuremath{\kappa}}^{>})={\ensuremath{\delta}}_{c}^{>}({\ensuremath{\kappa}}^{>})\ensuremath{\approx}0.25(5)$.We use the coupled cluster method to study the zero-temperature quantum phase diagram of the spin-$\frac{1}{2}{J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{1}^{\ensuremath{\perp}}$ model on the honeycomb bilayer lattice. In each layer, we include both nearest-neighbor and frustrating next-nearest-neighbor antiferromagnetic exchange couplings, of strength ${J}_{1}>0$ and ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, respectively. The two layers are coupled by an interlayer nearest-neighbor exchange, with coupling constant ${J}_{1}^{\ensuremath{\perp}}\ensuremath{\equiv}\ensuremath{\delta}{J}_{1}>0$. We calculate directly in the infinite-lattice limit both the ground-state energy per spin and the N\'eel magnetic order parameter, as well as the triplet spin gap. By implementing the method to very high orders of approximation we obtain an accurate estimate for the full boundary of the N\'eel phase in the $\ensuremath{\kappa}\ensuremath{\delta}$ plane. For each value $\ensuremath{\delta}<{\ensuremath{\delta}}_{c}^{>}(0)\ensuremath{\approx}1.70(5)$, we find an upper critical value ${\ensuremath{\kappa}}_{c}(\ensuremath{\delta})$, such that N\'eel order is present for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}(\ensuremath{\delta})$. Conversely, for each value $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}(0)\ensuremath{\approx}0.19(1)$, we find an upper critical value ${\ensuremath{\delta}}_{c}^{>}(\ensuremath{\kappa})$, such that N\'eel order persists for $0<\ensuremath{\delta}<{\ensuremath{\delta}}_{c}^{>}(\ensuremath{\kappa})$. Most interestingly, for values of $\ensuremath{\kappa}$ in the range ${\ensuremath{\kappa}}_{c}(0)<\ensuremath{\kappa}<{\ensuremath{\kappa}}^{>}\ensuremath{\approx}0.215(2)$, we find a reentrant behavior such that N\'eel order exists only in the range ${\ensuremath{\delta}}_{c}^{<}(\ensuremath{\kappa})<\ensuremath{\delta}<{\ensuremath{\delta}}_{c}^{>}(\ensuremath{\kappa})$, with ${\ensuremath{\delta}}_{c}^{<}(\ensuremath{\kappa})>0$. These latter upper and lower critical values coalesce when $\ensuremath{\kappa}={\ensuremath{\kappa}}^{>}$, such that ${\ensuremath{\delta}}_{c}^{<}({\ensuremath{\kappa}}^{>})={\ensuremath{\delta}}_{c}^{>}({\ensuremath{\kappa}}^{>})\ensuremath{\approx}0.25(5)$.

arXiv:1611.03287Physical review. B./Physical review. BApr 11, 201722 citations

Meandering stripes in the frustrated $J_1$ - $J_2$ Ising model on the honeycomb latticeMeandering stripes in the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice

