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

Research paper by Yuan-Ming Lu, Gil Young Cho, Ashvin Vishwanath

Indexed on: 26 Dec '14Published on: 26 Dec '14Published in: Physics - Strongly Correlated Electrons

#### Abstract

Recent numerical studies have provided strong evidence for a gapped $Z_2$ quantum spin liquid in the kagome lattice Heisenberg model. A special feature of spin liquids is that symmetries can be fractionalized, and different patterns of 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 which are either bosonic (Schwinger bosons) or fermionic (Abrikosov fermions), which are then treated within mean field theory. A longstanding question has been whether these two approaches are truly distinct or describe the same phase in complementary ways. Here we show that all 8 spin liquid phases in Schwinger boson representation can also be described in terms of Abrikosov fermions, unifying pairs of theories that seem rather distinct. The key idea is that for kagome lattice states that admit a Schwinger boson mean field (SBMF) description, the symmetry action on visions is uniquely fixed. Two promising candidate states for kagome Heisenberg model, Sachdev's $Q_{1}=Q_{2}$ SBMF state and Lu-Ran-Lee's $Z_2[0,\pi]\beta$ fermionic parton state, are found to describe the same 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 fermionic parton phases , where spin rotation, time reversal and kagome lattice symmetries protect gapless edge states, that do not admit a SBMF representation .