Unification of bosonic and fermionic $\mathbb{Z}_2$ spin liquids on a rectangular latticeUnification of bosonic and fermionic $\mathbb{Z}_2$ spin liquids on a rectangular lattice

Shubhayu Chatterjee, Julia Steinberg, Subir Sachdev A

Bulletin of the American Physical SocietyMar 15, 20160 citations

Spin Correlations in Quantum Spin Liquids on the Kagome Lattice

Tyler Dodds, Yong Baek Kim

Bulletin of the American Physical SocietyMar 21, 20130 citations

A Phenomenological Theory for the $Z_2$ Spin-Liquid Phase of the $S=1/2$ Kagome Heisenberg AntiferromagnetA Phenomenological Theory for the $Z_2$ Spin-Liquid Phase of the $S=1/2$ Kagome Heisenberg Antiferromagnet

Yuan Wan

Bulletin of the American Physical SocietyMar 21, 20130 citations

Unification of bosonic and fermionic theories of spin liquids on the kagome lattice

Yuan-Ming Lu, Gil Young Cho, Ashvin Vishwanath

Recent numerical studies have provided strong evidence for a gapped ${Z}_{2}$ quantum spin liquid in the kagome lattice spin-1/2 Heisenberg model. A special feature of spin liquids is that symmetries can be fractionalized, and different patterns of symmetry fractionalization imply distinct phases. The symmetry fractionalization pattern for the kagome spin liquid remains to be determined. A popular approach to studying spin liquids is to decompose the physical spin into partons obeying either Bose (Schwinger bosons) or Fermi (Abrikosov fermions) statistics, which are then treated within mean-field theory. A long-standing question has been whether these two approaches are truly distinct, or describe the same phase in complementary ways. Here we show that all $8{Z}_{2}$ spin liquid phases in the Schwinger-boson mean-field (SBMF) construction can also be described in terms of Abrikosov fermions, unifying pairs of theories that seem rather distinct. The key idea is that for ${Z}_{2}$ spin liquid states that admit a SBMF description on the kagome lattice, the symmetry fractionalization of visions is uniquely fixed. Two promising candidate states for the kagome Heisenberg model, Sachdev's ${Q}_{1}={Q}_{2}$ SBMF state and the Lu-Ran-Lee ${Z}_{2}[0,\ensuremath{\pi}]\ensuremath{\beta}$ Abrikosov-fermion state, are found to describe the same symmetric spin liquid phase. We expect these results to aid in a complete specification of the numerically observed spin liquid phase. We also discuss a set of ${Z}_{2}$ spin liquid phases in the fermionic parton approach, where spin rotation and lattice symmetries protect gapless edge states that do not admit a SBMF description.Recent numerical studies have provided strong evidence for a gapped ${Z}_{2}$ quantum spin liquid in the kagome lattice spin-1/2 Heisenberg model. A special feature of spin liquids is that symmetries can be fractionalized, and different patterns of symmetry fractionalization imply distinct phases. The symmetry fractionalization pattern for the kagome spin liquid remains to be determined. A popular approach to studying spin liquids is to decompose the physical spin into partons obeying either Bose (Schwinger bosons) or Fermi (Abrikosov fermions) statistics, which are then treated within mean-field theory. A long-standing question has been whether these two approaches are truly distinct, or describe the same phase in complementary ways. Here we show that all $8{Z}_{2}$ spin liquid phases in the Schwinger-boson mean-field (SBMF) construction can also be described in terms of Abrikosov fermions, unifying pairs of theories that seem rather distinct. The key idea is that for ${Z}_{2}$ spin liquid states that admit a SBMF description on the kagome lattice, the symmetry fractionalization of visions is uniquely fixed. Two promising candidate states for the kagome Heisenberg model, Sachdev's ${Q}_{1}={Q}_{2}$ SBMF state and the Lu-Ran-Lee ${Z}_{2}[0,\ensuremath{\pi}]\ensuremath{\beta}$ Abrikosov-fermion state, are found to describe the same symmetric spin liquid phase. We expect these results to aid in a complete specification of the numerically observed spin liquid phase. We also discuss a set of ${Z}_{2}$ spin liquid phases in the fermionic parton approach, where spin rotation and lattice symmetries protect gapless edge states that do not admit a SBMF description.

arXiv:1403.0575Physical review. B./Physical review. BNov 28, 201731 citations

Unification of bosonic and fermionic

\mathbb{Z}_2

spin liquids on a rectangular lattice

A Phenomenological Theory for the

Z_2

Spin-Liquid Phase of the

S=1/2

Kagome Heisenberg Antiferromagnet

Recent numerical studies have provided strong evidence for a gapped

{Z}_{2}

quantum spin liquid in the kagome lattice spin-1/2 Heisenberg model. A special feature of spin liquids is that symmetries can be fractionalized, and different patterns of symmetry fractionalization imply distinct phases. The symmetry fractionalization pattern for the kagome spin liquid remains to be determined. A popular approach to studying spin liquids is to decompose the physical spin into partons obeying either Bose (Schwinger bosons) or Fermi (Abrikosov fermions) statistics, which are then treated within mean-field theory. A long-standing question has been whether these two approaches are truly distinct, or describe the same phase in complementary ways. Here we show that all

8{Z}_{2}

spin liquid phases in the Schwinger-boson mean-field (SBMF) construction can also be described in terms of Abrikosov fermions, unifying pairs of theories that seem rather distinct. The key idea is that for

{Z}_{2}

spin liquid states that admit a SBMF description on the kagome lattice, the symmetry fractionalization of visions is uniquely fixed. Two promising candidate states for the kagome Heisenberg model, Sachdev's

{Q}_{1}={Q}_{2}

SBMF state and the Lu-Ran-Lee ${Z}_{2}[0,\ensuremath{\pi}]\ensuremath{\beta}$ Abrikosov-fermion state, are found to describe the same symmetric spin liquid phase. We expect these results to aid in a complete specification of the numerically observed spin liquid phase. We also discuss a set of

{Z}_{2}

spin liquid phases in the fermionic parton approach, where spin rotation and lattice symmetries protect gapless edge states that do not admit a SBMF description.