Denis Gessert, Martin Weigel, Wolfhard Janke E

We study the frustrated $J_1$ - $J_2$ Ising model on the honeycomb lattice with ferromagnetic nearest-neighbor couplings fixed at $J_1=1$ and strong antiferromagnetic next-nearest-neighbor interactions, i.e., $J_2 \leq -1/4$ . Little is known for this range of $J_2$ , whereas for less negative values of $J_2$ the system orders ferromagnetically at low temperatures and appears to remain in the Ising universality class. In previous work it was shown that the model has a largely degenerate ground state, and it was conjectured that there is some kind of phase transition. We introduce a complex-valued nematic order parameter, which can differentiate between the high-temperature paramagnetic phase and the observed partially-disordered stripe phase at lower temperatures. Configurations in this phase consist of stripes of spins parallel with respect to one lattice direction, which collectively meander along the remaining two, producing partially disordered ground states. The sharp peaks in the specific heat observed in earlier work only appear when using periodic boundary conditions and are absent for free boundaries. Additionally, we reveal a striking dependence of the behavior on the aspect ratio of the considered samples. Ultimately, even a careful finite-size scaling analysis for $J_2 = -0.5$ and $J_2 = -1$ is unable to clearly discern between a crossover without any singularities and some form of continuous transition, including the possibility of an infinite-order transition of the Berezinskii-Kosterlitz-Thouless (BKT) type. For $J_2=-1/4$ we find that the system remains disordered at all temperatures and that it exhibits a finite ground-state entropy per site, for which our simulations provide the accurate asymptotic estimate $S(T=0)/N = 0.230\,960\,93(14)$ in the thermodynamic limit $N\rightarrow\infty$ .We study the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice with ferromagnetic nearest-neighbor couplings fixed at $J_1=1$ and strong antiferromagnetic next-nearest-neighbor interactions, i.e., $J_2 \leq -1/4$. Little is known for this range of $J_2$, whereas for less negative values of $J_2$ the system orders ferromagnetically at low temperatures and appears to remain in the Ising universality class. In previous work it was shown that the model has a largely degenerate ground state, and it was conjectured that there is some kind of phase transition. We introduce a complex-valued nematic order parameter, which can differentiate between the high-temperature paramagnetic phase and the observed partially-disordered stripe phase at lower temperatures. Configurations in this phase consist of stripes of spins parallel with respect to one lattice direction, which collectively meander along the remaining two, producing partially disordered ground states. The sharp peaks in the specific heat observed in earlier work only appear when using periodic boundary conditions and are absent for free boundaries. Additionally, we reveal a striking dependence of the behavior on the aspect ratio of the considered samples. Ultimately, even a careful finite-size scaling analysis for $J_2 = -0.5$ and $J_2 = -1$ is unable to clearly discern between a crossover without any singularities and some form of continuous transition, including the possibility of an infinite-order transition of the Berezinskii-Kosterlitz-Thouless (BKT) type. For $J_2=-1/4$ we find that the system remains disordered at all temperatures and that it exhibits a finite ground-state entropy per site, for which our simulations provide the accurate asymptotic estimate $S(T=0)/N = 0.230\,960\,93(14)$ in the thermodynamic limit $N\rightarrow\infty$.

arXiv:2608.21261Aug 21, 20260 citations

Randomness-Induced Quantum Spin Liquid Behavior in the s = 1/2 Random J1–J2 Heisenberg Antiferromagnet on the Honeycomb Lattice

Kazuki Uematsu, Hikaru Kawamura

We investigate the ground-state and finite-temperature properties of the bond-random $s=1/2$ Heisenberg model on a honeycomb lattice with frustrated nearest- and next-nearest-neighbor antiferromagnetic interactions, $J_1$ and $J_2$ , by the exact diagonalization and the Hams--de Raedt methods. The ground-state phase diagram of the model is constructed in the randomness versus the frustration ( $J_2/J_1$ ) plane, with the aim of clarifying the effects of randomness and frustration in stabilizing a variety of distinct phases. We find that the randomness induces the gapless quantum spin liquid (QSL)-like state, the random-singlet state, in a wide range of parameter space. The observed robustness of the random-singlet state suggests that the gapless QSL-like behaviors might be realized in a wide class of frustrated quantum magnets possessing a certain amount of randomness or inhomogeneity, without fine-tuning the interaction parameters. Possible implications to recent experiments on the honeycomb-lattice magnets Ba $_3$ CuSb $_2$ O $_9$ and 6HB-Ba $_3$ NiSb $_2$ O $_9$ exhibiting the gapless QSL-like behaviors are discussed.We investigate the ground-state and finite-temperature properties of the bond-random $s=1/2$ Heisenberg model on a honeycomb lattice with frustrated nearest- and next-nearest-neighbor antiferromagnetic interactions, $J_1$ and $J_2$, by the exact diagonalization and the Hams--de Raedt methods. The ground-state phase diagram of the model is constructed in the randomness versus the frustration ($J_2/J_1$) plane, with the aim of clarifying the effects of randomness and frustration in stabilizing a variety of distinct phases. We find that the randomness induces the gapless quantum spin liquid (QSL)-like state, the random-singlet state, in a wide range of parameter space. The observed robustness of the random-singlet state suggests that the gapless QSL-like behaviors might be realized in a wide class of frustrated quantum magnets possessing a certain amount of randomness or inhomogeneity, without fine-tuning the interaction parameters. Possible implications to recent experiments on the honeycomb-lattice magnets Ba$_3$CuSb$_2$O$_9$ and 6HB-Ba$_3$NiSb$_2$O$_9$ exhibiting the gapless QSL-like behaviors are discussed.

