arXiv:2003.04269 · Physical review. B./Physical review. B

Symmetric spin liquids on the stuffed honeycomb lattice

Jyotisman Sahoo, Rebecca Flint

Published Mar 3, 2020• 12 citations

Abstract

We use a projective symmetry group analysis to determine all symmetric spin liquids on the stuffed honeycomb lattice Heisenberg model. This lattice interpolates between honeycomb, triangular, and dice lattices, always preserving hexagonal symmetry, and it already has one spin-liquid candidate, ${\mathrm{TbInO}}_{3}$, albeit with strong spin-orbit coupling not considered here. In addition to the stuffed honeycomb lattice itself, we gain valuable insight into potential spin liquids on the honeycomb and triangular lattices, as well as how they might be connected. For example, the sublattice pairing state proposed on the honeycomb lattice connects to the uniform spinon Fermi surface that may be relevant for the triangular lattice with ring exchange, while there are no spin liquids competitive on both the ${J}_{1}\ensuremath{-}{J}_{2}$ honeycomb and triangular lattice limits. In particular, we find three stuffed honeycomb descendants of the U(1) Dirac spin liquid widely believed to be found on the ${J}_{1}\ensuremath{-}{J}_{2}$ triangular lattice. We also discuss how spin liquids near the honeycomb limit can potentially explain the physics of ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$.

DOI: 10.1103/physrevb.101.115103

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arXiv:2003.04269 · Physical review. B./Physical review. B

Symmetric spin liquids on the stuffed honeycomb lattice

Jyotisman Sahoo, Rebecca Flint

Published Mar 3, 2020• 12 citations

arXiv HTML PDF

Abstract

{\mathrm{TbInO}}_{3}

, albeit with strong spin-orbit coupling not considered here. In addition to the stuffed honeycomb lattice itself, we gain valuable insight into potential spin liquids on the honeycomb and triangular lattices, as well as how they might be connected. For example, the sublattice pairing state proposed on the honeycomb lattice connects to the uniform spinon Fermi surface that may be relevant for the triangular lattice with ring exchange, while there are no spin liquids competitive on both the

{J}_{1}\ensuremath{-}{J}_{2}

honeycomb and triangular lattice limits. In particular, we find three stuffed honeycomb descendants of the U(1) Dirac spin liquid widely believed to be found on the

{J}_{1}\ensuremath{-}{J}_{2}

triangular lattice. We also discuss how spin liquids near the honeycomb limit can potentially explain the physics of

{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}

DOI: 10.1103/physrevb.101.115103

Related papers

Extended symmetric quantum phase in a honeycomb Heisenberg model with sublattice-selective interactions

Nai Chao Hu, Xing-Yu Zhang, Yuchi He +1 more

Motivated by two-dimensional bilayer systems we numerically study an anti-ferromagnetic spin- $1/2$ Heisenberg model on the honeycomb lattice with a nearest-neighbour exchange coupling $J_1$ , and a next-nearest-neighbour exchange coupling $J_2'$ for the B sublattice sites only. Using infinite Projected Entangled-Pair States (iPEPS), variational uniform matrix-product states on cylinders, and exact diagonalization, we find an extended symmetric regime $0.4\lesssim J'_2/J_1\lesssim0.6$ , in which local observables show no magnetic, valence-bond, or chiral spin order. At $J'_2/J_1=0.5$ , the PEPS correlation length grows systematically with bond dimension, and an inverse-correlation-length extrapolation favors a vanishing limit. We also find that various observables scale algebraically with the finite bond-dimension-induced correlation length, which points to a gapless spin liquid ground state. We propose a $\mathbb{Z}_2$ Dirac spin liquid parton state, with Dirac points that are protected by translation, time-reversal and three-fold rotation symmetry, as a promising candidate state to explain the numerical results. We also discuss the possibility that the symmetric ground state is a featureless, short-range entangled state with a small gap.Motivated by two-dimensional bilayer systems we numerically study an anti-ferromagnetic spin-$1/2$ Heisenberg model on the honeycomb lattice with a nearest-neighbour exchange coupling $J_1$, and a next-nearest-neighbour exchange coupling $J_2'$ for the B sublattice sites only. Using infinite Projected Entangled-Pair States (iPEPS), variational uniform matrix-product states on cylinders, and exact diagonalization, we find an extended symmetric regime $0.4\lesssim J'_2/J_1\lesssim0.6$, in which local observables show no magnetic, valence-bond, or chiral spin order. At $J'_2/J_1=0.5$, the PEPS correlation length grows systematically with bond dimension, and an inverse-correlation-length extrapolation favors a vanishing limit. We also find that various observables scale algebraically with the finite bond-dimension-induced correlation length, which points to a gapless spin liquid ground state. We propose a $\mathbb{Z}_2$ Dirac spin liquid parton state, with Dirac points that are protected by translation, time-reversal and three-fold rotation symmetry, as a promising candidate state to explain the numerical results. We also discuss the possibility that the symmetric ground state is a featureless, short-range entangled state with a small gap.

