In quantum spin liquids, fractional spinon excitations carry half-integer spins and other fractional quantum numbers of lattice and time-reversal symmetries. Different patterns of symmetry fractionalization distinguish different spin liquid phases. In this work, we derive a general constraint on the symmetry fractionalization of spinons in a gapped spin liquid, realized in a system with an odd number of spin- $\frac{1}{2}$ per unit cell. In particular, when applied to kagome/triangular lattices, we obtain a complete classification of symmetric gapped ${\mathbb{Z}}_{2}$ spin liquids.In quantum spin liquids, fractional spinon excitations carry half-integer spins and other fractional quantum numbers of lattice and time-reversal symmetries. Different patterns of symmetry fractionalization distinguish different spin liquid phases. In this work, we derive a general constraint on the symmetry fractionalization of spinons in a gapped spin liquid, realized in a system with an odd number of spin-$\frac{1}{2}$ per unit cell. In particular, when applied to kagome/triangular lattices, we obtain a complete classification of symmetric gapped ${\mathbb{Z}}_{2}$ spin liquids.

arXiv:1606.04544Physical review. B./Physical review. BMar 19, 201823 citations

Entanglement and elementary excitations in quantum spin chain

Bo Li, Yan Shen Wang

Physica B Condensed MatterApr 9, 20113 citations

Observing spinon excitations in quantum spin models

Ying Tang, Anders W. Sandvik

Bulletin of the American Physical SocietyMar 1, 20120 citations

Projective symmetry group classification of fermionic $Z_2$ spin liquids on the dipolar-octupolar pyrochlore magnetsProjective symmetry group classification of fermionic $Z_2$ spin liquids on the dipolar-octupolar pyrochlore magnets

Rohit Deb, Sambuddha Sanyal

We construct and classify $Z_2$ quantum spin liquids (QSLs) of fermionic partons on the dipolar-octupolar (DO) pyrochlore lattice. The DO pseudospin shares the space-group and time-reversal algebra of the effective spin-1/2 Kramers doublet, its projective symmetry group (PSG) yields the same 48 symmetric $Z_2$ classes as the generic fermionic classification. We show, the distinct DO symmetry action, encoded in a set of sublattice-independent operators, selects a physically different set of symmetry-allowed mean-field channels, so that the resulting ansatze, spinon spectra, and observables differ from both the effective spin-1/2 case and the bosonic DO classification. Decomposing the anisotropic XYZ exchange model into all symmetric singlet and triplet hopping and pairing channels and minimizing the mean-field energy self-consistently, we obtain phase diagrams in the ( $\tilde{J_x}, \tilde{J_z}$ ) plane in which only a few $Z_2$ states, several supporting gapless or flat-band spinon spectra, are stabilized. For these states we compute the spinon band structures, the low-temperature specific heat, and the dynamical spin structure factor, and we argue that the power-law specific-heat exponent is a diagnostic of the spinon nodal structure. A near-linear-in-temperature specific heat together with broad continua in the structure factor gives a fermionic-parton account of the gapless, fractionalized thermodynamics reported in DO materials such as $Nd_2ScNbO_7$ , complementing the bosonic quantum-spin-ice picture of the Ce-based compounds. The work extends the fermionic-parton classification of DO pyrochlore QSLs beyond the $U(1)$ sector, where $Z_2$ topological order is realized equally naturally by fermionic and bosonic spinons.We construct and classify $Z_2$ quantum spin liquids (QSLs) of fermionic partons on the dipolar-octupolar (DO) pyrochlore lattice. The DO pseudospin shares the space-group and time-reversal algebra of the effective spin-1/2 Kramers doublet, its projective symmetry group (PSG) yields the same 48 symmetric $Z_2$ classes as the generic fermionic classification. We show, the distinct DO symmetry action, encoded in a set of sublattice-independent operators, selects a physically different set of symmetry-allowed mean-field channels, so that the resulting ansatze, spinon spectra, and observables differ from both the effective spin-1/2 case and the bosonic DO classification. Decomposing the anisotropic XYZ exchange model into all symmetric singlet and triplet hopping and pairing channels and minimizing the mean-field energy self-consistently, we obtain phase diagrams in the ($\tilde{J_x}, \tilde{J_z}$) plane in which only a few $Z_2$ states, several supporting gapless or flat-band spinon spectra, are stabilized. For these states we compute the spinon band structures, the low-temperature specific heat, and the dynamical spin structure factor, and we argue that the power-law specific-heat exponent is a diagnostic of the spinon nodal structure. A near-linear-in-temperature specific heat together with broad continua in the structure factor gives a fermionic-parton account of the gapless, fractionalized thermodynamics reported in DO materials such as $Nd_2ScNbO_7$, complementing the bosonic quantum-spin-ice picture of the Ce-based compounds. The work extends the fermionic-parton classification of DO pyrochlore QSLs beyond the $U(1)$ sector, where $Z_2$ topological order is realized equally naturally by fermionic and bosonic spinons.