arXiv:1701.02255Journal of the Physical Society of JapanMar 7, 201749 citations

\mathrm{SU}(N

) symmetry and the frustration in a

{J}_{1}\text{\ensuremath{-}}{J}_{2}\phantom{\rule{0.16em}{0ex}}\mathrm{SU}(N

) Heisenberg model on a honeycomb lattice, where

{J}_{1}

is the nearest-neighbor coupling and

{J}_{2}

is the next-nearest-neighbor coupling. With a large-

N

analysis, we obtain a rich phase diagram by varying both

N

and the ratio

{J}_{2}/{J}_{1}

. The ground states include Dirac spin liquid, chiral spin liquid, valence cluster solids, flux ordered state, and stripe states. The physical properties of each phase are discussed.

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.

Quantum phase diagram of a frustrated spin-

\frac{1}{2}

J_{1}

J_{2}

J_{1}^{\perp}

Heisenberg model on an

AA

-stacked bilayer honeycomb lattice

The zero-temperature quantum phase diagram of the spin-

\frac{1}{2}

J_{1}

J_{2}

J_{1}^{\perp}

model on an

AA

-stacked bilayer honeycomb lattice is investigated using the coupled cluster method (CCM). The model comprises two monolayers in each of which the spins, residing on honeycomb-lattice sites, interact via both nearest-neighbor (NN) and frustrating next-nearest-neighbor isotropic antiferromagnetic (AFM) Heisenberg exchange iteractions, with respective strengths

J_{1} > 0

and

J_{2} \equiv \kappa J_{1}>0

. The two layers are coupled via a comparable Heisenberg exchange interaction between NN interlayer pairs, with a strength

J_{1}^{\perp} \equiv \delta J_{1}

. The complete phase boundaries of two quasiclassical collinear AFM phases, namely the Neel and Neel-II phases, are calculated in the

\kappa \delta

half-plane with

\kappa > 0

. Whereas on each monolayer in the Neel state all NN pairs of spins are antiparallel, in the Neel-II state NN pairs of spins on zigzag chains along one of the three equivalent honeycomb-lattice directions are antiparallel, while NN interchain spins are parallel. We calculate directly in the thermodynamic (infinite-lattice) limit both the magnetic order parameter

M

and the excitation energy

\Delta

from the

s^{z}_{T}=0

ground state to the lowest-lying

|s^{z}_{T}|=1

excited state (where

s^{z}_{T}

is the total

z

component of spin for the system as a whole, and where the collinear ordering lies along the

z

direction) for both quasiclassical states used (separately) as the CCM model state, on top of which the multispin quantum correlations are then calculated to high orders (

n \leq 10

) in a systematic series of approximations involving

n

-spin clusters. The sole approximation made is then to extrapolate the sequences of

n

th-order results for

M

and

\Delta

to the exact limit,

n \to \infty

\frac{1}{2}

XY model with nearest-neighbor

({J}_{1})

, and next-nearest-neighbor

({J}_{2})

interactions in the presence of a three-spins chiral $({J}_{\ensuremath{\chi}})$ term using density matrix renormalization group methods. We obtain a quantum phase diagram with both conventionally ordered and topologically ordered phases. In particular, the long-sought Kalmeyer-Laughlin CSL is shown to emerge under a small ${J}_{\ensuremath{\chi}}$ perturbation due to the interplay of the magnetic frustration and chiral interactions. The CSL, which is a nonmagnetic phase, is identified by the scalar chiral order, the finite spin gap on a torus, and the chiral entanglement spectrum described by chiral

SU{(2)}_{1}

conformal field theory.