cond-mat.str-elCross-listedarXiv:2609.25243Sep 23, 20260 citations

Spinon Fermi surface U(1) spin liquid in the spin-orbit-coupled triangular-lattice Mott insulator YbMgGaO4

Yaodong Li, Yuan-Ming Lu, Gang Chen

Motivated by the recent progress in the spin-orbit-coupled triangular lattice spin liquid candidate ${\mathrm{YbMgGaO}}_{4}$ , we carry out a systematic projective symmetry group analysis and mean-field study of candidate $U(1)$ spin-liquid ground states. Due to the spin-orbital entanglement of the Yb moments, the space-group symmetry operation transforms both the position and the orientation of the local moments, and hence it brings different features for the projective realization of the lattice symmetries from the cases with spin-only moments. Among the eight $U(1)$ spin liquids that we find with the fermionic parton construction, only one spin-liquid state, which was proposed and analyzed by Yao Shen et al. [Nature (London) 540, 559 (2016)] and labeled as U1A00 in the present work, stands out and gives a large spinon Fermi surface and provides a consistent explanation for the spectroscopic results in ${\mathrm{YbMgGaO}}_{4}$ . Further connection of this spinon Fermi surface $U(1)$ spin liquid with ${\mathrm{YbMgGaO}}_{4}$ and the future directions are discussed. Finally, our results may apply to other spin-orbit-coupled triangular lattice spin-liquid candidates, and more broadly, our general approach can be well extended to spin-orbit-coupled spin-liquid candidate materials.Motivated by the recent progress in the spin-orbit-coupled triangular lattice spin liquid candidate ${\mathrm{YbMgGaO}}_{4}$, we carry out a systematic projective symmetry group analysis and mean-field study of candidate $U(1)$ spin-liquid ground states. Due to the spin-orbital entanglement of the Yb moments, the space-group symmetry operation transforms both the position and the orientation of the local moments, and hence it brings different features for the projective realization of the lattice symmetries from the cases with spin-only moments. Among the eight $U(1)$ spin liquids that we find with the fermionic parton construction, only one spin-liquid state, which was proposed and analyzed by Yao Shen et al. [Nature (London) 540, 559 (2016)] and labeled as U1A00 in the present work, stands out and gives a large spinon Fermi surface and provides a consistent explanation for the spectroscopic results in ${\mathrm{YbMgGaO}}_{4}$. Further connection of this spinon Fermi surface $U(1)$ spin liquid with ${\mathrm{YbMgGaO}}_{4}$ and the future directions are discussed. Finally, our results may apply to other spin-orbit-coupled triangular lattice spin-liquid candidates, and more broadly, our general approach can be well extended to spin-orbit-coupled spin-liquid candidate materials.

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arXiv:1505.06495Physical review. B./Physical review. BApr 11, 201658 citations

Classification and Monte Carlo study of symmetric $Z_{2}$ spin liquids on the triangular latticeClassification and Monte Carlo study of symmetric $Z_{2}$ spin liquids on the triangular lattice