arXiv:2610.02409Oct 1, 20260 citations

Dynamical signatures of quantum spin liquids

Frank Pollmann

WORLD SCIENTIFIC eBooksAug 14, 20180 citations

$Z_{2}$ spin liquid ground state of the spin- $\frac{1}{2}$ Kagome antiferromagnetic Heisenberg model$Z_{2}$ spin liquid ground state of the spin-$\frac{1}{2}$ Kagome antiferromagnetic Heisenberg model

Tao Li

We show that the best variational ground state of the spin- $\frac{1}{2}$ Kagome antiferromagnetic Heisenberg model with nearest-neighboring exchange coupling(NN-KAFH) is a $Z_{2}$ spin liquid state, rather than the widely believed $U(1)$ Dirac spin liquid state. The spinon excitation in the $Z_{2}$ spin liquid state has a small gap of about $1/40$ of the spinon band width. We find that while the $Z_{2}$ and the $U(1)$ spin liquid state have a large overlap on finite clusters and are thus very close in energy, they host totally different spinon excitation spectrum. The strength of the RVB theory becomes particularly clear in such a situation, as it provides not only a variational understanding of the ground state structure, but also a comprehensive picture for the excitation spectrum of the system. Our result indicates that the spin- $\frac{1}{2}$ NN-KAFH should be better understood as a nearly critical system, rather than a prototypical gapped $Z_{2}$ spin liquid system.We show that the best variational ground state of the spin-$\frac{1}{2}$ Kagome antiferromagnetic Heisenberg model with nearest-neighboring exchange coupling(NN-KAFH) is a $Z_{2}$ spin liquid state, rather than the widely believed $U(1)$ Dirac spin liquid state. The spinon excitation in the $Z_{2}$ spin liquid state has a small gap of about $1/40$ of the spinon band width. We find that while the $Z_{2}$ and the $U(1)$ spin liquid state have a large overlap on finite clusters and are thus very close in energy, they host totally different spinon excitation spectrum. The strength of the RVB theory becomes particularly clear in such a situation, as it provides not only a variational understanding of the ground state structure, but also a comprehensive picture for the excitation spectrum of the system. Our result indicates that the spin-$\frac{1}{2}$ NN-KAFH should be better understood as a nearly critical system, rather than a prototypical gapped $Z_{2}$ spin liquid system.

arXiv:1807.09463Jul 25, 20181 citation

\frac{1}{2}

per unit cell. In particular, when applied to kagome/triangular lattices, we obtain a complete classification of symmetric gapped

{\mathbb{Z}}_{2}

spin liquids.

Projective symmetry group classification of fermionic

Z_2

spin liquids on the dipolar-octupolar pyrochlore magnets

We construct and classify

Z_2

quantum spin liquids (QSLs) of fermionic partons on the dipolar-octupolar (DO) pyrochlore lattice. The DO pseudospin shares the space-group and time-reversal algebra of the effective spin-1/2 Kramers doublet, its projective symmetry group (PSG) yields the same 48 symmetric

Z_2

classes as the generic fermionic classification. We show, the distinct DO symmetry action, encoded in a set of sublattice-independent operators, selects a physically different set of symmetry-allowed mean-field channels, so that the resulting ansatze, spinon spectra, and observables differ from both the effective spin-1/2 case and the bosonic DO classification. Decomposing the anisotropic XYZ exchange model into all symmetric singlet and triplet hopping and pairing channels and minimizing the mean-field energy self-consistently, we obtain phase diagrams in the (

\tilde{J_x}, \tilde{J_z}

) plane in which only a few

Z_2

states, several supporting gapless or flat-band spinon spectra, are stabilized. For these states we compute the spinon band structures, the low-temperature specific heat, and the dynamical spin structure factor, and we argue that the power-law specific-heat exponent is a diagnostic of the spinon nodal structure. A near-linear-in-temperature specific heat together with broad continua in the structure factor gives a fermionic-parton account of the gapless, fractionalized thermodynamics reported in DO materials such as

Nd_2ScNbO_7

, complementing the bosonic quantum-spin-ice picture of the Ce-based compounds. The work extends the fermionic-parton classification of DO pyrochlore QSLs beyond the

U(1)

sector, where

Z_2

topological order is realized equally naturally by fermionic and bosonic spinons.

Z_{2}

spin liquid ground state of the spin-

\frac{1}{2}

Kagome antiferromagnetic Heisenberg model

We show that the best variational ground state of the spin-

\frac{1}{2}

Kagome antiferromagnetic Heisenberg model with nearest-neighboring exchange coupling(NN-KAFH) is a

Z_{2}

spin liquid state, rather than the widely believed

U(1)

Dirac spin liquid state. The spinon excitation in the

Z_{2}

spin liquid state has a small gap of about

1/40

of the spinon band width. We find that while the

Z_{2}

and the

U(1)

spin liquid state have a large overlap on finite clusters and are thus very close in energy, they host totally different spinon excitation spectrum. The strength of the RVB theory becomes particularly clear in such a situation, as it provides not only a variational understanding of the ground state structure, but also a comprehensive picture for the excitation spectrum of the system. Our result indicates that the spin-

\frac{1}{2}

NN-KAFH should be better understood as a nearly critical system, rather than a prototypical gapped

Z_{2}

spin liquid system.