{J}_{1}>0

and ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, respectively. The two layers are coupled by an interlayer nearest-neighbor exchange, with coupling constant ${J}_{1}^{\ensuremath{\perp}}\ensuremath{\equiv}\ensuremath{\delta}{J}_{1}>0$. We calculate directly in the infinite-lattice limit both the ground-state energy per spin and the N\'eel magnetic order parameter, as well as the triplet spin gap. By implementing the method to very high orders of approximation we obtain an accurate estimate for the full boundary of the N\'eel phase in the $\ensuremath{\kappa}\ensuremath{\delta}$ plane. For each value $\ensuremath{\delta}<{\ensuremath{\delta}}_{c}^{>}(0)\ensuremath{\approx}1.70(5)$, we find an upper critical value ${\ensuremath{\kappa}}_{c}(\ensuremath{\delta})$, such that N\'eel order is present for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}(\ensuremath{\delta})$. Conversely, for each value $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}(0)\ensuremath{\approx}0.19(1)$, we find an upper critical value ${\ensuremath{\delta}}_{c}^{>}(\ensuremath{\kappa})$, such that N\'eel order persists for $0<\ensuremath{\delta}<{\ensuremath{\delta}}_{c}^{>}(\ensuremath{\kappa})$. Most interestingly, for values of $\ensuremath{\kappa}$ in the range ${\ensuremath{\kappa}}_{c}(0)<\ensuremath{\kappa}<{\ensuremath{\kappa}}^{>}\ensuremath{\approx}0.215(2)$, we find a reentrant behavior such that N\'eel order exists only in the range ${\ensuremath{\delta}}_{c}^{<}(\ensuremath{\kappa})<\ensuremath{\delta}<{\ensuremath{\delta}}_{c}^{>}(\ensuremath{\kappa})$, with ${\ensuremath{\delta}}_{c}^{<}(\ensuremath{\kappa})>0$. These latter upper and lower critical values coalesce when $\ensuremath{\kappa}={\ensuremath{\kappa}}^{>}$, such that ${\ensuremath{\delta}}_{c}^{<}({\ensuremath{\kappa}}^{>})={\ensuremath{\delta}}_{c}^{>}({\ensuremath{\kappa}}^{>})\ensuremath{\approx}0.25(5)$.

Meandering stripes in the frustrated

J_1

J_2

Ising model on the honeycomb lattice

We study the frustrated

J_1

J_2

Ising model on the honeycomb lattice with ferromagnetic nearest-neighbor couplings fixed at

J_1=1

and strong antiferromagnetic next-nearest-neighbor interactions, i.e.,

J_2 \leq -1/4

. Little is known for this range of

J_2

, whereas for less negative values of

J_2

the system orders ferromagnetically at low temperatures and appears to remain in the Ising universality class. In previous work it was shown that the model has a largely degenerate ground state, and it was conjectured that there is some kind of phase transition. We introduce a complex-valued nematic order parameter, which can differentiate between the high-temperature paramagnetic phase and the observed partially-disordered stripe phase at lower temperatures. Configurations in this phase consist of stripes of spins parallel with respect to one lattice direction, which collectively meander along the remaining two, producing partially disordered ground states. The sharp peaks in the specific heat observed in earlier work only appear when using periodic boundary conditions and are absent for free boundaries. Additionally, we reveal a striking dependence of the behavior on the aspect ratio of the considered samples. Ultimately, even a careful finite-size scaling analysis for

J_2 = -0.5

and

J_2 = -1

is unable to clearly discern between a crossover without any singularities and some form of continuous transition, including the possibility of an infinite-order transition of the Berezinskii-Kosterlitz-Thouless (BKT) type. For

J_2=-1/4

we find that the system remains disordered at all temperatures and that it exhibits a finite ground-state entropy per site, for which our simulations provide the accurate asymptotic estimate

S(T=0)/N = 0.230\,960\,93(14)

in the thermodynamic limit

N\rightarrow\infty

We investigate the ground-state and finite-temperature properties of the bond-random

s=1/2

Heisenberg model on a honeycomb lattice with frustrated nearest- and next-nearest-neighbor antiferromagnetic interactions,

J_1

and

J_2

, by the exact diagonalization and the Hams--de Raedt methods. The ground-state phase diagram of the model is constructed in the randomness versus the frustration (

J_2/J_1

) plane, with the aim of clarifying the effects of randomness and frustration in stabilizing a variety of distinct phases. We find that the randomness induces the gapless quantum spin liquid (QSL)-like state, the random-singlet state, in a wide range of parameter space. The observed robustness of the random-singlet state suggests that the gapless QSL-like behaviors might be realized in a wide class of frustrated quantum magnets possessing a certain amount of randomness or inhomogeneity, without fine-tuning the interaction parameters. Possible implications to recent experiments on the honeycomb-lattice magnets Ba

_3

CuSb

_2

_9

and 6HB-Ba

_3

NiSb

_2

_9

exhibiting the gapless QSL-like behaviors are discussed.