Wayne Zheng, Jia‐Wei Mei, Yang Qi

We study different ways of symmetry fractionalization in $Z_{2}$ spin liquids on the triangular lattice. Our classification can be used to identify the symmetry fractionalization in the $Z_{2}$ spin liquid reported in recent density-matrix-renormalization-group simulations for $J_{1}-J_{2}$ spin model on the triangular lattice. We find 64 types of symmetry enriched $Z_{2}$ spin liquid states on triangular lattice. Besides 8 states constructed in Schwinger-boson parton wavefunctions, 12 more states can be realized in Abrikosov-fermion parton construction. Within a larger gauge group than SU(2), the rest 44 states are also found in a spin-3/2 system. Among 20 types of Abrikosov-fermion Gutzwillerprojected wavefunctions, No.B5 state is a promising candidate for the $Z_{2}$ spin liquid for $J_{1}-J_{2}$ spin model on the triangular lattice. No.B5 lies close to Dirac spin liquid (DSL). However, variational Monte Carlo simulation find that DSL has a good variational energy and $J_{1}-J_{2}$ spin model cannot open a gap for spinons on top of DSL to stabilize No.B5 state.We study different ways of symmetry fractionalization in $Z_{2}$ spin liquids on the triangular lattice. Our classification can be used to identify the symmetry fractionalization in the $Z_{2}$ spin liquid reported in recent density-matrix-renormalization-group simulations for $J_{1}-J_{2}$ spin model on the triangular lattice. We find 64 types of symmetry enriched $Z_{2}$ spin liquid states on triangular lattice. Besides 8 states constructed in Schwinger-boson parton wavefunctions, 12 more states can be realized in Abrikosov-fermion parton construction. Within a larger gauge group than SU(2), the rest 44 states are also found in a spin-3/2 system. Among 20 types of Abrikosov-fermion Gutzwillerprojected wavefunctions, No.B5 state is a promising candidate for the $Z_{2}$ spin liquid for $J_{1}-J_{2}$ spin model on the triangular lattice. No.B5 lies close to Dirac spin liquid (DSL). However, variational Monte Carlo simulation find that DSL has a good variational energy and $J_{1}-J_{2}$ spin model cannot open a gap for spinons on top of DSL to stabilize No.B5 state.

arXiv:1505.05351May 20, 201513 citations

Spin liquids on a honeycomb lattice: Projective Symmetry Group study of Schwinger fermion mean-field theory

Yuan-Ming Lu, Ying Ran

Spin liquids are novel states of matter with fractionalized excitations. A recent numerical study of Hubbard model on a honeycomb lattice\cite{Meng2010} indicates that a gapped spin liquid phase exists close to the Mott transition. Using Projective Symmetry Group, we classify all the possible spin liquid states by Schwinger fermion mean-field approach. We find there is only one fully gapped spin liquid candidate state: "Sublattice Pairing State" that can be realized up to the 3rd neighbor mean-field amplitudes, and is in the neighborhood of the Mott transition. We propose this state as the spin liquid phase discovered in the numerical work. To understand whether SPS can be realized in the Hubbard model, we study the mean-field phase diagram in the $J_1-J_2$ spin-1/2 model and find an s-wave pairing state. We argue that s-wave pairing state is not a stable phase and the true ground state may be SPS. A scenario of a continuous phase transition from SPS to the semimetal phase is proposed. This work also provides guideline for future variational studies of Gutzwiller projected wavefunctions.Spin liquids are novel states of matter with fractionalized excitations. A recent numerical study of Hubbard model on a honeycomb lattice\cite{Meng2010} indicates that a gapped spin liquid phase exists close to the Mott transition. Using Projective Symmetry Group, we classify all the possible spin liquid states by Schwinger fermion mean-field approach. We find there is only one fully gapped spin liquid candidate state: "Sublattice Pairing State" that can be realized up to the 3rd neighbor mean-field amplitudes, and is in the neighborhood of the Mott transition. We propose this state as the spin liquid phase discovered in the numerical work. To understand whether SPS can be realized in the Hubbard model, we study the mean-field phase diagram in the $J_1-J_2$ spin-1/2 model and find an s-wave pairing state. We argue that s-wave pairing state is not a stable phase and the true ground state may be SPS. A scenario of a continuous phase transition from SPS to the semimetal phase is proposed. This work also provides guideline for future variational studies of Gutzwiller projected wavefunctions.

arXiv:1005.4229May 23, 201024 citations

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

Xu-Ping Yao, Rui Leonard Luo, Gang Chen

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.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.

arXiv:2111.01611Physical review. B./Physical review. BJan 3, 202210 citations

{\mathrm{TbInO}}_{3}

{J}_{1}\ensuremath{-}{J}_{2}

honeycomb and triangular lattice limits. In particular, we find three stuffed honeycomb descendants of the U(1) Dirac spin liquid widely believed to be found on the

{J}_{1}\ensuremath{-}{J}_{2}

triangular lattice. We also discuss how spin liquids near the honeycomb limit can potentially explain the physics of

{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}

Motivated by two-dimensional bilayer systems we numerically study an anti-ferromagnetic spin-

1/2

Heisenberg model on the honeycomb lattice with a nearest-neighbour exchange coupling

J_1

, and a next-nearest-neighbour exchange coupling

J_2'

for the B sublattice sites only. Using infinite Projected Entangled-Pair States (iPEPS), variational uniform matrix-product states on cylinders, and exact diagonalization, we find an extended symmetric regime

0.4\lesssim J'_2/J_1\lesssim0.6

, in which local observables show no magnetic, valence-bond, or chiral spin order. At

J'_2/J_1=0.5

, the PEPS correlation length grows systematically with bond dimension, and an inverse-correlation-length extrapolation favors a vanishing limit. We also find that various observables scale algebraically with the finite bond-dimension-induced correlation length, which points to a gapless spin liquid ground state. We propose a

\mathbb{Z}_2

Dirac spin liquid parton state, with Dirac points that are protected by translation, time-reversal and three-fold rotation symmetry, as a promising candidate state to explain the numerical results. We also discuss the possibility that the symmetric ground state is a featureless, short-range entangled state with a small gap.

Motivated by the recent progress in the spin-orbit-coupled triangular lattice spin liquid candidate

{\mathrm{YbMgGaO}}_{4}

, we carry out a systematic projective symmetry group analysis and mean-field study of candidate

U(1)

spin-liquid ground states. Due to the spin-orbital entanglement of the Yb moments, the space-group symmetry operation transforms both the position and the orientation of the local moments, and hence it brings different features for the projective realization of the lattice symmetries from the cases with spin-only moments. Among the eight

U(1)

spin liquids that we find with the fermionic parton construction, only one spin-liquid state, which was proposed and analyzed by Yao Shen et al. [Nature (London) 540, 559 (2016)] and labeled as U1A00 in the present work, stands out and gives a large spinon Fermi surface and provides a consistent explanation for the spectroscopic results in

{\mathrm{YbMgGaO}}_{4}

. Further connection of this spinon Fermi surface

U(1)

spin liquid with

{\mathrm{YbMgGaO}}_{4}

and the future directions are discussed. Finally, our results may apply to other spin-orbit-coupled triangular lattice spin-liquid candidates, and more broadly, our general approach can be well extended to spin-orbit-coupled spin-liquid candidate materials.

Motivated by recent numerical discovery of a gapped spin liquid phase in spin-

1/2

triangular-lattice ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model, we classify symmetric

{Z}_{2}

spin liquids on triangular lattice in the Abrikosov-fermion representation. We find 20 phases with distinct spinon symmetry quantum numbers, eight of which have their counterparts in the Schwinger-boson representation. Among them we identify two promising candidates (#1 and #20), which can realize a gapped

{Z}_{2}

spin liquid with up to next nearest neighbor mean-field amplitudes. We analyze their neighboring magnetic orders and valence bond solid patterns, and find one state (#20) that is connected to 120-degree Neel order by a continuous quantum phase transition. We also identify gapped nematic

{Z}_{2}

spin liquids in the neighborhood of the symmetric states and find three promising candidates (#1, #6, and #20).

Classification and Monte Carlo study of symmetric

Z_{2}

spin liquids on the triangular lattice

We study different ways of symmetry fractionalization in

Z_{2}

spin liquids on the triangular lattice. Our classification can be used to identify the symmetry fractionalization in the

Z_{2}

spin liquid reported in recent density-matrix-renormalization-group simulations for

J_{1}-J_{2}

spin model on the triangular lattice. We find 64 types of symmetry enriched

Z_{2}

spin liquid states on triangular lattice. Besides 8 states constructed in Schwinger-boson parton wavefunctions, 12 more states can be realized in Abrikosov-fermion parton construction. Within a larger gauge group than SU(2), the rest 44 states are also found in a spin-3/2 system. Among 20 types of Abrikosov-fermion Gutzwillerprojected wavefunctions, No.B5 state is a promising candidate for the

Z_{2}

spin liquid for

J_{1}-J_{2}

spin model on the triangular lattice. No.B5 lies close to Dirac spin liquid (DSL). However, variational Monte Carlo simulation find that DSL has a good variational energy and

J_{1}-J_{2}

spin model cannot open a gap for spinons on top of DSL to stabilize No.B5 state.

J_1-J_2

spin-1/2 model and find an s-wave pairing state. We argue that s-wave pairing state is not a stable phase and the true ground state may be SPS. A scenario of a continuous phase transition from SPS to the semimetal phase is proposed. This work also provides guideline for future variational studies of Gutzwiller projected wavefunctions.

\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.